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OmegaMoo has Authored 403 Questions  | A. assimilate B. populate C. integrate D. stagnate E. allocate Integrate means to bring together or incorporate (parts) into a whole. |
| A. severance B. platitude C. prospectus D. sacrament E. flatulence Severance is a payment given when a relationship is ended such as a employment contract in this situation. |
| A. regulated B. reneged C. reconstituted D. repatriated E. resolved Reneged means to fail to carry out a promise or commitment. |
| A. intervened B. ordained C. instantiated D. castigated E. radicalized Intervened means to come between disputing people or groups. |
| A. constitution B. paternity C. capitalization D. coalition E. grouping A coalition is an alliance, especially a temporary one, of people, factions, parties, or
nations. |
| A. holiday B. vacation C. pilgrimage D. restitution E. constitution A pilgrimage is a journey made to some sacred place as an act of religious
devotion. |
| A. solace B. countermeasures C. continuance D. restitution E. patience A countermeasure is a measure or action taken to counter or offset another one. |
| A. optimist .. emasculate B. elitist .. entertain C. loner .. apprehend D. cynic .. eradicate E. pacifist .. emancipate A pacifist is a person who is opposed to war or to violence of any
kind. Emancipate means to free (a slave) from bondage. |
| A. extrovert B. introvert C. anarchist D. elitist E. optimist An introvert is someone who turns inward and concentrates on their own actions. |
| A. interred .. callous B. castigated .. anterior C. acquiesced .. obscure D. contemplated .. alternate E. pondered .. ulterior Pondered means to consider or examine attentively or deliberately. Ulterior means going beyond what is openly said or shown. |
| A. seamless .. handily B. volatile .. prudently C. coagulated .. haphazardly D. homogeneous .. periodically E. viscous .. particularly Volatile means readily vaporizable at a relatively low temperature. Prudently means to act with wisdom or judiciousness. |
| A. archetype B. arkanoid C. anomaly D. asinine E. arrhythmia An anomaly is a deviation from the common rule. |
| A. volume .. impressed B. plethora .. divulged C. plebeian .. ordained D. number .. effaced E. dearth .. concealed Plethora is an excessive amount or an abundance. Divulged means to make public or known. |
| A. strains B. embeds C. digresses D. subsides E. implores To digress is to turn aside especially from the main subject of attention or course of argument. |
| A. integrity .. devised B. absolution .. imported C. demand .. derived D. splendor .. enlisted E. challenge .. dispensed Integrity is an unimpaired condition while devised is to plan to obtain or bring about. |
| A. static B. rigorous C. ironic D. dubious E. enviable Dubious means questionable or suspect as to true nature or quality. |
| A. emaciated..audience B. emancipated..despots C. ensconced..pacifists D. enthralled..connoisseurs E. enraptured..scapegoats Enthralled means is to fascinate, charm or captivate. Connoisseurs are expert judges on matters of taste
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| A. gothic .. strict B. ecstatic .. bellicose C. irate .. stringent D. heralded .. passive E. fatigued .. suggestive Irate means angry while stringent is defined as strict with firm restrictions. |
| A. annual B. semisesquicentennial C. centennial D. bicentennial E. millennial In 1976 USA celebrated its 200th anniversary which is known as a bicentennial. Annual means every year, semisesquicentennial is 75 years. centennial is one hundred years and millennial is 1000 years. |
| A. inspired B. enlisted C. crowned D. vilified E. revoked Vilified means to make vicious and defamatory statements about. |
| A. pro bono B. procreate C. pro forma D. per diem E. per domain Pro bono is a phrase derived from Latin meaning "for the public good." The term is generally used to describe professional work undertaken voluntarily and without payment as a public service.
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| A. opposing B. reneged C. grassroots D. credulous E. spontaneous A grassroots movement is one driven by the constituents of a community. Often, grassroots movements are at the local level, as many volunteers in the community give their time to support the local party, which can lead to helping the national party. |
| A. The man himself. B. The man's wife. C. The party hosts. D. The man's boss. E. The other party guests. On line 5 the author states 'it often disappointments the women.' To be scotched is another word for disappointing someone. Women in the sense is speaking generically. In other words the author is really stating one woman and one man (her husband). The author uses the plural because she believes this is a common occurrence between married couples. |
| A. The man. B. The man's wife. C. Both the man and his wife. D. The man's boss. E. The party host. The author states that it is important that the party host conveys a clear message as to how the guests should be dressed and that the invitation should set the tone of the party and not all for interpretation by the guest. |
| A. Mosquito bites. B. Liver damage. C. Modified proteins. D. Ineffective cells in the blood. E. Weakened immune response. In lines 5 and 6 the author states that sporozoites (infective cells) are released into the blood, causing death and fatal complications. |
| A. Killing sporozites. B. Regrowing liver cells. C. Stimulate an immune response. D. Control mosquito populations. E. Modify blood proteins. In lines 6 through 8 the author states that the genetically modified proteins will weaken the sporozites and stimulate an immune response. The treatment will not kill sporozites nor control mosquito populations. It will modify the proteins necessary for sporozite development not blood proteins. There is no mention of regrowing liver cells. |
| A. Religion. B. Politics. C. History. D. Art. E. Science. The best option would be science as the argument is over climate change. |
| A. Competitive. B. Contentious. C. Generalist. D. Impulsive. E. Co-operative. The best option would be contentious. Contentious is a synonym for argumentative. The author is clearly arguing his point with another party in this passage. |
| A. Asiacentric. B. Historic. C. Retail hub. D. Best-kept secret. E. Richmond's top attraction. The term Asiacentric best describes the market as it is modeled after
other Asian street markets and has an Asian focus in regards to it's
goods and services found there. |
| A. China. B. Vancouver. C. In the Fraser River. D. Richmond. E. Malaysia. The Richmond Night Market is held in Richmond, Canada. Be careful. Option 3 sounds more correct as the night market is held along the Fraser River but the option given reads in the river which is not correct. |
| A. 5. B. 6. C. 10. D. 12. E. 30. In line 7 the author suggest that as many as 30 players were on each side. |
| A. Scotland. B. Canada. C. UK. D. US. E. Norther Europe. In line lines 4 and 5 the author states the first game of ice hockey using the modern rules was played in Montreal, Canada. |
| A. The Department of Agriculture. B. A Hawaii State scientist. C. Tanzania. D. The Eurytoma Erythrinae. E. The gall wasp. The Eurytoma Erythrinae will lay eggs on the leaves of the Wiliwili trees. When these eggs hatch they will feed on the larvae of the gall wasp which is the enemy of the tree. |
| A. Over foresting. B. The Eurytoma Erythrinae. C. Eggs. D. Larvae. E. The Gall wasp. In the last line the author states the enemy of the wiliwili tree is that gall wasp. |
| A. Hawaii. B. Lake Huron. C. Mississippi. D. Hudson's Bay. E. All of the above. This technology requires deep warm seawater. Hawaii would be the only place that first that description. |
| A. Cold water. B. Hot water. C. A turbine. D. Oil. E. Fiberglass tubes. In lines 5 and 6 the author states that the fluid boils producing a gas
which creates pressure to drive a turbine that generates power. The
fluid that boils is not necessarily water and thus hot water is not the
correct option. |
| A. Table tennis. B. Indoor tennis. C. Victorian tennis. D. Ping-pong. E. Whiff-Whaff. The initial name of this sport was table tennis. It begins to be called ping pong and whiff whaff after it is marketed and manufactured. |
| A. Books. B. Champagne bottle. C. Knot of string. D. Box lid. E. Parchment stretched onto a frame. As stated in line 3 a cigar box lid was used as the racket. |
| A. Inflation. B. Risk of a recession. C. An announcement from the government stating inflation is less important than a recession. D. High interest rates. E. Lack of credit. In lines 5-8 the author states that the Fed gave a warning which triggered people to dump stocks and buy bonds. There was no lack of credit (in fact there was the opposite) and interest rates were the lowest in 41 years. |
| A. To push up the price of treasury notes. B. To boost consumer spending. C. To take money from the stock market and put it in the real estate market. D. To lower inflation. E. To allow more people to own their own home. The author state the government lowered mortgage rates in order to fight a potential for recession. Thus the Fed took this action in order to boost the economy by enabling people to take the equity out of their homes and buy goods and services. |
| A. Sex of the donor. B. Sex of the organ receiver. C. Pumping capacity. D. Immune stimulation. E. Available organs. The most important factor in the success of the transplant procedure is
available organs. While the author states that sex may play an
important role in the success having an organ available to transplant
is tantamount. |
| A. Males will only receive transplants from other males. B. Females will only receive transplants from other females . C. Large males will only receive transplants from males of equal size. D. Females who have given birth will only receive transplants from other females who have given birth. E. Nothing will have changed. No changes will be made in regards to procedures as there are few transplant organs available for the many people needing transplants. |
| A. 25 B. 30 C. 37 D. 60 E. 74 In line 4 and 5 the author quotes a WHO study that says the current
number of 37 million diabetics will double in 25 years. This would mean
there would be 74 million diabetics by 2035.SAT |
| A. Government of India numbers. B. Canada based professor of medicine's study. C. The World Health Organization. D. School surveys. E. All of the above. In lines 7 and 8 the author quotes that "School surveys have shown that 30 percent of adolescents in our cities are already overweight." |
| A. Salt water. B. Slipping in the boat. C. The sun. D. The dazzle of the blue water. E. Bumping into a boatman. In line 7 the author states "the saline water stinging my eyes." Saline water is another word for salt water. |
| A. Boracay. B. Banca. C. Outrigger. D. Canoe. E. Banana boat. In lines 7 and 8 the author states the she is floating in a Banca. While an outrigger is mentioned in the article it isn't the native name for the boat. Boracay is the name of the town in the Philippines. |
| A. Hyphenate their last name. B. Take their husband's family name. C. Keep their last name. D. Changed their last name to Gandhi. E. Only use their first name. In lines 8 and 9 the author states that a small number of Indian women kept thier names. |
| A. Adhered to tradition. B. It was compromise as she hyphenated her name. C. Gandhi was a respected political name. D. Made her seem modern and western leaning. E. It made her husband's family happy to have a traditional woman in the family. Indira Nehru became Indira Gandhi. Even though this article is about women retaining thier names for their own personal power she took her husband's name for political reasons as suggested by the author. |
| A. Heladeria. B. Coromoto. C. Mérida. D. Andes. E. Pico Bolivar. The ice cream parlor is located at the foothills of the Andes mountain range. You have clues here to the geographic location.The ice cream parlor is called the Heladería Coromoto and it is located in Mérida which is a city in Venezuela. Mountain ranges are usually in plural such as the Rockies, the Alps, or in this case the Andes. Thus even if they call it the Andean hills one can infer the author means the Andes mountains and not hills. The Pico Bolivar seems like the mountain range but it is a single mountain and thus is in the singular form. The Pico Bolivar is a mountain in the Andes range. |
| A. Smoked trout. B. Pumpkin. C. Fried Pork. D. Avocado. E. Black beans and rice. The author states that she "had to force down a spoonful of black beans and rice" flavored ice cream. Meanwhile she didn't mind the pumpkin (her eventual choice) or the avocado. She didn't give an opinion on the taste of the trout flavored ice cream. While pork rind seems like an option here the author writes that she refused to try it and the question asks which flavor did the author taste and dislike thus eliminating this option. |
| A. Soviet Union. B. People of the Ukraine. C. Government of the Ukraine. D. Russia. E. The school board. In lines 3 and 4 it states, "Ukraine is demanding that students pass college entrance exams in Ukrainian ..." In this sense Ukraine is the Government of the Ukraine which would legislate such a law as opposed to the people of the Ukraine which would have the power to demand this action but it would require the government to enact it. |
| A. It wasn't considered a native language. B. It wasn't a practical language for school. C. People were content to speak Russian instead. D. The Soviet Union wanted to have a common language throughout their empire. E. There were more Russians than Ukrainians in the Ukraine. In the second and third line the author states that a common language, Russian, was expanded at the expense of native languages. Thus Russian was taught in schools instead of Ukrainian. |
| A. -4 B. -3 C. -2 D. -1 E. 1 To solve 8 - 3x = 2x + 13, collect the numbers on the left side of the equation and the letters on the right side.
8 - 3x = 2x + 13
8 - 13 = 2x + 3x
-5 = 5x
-5 / 5 = 5x / 5
-1 = x |
| A. 4 B. 9 C. 16 D. 25 E. 36 Since 2x + 1 = 32 and 32 = 25, then 22 + 1 = 25. Hence, x + 1 = 5, thus
(x + 1)2 = (5)2 = 25. |
| A. 1 B. 4 C. 8 D. 13 E. 14 3(x - 2) - 2x = 7
3x + 3(-2) - 2x = 7
3x - 6 -2x = 7 + 6
x = 13 |
| A. 2 B. 4 C. 6 D. 8 E. 12 (9 - 4)(x + 4) = 30
5(x + 4) = 30 / 5 = 6
x = 6 - 4
= 2 |
| A. -4 B. -2 C. 0 D. 2 E. 6 x + 4x - 3x + 8 = 0
5x - 3x + 8 = 0
2x + 8 = 0
2x = -8
x = -8 / 2 = -4 |
| A. 24 B. 30 C. 36 D. 42 E. 50 Two students use the computer a total of 28% + 52% or 80% of the total time of 3 hours or 180 minutes. The third student uses the computer for 100% - 80% or 20% of 180 minutes, which equals 0.2 x 180 = 36 minutes. |
| A. 1 B. 2 C. 3 D. 4 E. 5 20% of 2/3 of 15 = 1/5 x 2/3 x 15 = 2. |
| A. $0.24 B. $0.32 C. $0.34 D. $0.48 E. $0.56 For a total of 48 ounces of apple juice, six 8-ounce containers must be purchased since 6 x 8 ounces = 48 ounces. If each 12-ounce container costs $0.95, four of these containers will cost 4 x $0.95 = $3.80. The amount of money that will be saved by purchasing the 12-ounce containers is $4.14 - $3.80 = $0.34. |
| A. 16 B. 24 C. 30 D. 36 E. 40 Eight pencils cost $0.42 and $2.10 ÷ = 5. Hence, 8 x 5 = 40 pencils can be purchased. |
| A. 0.003 B. 0.030 C. 0.300 D. 30.000 E. 300.000 In 0.030, the digit 3 is located two places to the right of the decimal point, so it is in the hundredths place. |
| A. 0.2093 B. 0.2908 C. 0.2893 D. 0.2938 E. 0.2909 To find the number that has the greatest value, compare each digit, reading from left to right. The number is options A and C can be eliminated since they are less than any of the other choices. Since the thousandths digit of 0.2938 is greater than the thousandths digit of each of the remaining answer options, 0.2938 is the largest number. |
| A. bc B. b2c C. ac D. ab E. bc2 Since a2b3c5 = (a2b2c4)bc < 0 and a2b2c4 is always positive, it must be the case that bc is negative. |
| A. -4 B. 1 C. 7 D. 16 E. 49 If (y - 3)2 = 16, then the number inside the parentheses must be either 4 or -4. If y - 3 = 4, then y = 7 and y2 = 49. If y - 3 = -4, then y = 3 - 4 = -1, so y2 = 1. The smallest possible value of y2 is 1. |
| A. -12 B. -1 C. 0 D. 1 E. 2 As (-2)3 = (-2) x (-2) x (-2) = -8 and (-3)2 = (-3) x (-3) = 9, then (-2)3 + (-3)2 = -8 + 9 = 1. |
| A. -7 B. -3 C. -2 D. -1 E. 1 If n + 5 is an odd integer, then n could be -2 since -2 + 5 = 3. |
| A. -4p2 B. -p2 C. -2p2 D. 2p2 E. 4p2 p2(2 - 5) + (-p)2 = -3p2 + p2 = -2p2. |
| A. -2 B. -1 C. 0 D. 2 E. 3 If k equals 0, 2, or -1, k(k - 2)(k + 1) evaluates to 0. Thus eliminate options B, C, and D. Plug the two remaining answer options into k(k - 2)(k + 1)
K = 2
k(k - 2)(k + 1) = -2(-2 - 2)(-2 + 1)
= -2 (-4) (-1)
= -8. Thus option A. |
| A. -7 B. -5 C. 5 D. 6 E. 7 Multiplying both sides of the given equation, 2b = -3, by -2 gives
-4b = -2(2b) = -2(-3) = 6
Since -4b = 6, then 1 - 4b = 1 + 6 = 7. |
| A. 41 B. 43 C. 44 D. 47 E. 49 Find the option that produces remainders of 2 and 4 when divided by 3 and 5, respectively.
* A The remainder when 41 is divided by 3 is 2, and the remainder when 41 is dived by 5 is 1.
* B The remainder when 43 is dived by 3 is 1.
* C The remainder when 44 is divided by 3 is 2, and the remainder when 44 is divided by 5 is 4.
C is the correct option. |
| A. 0 B. 1 C. 2 D. 3 E. 4 Since n is any even integer, pick a simple number for n. IF n = 4, then (n + 1)2 = (4 + 1)2 = 25. When 25 is divided by 4, the remainder is 1. |
| A. $30 B. $60 C. $90 D. $120 E. $1280 You are told that , if the number of people who contribute equally to a gift decreases from four to three, each person must pay an additional $10.00. You can eliminate options A and C as they are not divisible by both 3 and 4. Check each of the remaining options until you have the true one.
* (B) 60 divided by 3 is 20, and 60 divided by4 is 15. The difference between 20 and 15 is 5.
* (D) 120 divided by 3 is 40, and 120 divided by 4 is 30. The difference between 40 and 30 is 10. This is the correct choice. |
| A. I only. B. I and II only. C. I and III only. D. II and III only. E. I, II, and III. Determine whether each Roman numeral statement is true or false.
* I. Subtracting any multiple of 2 from an odd integer always produces another odd integer. Ie. 7 - 4 = 3. Since n2 + 5 is an odd integer and (n2 + 5) - 6 = n2 - 1, n2 - 1 is also an odd integer. Statement I is false.
* II. The sum of an even integer and an odd integer is an odd integer. Since n2 + 5 is an odd integer, n2 must be even, so n must also be even. Statement II is true.
* III. The product of an odd integer and an even integer is an even integer. Since you have determined that n is even, 5n is also even. Statement III is true. |
| A. 8 B. 11 C. 15 D. 18 E. 21 You are told that when p is divided by 4, the remainder is 3, and when p is divided by 3, the remainder is 0. Identify the answer choices that are divisible by 3. Then substitute each of these choices for p until you find the option that produces a remainder of 3 when divided by 4.
Options C, D, and E are each divisible by 3. Option C, let p = 15. When 15 is divided by 4 the remainder is 3. |
| A. k + 1 B. 4k C. k - 5 D. k + 3 E. 4(k - 1) Consecutive multiples of 4, such as 4, 8, and 12, always differ by 4. If k - 1 is a multiple of 4, then the next larger multiple of 4 is obtained by adding 4 to k -1, which gives k - 1 + 4 or k + 3. |
| A. y + 2 B. x - 1 C. (x + 1)(y - 1) D. y(y+2) E. x+y Since x represents any even number and y represents any odd number, let x = 2 and y = 3. Evaluate the expression in each of the answer choices until you find one that produces an even number:
* (A) y + 2 = 3 + 2 = 5
* (B) x - 1 = 2 -1 = 1
* (C) (x + 1)(y - 1) = (2 + 1) = (3 - 1) = (3)(2) = 6. There is no need to go further as this is the correct choice. |
| A. 4 B. 9 C. 12 D. 15 E. 20 Pick and easy number that is divisible by both 3 and 10, say 30. Then divide 30 by each of the answer choices in turn. Stop when you find a number (15) that divides evenly into 30. 15 does this twice. |
| A. 112 B. 4,308 C. 6,122 D. 23,451 E. 701,546 A number is divisible by 3 if the sum of its digits is divisible by 3. In choice B, the sum of the digits of 4308 is 4 + 3 + 0 + 8 = 15, which is divisible by 3. In choice D, the sum of the digits is 23,451 is 2 + 3 +4 + 5 + 1 = 15, so choice D is also divisible by three. A number is divisible by 2 only if its last digit is even. Since the last digit of 4308 is even but the last digit of 23,451 is odd, the correct choice must be option B. |
| A. 12 B. 18 C. 25 D. 70 E. 100 When figuring out how many factors a number has, be sure to include the number itself and 1. Try each choice in turn:
* (A) There are 5 factors of 12: 1,3,4,6,12.
*(B) There are 6 factors of 18: 1,2,3,6,9, and 18.
*(C) There are 3 factors of 25: 1,5, and 25.
*(D) There are 8 factors of 70: 1,2,5,7.10,14,35,and 70.
*(E) There are 9 factors of 100: 1,2,4,5,20,25,50, and 100.
Thus 100 has the most factors. |
| A. 3 B. 4 C. 6 D. 9 E. 12 If p is divisible by 3 and q is divisible by 4, then pq must be divisible by any combination of prime factors of 3 and 4. Since 3 = 3 X 1 and 4 = 2 X 2, pq is divisible by each of the following: 3, 4, 3 X 2 or 6, and 3 X 2 X 2 or 12. Since no product of prime factors of 3 and 4 equals 9, pq cannot be divisible by 9. |
| A. 55 B. 59 C. 65 D. 69 E. 79 In any division example, the divisor times the quotient plus the remainder should equal the dividend. If the quotient of N divided by 5 is 13 and the remainder is 4(n/5 = 13 + 4/5) then,
N = (5 X 13) + 4 = 65 + 4 = 69 |
| A. 11 B. 13 C. 15 D. 17 E. 19 Find the value of P - S:
* If S represents the sum of the factors of 18, then
S = 1 + 2 + 3 + 6 + 9 + 18 =39.
*If P represents the sum of the prime numbers less than 18, then
P = 2 + 3 + 5 + 7 + 11 + 13 + 17 = 58.
P - S = 58 - 39 = 19 |
| A. 0 B. 1 C. 5 D. 10 E. 15 If y = 25 - x2, the smallest possible value of y is obtained by subtracting the largest possible value of x2 from 25. Since 1 ≤ x ≤ 5, the largest possible value of x2 is 5 = 25. When x2 = 25, then y = 25 - 25 = 0. |
| A. 182a+b B. 18a(a+b) C. 36(2a+b) D. 9a+b · 2a E. 32a+b · 2a
Rewrite 6a as (3 · 2)a. Then use the laws of exponents:
3a+b · (3 · 2)a
= 3a+b · 3a · 2a
= (3a+b · 3a) · 2a
= 32a+b · 2a
|
| A. 182a+b B. 18a(a+b) C. 36(2a+b) D. 9a+b · 2a E. 32a+b · 2a Rewrite 6a as (3 · 2)a. Then use the laws of exponents:
3a+b · (3 · 2)a
= 3a+b · 3a · 2a
= (3a+b · 3a) · 2a
= 32a+b · 2a |
| A. 3 B. 6 C. 9 D. 27 E. 81 If (23)2 = 4p, you can find p by expressing each side of the equation as a power of the same base and then setting the exponents of the two bases equal:
(23)2 = 4p
26 = 22p
6 = 2p
3 = p
Therefore 3p = 33 = x X 3 X 3 = 27. |
| A. 1 B. 2 C. 4 D. 6 E. 8 Given y = wx2 and y is not 0. Since the values of x and w are each doubled, replace w with 2w and x with 2x in the original equation:
ynew = (2w)(2x)2
= (2w)(4x2)
= 8(wx2)
= 8y.
Therefore the original value of y is multiplied by 8. |
| A. 1 B. 3 C. 9 D. 27 E. 81 If powers of the same base are equal, then their exponents must be equal. Since 8x+1 = 64 = 82, then x + 1 = 2, so x = 1. To find the value of 32x + 1, replace x with 1.
32x + 1 = 32(1) + 1
= 33
= 27 |
| A. 0 B. 2 C. 4 D. 8 E. 32 Given x = 32 - 16 ÷ 2 X 4, find the value of x by working from left to right, doing any divisions and multiplications before any additions or subtractions
x = 32 - 16 ÷ 2 X 4
x = 32 - 8 X 4
x = 32 - 32
x = 0 |
| A. 5 B. 6 C. 7 D. 8 E. 9 If 2x + y < 29, the expression x - y will have its greatest possible value when y has its least possible value and x has its maximum value.
* As y is an integer and y > 4, the least possible value for y is 5.
*If y = 5, then 2x + y < 29 becomes 2x + 5 < 29 so 2x < 24 and x < 12.
* As x is an integer and x < 12, the maximum value of x is 11.
* Hence 11- 5 = 6 is the greatest possible value of x - y. |
| A. x < y < w B. w < x < y C. y < w < x D. y < x < w E. w < y < x Each product contains 6, so 6 can be ignored. Then w = 36, x = 35, and y = 32, so y < x < w. |
| A. + only B. X only C. - only D. - and X E. + and divide If r # 0 = r, then the symbol # can represent either addition or subtraction, but not multiplication or division. Since it is also given that r # s = s # r, the operation # is commutative. Since addition is commutative and subtraction is not commutative, the symbol # represents only addition. |
| A. 4:00 PM B. 4:00 AM C. 9:00 PM D. 9:00 AM E. 10:00 PM Since 24 hours + 3 hours = 39 hours, break down the problem by figuring out the time 24 hours ago, 12 hours before that time, and then 3 hours earlier. If the present time is exactly 1:00 PM then 24 hour ago it was also 1:00 PM, and 12 hours before that it was 1:00 AM. Three hours before 1:00 AM is 10:00 PM. |
| A. 20 B. 24 C. 25 D. 30 E. 40 Since Jones has saved $160 to buy a TV that costs $400, he needs to earn an additional $400 - $160 = $240. Earning $8 an hour, he will need to work 240 / 8 = 30 hours to have enough money for the TV. |
| A. + only B. - only C. + and - D. X only E. +, -, or X If r * o = r, then * represents either addition or subtraction or both. It is also given that r * r = 0. Since r - r = 0 and r + r ≠ 0 when r is not 0, * can represent only subtraction. |
| A. 4 B. 12 C. 15 D. 18 E. 21 In store A 10 hats cost 10 X $12 = $120. Since the same hat costs $8 in store B, 120 / 8 = 15 hats. |
| A. 17 B. 239 C. 350 D. 650 E. 1650 Find the sum of 31,983 and the number given in each answer choice beginning with (A). Stop when you get a sum (31,983 + 239) in which at least four of the digits are the same. |
| A. 6 B. 8 C. 10 D. 12 E. 14 Since 1 quart = 32 fluid ounces, 5 quarts = 5 X 32 = 160 fluid ounces, then 160 / 16 = 10 containers needed to hold 5 quarts of milk. |
| A. 25 B. 50 C. 75 D. 100 E. 125 To figure out by what amount quantity A exceeds quantity B, calculate A - B:
(8 X 25) - (15 X 10) = 200 - 150 = 50 |
| A. 901 B. 903 C. 906 D. 909 E. 911 If a = 9 X 23 and b = 9 X 124, then
b - a = 9 X 23
b - a = 9(124 - 23)
= 9(101)
= 909 |
| A. x4 + x6 + x10 B. x4 + 2x5 C. x4 + 2x6 D. 2x9 E. 2x10 w = ys = x(x2 = x2
y2 + z2 + w2 = (x2)2 + (x3)2 + (x3)2
= x4 + x6 + x6 = x4 + 2x6 |
| A. a line II to AB and 150 miles north of AB. B. a transverse segment cutting through AB at a 450 angle. C. a circle with AB as its diameter. D. the perpendicular bisector of AB. E. the line AB. The path of all points equidistant from two points is the perpendicular bisector of the segment that connects the two points. Therefore, the line that is perpendicular to AB and intersects it at 150 miles from A is the perpendicular bisector of AB. (Don't forget, A and B are 300 miles apart.) |
| A. x X a X b B. xa+b C. xab D. (ax)b E. bxa By definition, (xa)b is the same as xab. |
| A. $9,750 B. $11,475 C. $12,750 D. $13,500 E. $14,125 After the 15% deduction, $12,750 is left. After the 10% is deducted from $12,750, $11,475 is left.
(Note you cannot simply deduct 25% from $15,000). |
| A. 26 yards, 1 foot B. 26 2/3 yards C. 52 yards, 2 feet D. 53 1/3 yards E. 37 2/3 yards The perimeter of a 46 |
| A. (3 X 100) + 6 X 10) + 16 B. (2 X 100) + 17 X 10) + 6 C. (3 X 100) + 7 X 10) + 6 D. (2 X 100) + 16 X 10) + 6 E. (2 X 100) + 7 X 10) + 106 (2 X 100) + (16 + 10) + 6 = 200 + 160 + 6
= 366 |
| A. 17 B. 34 2/7 C. 35 D. 43 1/3 E. 70 The time it takes Jones to arrive at his destination is 60 miles divided by 40 miles per hour = 1.5 hours. The time it takes to return is 60 miles divided by 30 miles per hour = 2 hours, making the total time for this 120 mile trip
1.5 + 2 = 3.5 hours. The average speed for the entire trip is 120 miles divided by 3.5 = 34 2/7 miles per hour. |
| A. 1/6 B. 1/4 C. 5/12 D. 1/2 E. 7/12 3/4 evaporates the second day; thus there is 1/4 of the 2/3 of liquid left after evaporation the first day. 1/4 of 2/3 = 1/6 so 1/6 of the original contents remains after two days. |
| A. 5/6 B. 1 C. 1.2 D. 2.5 E. 5 As it takes Jones 2 hours to paint 1 total fence, he paints 1/2 the fence in one hour. White paints 1/3 of the fence per hour. Together their speed is 1/2 + 1/3 = 5/6 fence/hr. The time to paint the fence working together is 1 fence divided by 5/6 fence / hour.
=1.2 hours. |
| A. 0.0016 B. 0.16 C. 1.6 D. 16 E. 1,600 The square root of 0.16 is 0.4, so 0.16 is a perfect square. The square root of 1,600 is 40, so 1,600 is a perfect square. The square root of 0.0016 is 0.04 so 0.0016 is a perfect square. Only 1.6 is not a perfect square. |
| A. 0.045 B. 0.45 C. 1 D. 2.2 E. 4.5 If there are 28.35 grams per ounce, then 28.35 grams per ounce + 1,000 grams per kilogram = 0.02835 kilograms per ounce. Since there are 16 ounces to the pound, 0.2835 kilograms per ounce times 16 ounces per pound = 0.45 kilograms per pound. |
| A. 32 B. 34 C. 40 D. 50 E. 64 Let x be the second angle. The first angle is 3x, and the third angles is x + 20. The angles of a triangle must equal 1800, so 3x + x + (x + 20) = 180, 5x = 160, and x = 32. |
| A. sometimes an even number. B. always divisible by 3 or 5 or 7. C. always an odd number. D. always a prime number. E. always divisible by 2. If 2n is an even number, 2n + 1 is odd. |
| A. -27 B. 0 C. 27 D. 54 E. 108 (4 - 1) X (5 - 2) X (6 - 3)
=3 X 3 X 3 = 27. |
| A. negative and greater than -1. B. negative and less than -1. C. a positive fraction grater than 1. D. positive and less than 1. E. 1 and 1 only. Squaring a negative number will make it positive eliminating options A and B. 12 = 1, so option E is not correct either. Squaring any number greater than 1 will always be larger than the number itself, but squaring a fraction less than 1, where the deonimator is larger than the numerator, will make the denominator much larger than the numerator, thus making the whole fraction smaller. |
| A. 8 B. 16 C. 32 D. 48 E. 80 The average is found by taking the sum of a list of numbers and dividing the sum by the number in the list. If n is the number of numbers in the series, 160 / n = 20, so n = 8 numbers. |
| A. 20 B. 40 C. 100 D. 110 E. 180 All the numbers from 200 to 299 begin with 2. There are 100 of these. Then all numbers like 102, 112, …, 192 end with 2. There are 10 of these.
Therefore there are 110 such numbers. |
| A. 18,600 B. 186,000 C. 1,860,000 D. 18,600,000 E. 186 X 500,000 1.86 X 105 = 1.86 X 100,000 = 186,000. |
| A. 68 B. 72 C. 78 D. 88 E. This cannot be determined with the amount of information provided. If the average for the eight tests is 84%, then the sum of the eight tests must be 8 times 84 or 672. For the six tests the sum must be 6 times 86 or 516. The two dropped tests must have accounted for 156 points.
156 / 2 = 78. |
| A. 1 B. π / 2 C. 2 D. π E. 4 The area of the circle is πr2 and the circumference is 2πr. If the area equals the circumference, solve the equation πr2 = 2πr, or r = 2. The diameter is 2r, or 4 inches. |
| A. 8 B. 256 C. 792 D. 1,258 E. 3,456 Once cubic foot equals 123 cubic inches, or 1,728. Thus one cubic foot of the metal would weigh 3,456 pounds. |
| A. 5X5 + x6 B. 17X5 + x6 C. 6x6 D. 18x6 E. 6x18 x6 + (2x2)3 + (3x3)2
= x6 + 8x6 + 9x6
= 18x6. |
| A. the distance between B and C is 60 miles. B. Sic times the distance from A to B equals 10 times the distance from A to C. C. the distance from B to C is 240 miles. D. the distance from A to B exceeds by 30 miles twice the distance from A to C. E. three times the distance from A to C exceeds by 30 miles twice the distance from A to B. Cities A, B, and C need not be on a straight line; therefore, one cannot add or subtract miles. Six times the distance between A and B is 150 X 6 = 900, which is 10 times the distance between A and C, or 10 X 90 = 900. |
| A. (75)5 B. (75)10 C. (150)10 D. (5625)10 E. (75)21 753 X 757 = (75)3 + 7 = (75)10 |
| A. 3.60% B. 4% C. 4.80% D. 5.20% E. 6% The original 6 pounds contained .24 pounds of salt. The same .24 pounds are in 5 pounds of solution, so the percentage is:
(0.24/5)(100) = 4.8%. |
| A. exceeds 20,500. B. is closer to 20,000 than 21,000. C. exceeds 21,000. D. exceeds 21,000 but does not exceed 21,500. E. is less than 20,500. Three meals a day times 365 days in a year. Thus,
3 X 365 = 1,095 meals a year.
Over 19 years would be:
19 X 1,095 = 20, 805 meals.
this number exceeds 20,500. |
| A. 5/11 B. 2/3 C. 3/4 D. 5/7 E. This cannot be determined with the information given. There is no indication as to the exact percentage of students who eat in the cafeteria since we do not know how many boys or girls there are. |
| A. 256 B. 1024 C. 2048 D. 15384 E. 16000 s = 16 X 8 X 8
s = 1024. |
| A. $2.52 B. $4.60 C. $5.33 D. $7.00 E. $10.50 Let x = the original price.
Then .60x = $4.20
or 6x = $42.00
x = $7.00. |
| A. 30 B. 32 C. 36 D. 41 E. 46 If 9x + 5 = 23, 9x = 18 or x = 2.
Thus, 18x + 5 = 36 + 5 = 41. |
| A. (6,6) B. (-4,6) C. (-4,-4) D. (6,-4) E. (4,-6) The opposite vertices may be any of the number pairs(1+-5, 1+-5), or (6,6), (-4,-4), (-4,6), and (6, -4). Thus, (4, -6) is not possible. |
| A. 1.04 B. 0.104 C. 0.0104 D. 0.00104 E. 0.000104 Convert the percent to decimal form before multiplying
0.04% = 0.0004
.0004 X 0.26 = 0.000104 |
| A. 0.63 B. 0.063 C. 0.0063 D. 0.00063 E. 0.000063 Convert the percent to decimal form before multiplying
0.03% = 0.0003
.0003 X 0.21 = 0.000063 |
| A. -5 B. -1 C. 1 D. 2 E. 5 3x3 + 2x2 + x + 1
=3(-1)3 + 2(-1)2 + (-1) + 1
= 3(-1) + 2(1) - 1 + 1
= 3 + 2 + 0
= -1 |
| A. I only. B. II only. C. I and II only. D. I and III only. E. I, II, and III. I. If p > q and r < 0, multiplying both sides by r reverses the inequality pr < qr.
II. Also, p + r > q + r.
III. However, subtracting r from both sides leaves inequality in same order.
Thus I and II are only true. |
| A. 4% B. 5% C. 10% D. 25% E. 104% An increase of 30% in the base (b) means that the new base will be b + .30b. A 20% decrease in the new altitude (a) means that the new altitude will be a - .20a. The new area is (b + .30b) (a - .20a) = 1.04ba.
The new area is 104% of the old, an increase of 104% - 100% = 4%. |
| A. 78 B. 93 C. 132 D. 204 E. 396 The dimensions of the flower bed including the walk are (12 + 6) and (16 + 6). Thus, the area of the flower bed alone is 12 X 16 = 192 square yards. Therefore, the area of the walk is 396 square yards - 192 square yards = 204 square yards. |
| A. 126 B. 180 C. 270 D. 315 E. 630 The distance traveled is the circumference of the wheel times the number of revolutions. If r is the number of revolutions of the back wheel, r + 10 will be the number of revolutions of the front wheel. They will have traveled the same distance, so 7 ft. X (r + 10) = 9 ft. X r, and r = 35. The wagon has gone 9 ft. X 35 revolutions = 315 feet. |
| A. 50 B. 63 C. 75 D. 86 E. 88 In the 3, 7, 12, 18, 25, differences are 4, 5, 6, 7, 8, … etc. Thus the series would progress as follows:
3, 7, 12, 18, 25, 33, 42, 52, 63. |
| A. 66 B. 72 C. 126 D. 732 E. 792 A clock has 360 degrees from 12 noon to 12 midnight. In one hour there are 360 degrees divided by 12 hours which is 60 degrees. Therefore in 2 hours and 12 minutes the hour hand moves 66 degrees. |
| A. 9 B. 11 C. 13 D. 14 E. 16 Let x = the number of years for the two populations to be equal.
6800 - 120X = 4200 + 80x
2600 = 200x
x = 13 |
| A. 15 B. 25 C. 28 D. 38 E. 82 Let the other two angles be 2x and 5x. Thus
2x + 5x + 82 = 180
7x = 98
x = 14
2x = 28
5x = 70.
The smallest angle is 280 |
| A. 1:2 B. 1:3 C. 1:4 D. 1:5 E. 2:5 The area of triangle ADE equals the area of triangle AEC, since they have the same base and altitude. The area of triangle ABC equals that of triangle ADC, since the diagonal of a parallelogram divides it equally. |
| A. 25% B. 48% C. 73% D. 95% E. 122% A cube with an edge of 4 has a volume of 64 cubic inches. A cubes with an edge of 5 has a volume of 125 cubic inches. The percentage increases is 61/64 or 95%. |
| A. 6 B. 12 C. 18 D. 22 E. 24 There is no waste if the lengths are multiples of 5.5 feet. This occurs between 6 and 24 feet only for 22 feet. |
| A. Europe's B. species C. uncertain D. warned. E. No error. There are no errors in this sentence. |
| A. has suggested B. will not C. effect D. relations E. No error. Here answer 1 is correct. There are more than one analyst. The verb |
| A. concise B. pointed out C. needed D. and E. No error. There are no errors in this sentence. |
| A. activists B. warned C. in advance D. nearby. E. No error. Here answer 3 is correct. |
| A. plans B. celebrate C. centenary D. nearby E. No error. There are no errors in this sentence. |
| A. is B. used C. local currency D. rubles. E. No error. Answer 1 is correct. When talking about an amount of money, it requires a singular verb, but when referring to the dollars themselves, a plural verb is required. |
| A. spending B. traveling C. realized D. are E. No error. Answer 4 is correct. A phrase or clause often separates the subject and the verb. The verb must still agree with the subject. Climate is the subject, not places. It takes the verb is not are. |
| A. Neither B. nor C. knows D. happened E. No error. Answer 3 is correct. Brothers is closer to the verb and is plural; the verb should agree with brothers. Thus this should read, |
| A. testimony B. deliberating C. accused D. killing E. No error. There are no errors in this sentence. |
| A. official B. is used C. patients D. doubled E. No error. Here option 1 is correct. Official should be the plural officials. The verb say does not agree with a singular official. |
| A. City officials B. are C. saying D. are heard. E. No error. There are no errors in this sentence. |
| A. spoke B. costs C. various D. complaints. E. No error. Here option 1 is correct. The word spoke does not work in this sentence. It should be said or stated. |
| A. stretch B. giving C. reduced D. usual site. E. No error. There are no errors in this sentence. |
| A. was happy B. Monday C. was hoping D. romantic E. No error. There are no errors in this sentence. |
| A. unearthed B. canister C. dating back D. AB. E. No error. Here option 4 is correct. AB should be either BC or AD which refer to time. |
| A. thaw B. accelerating C. region D. deadlocked E. No error. There are no errors in this sentence. |
| A. set of fingerprints B. were C. to make D. definitive E. No error. Here option 2 is correct. Set of fingerprints does not agree with were. A set of fingerprints is singular. There is only one set. Thus |
| A. mandatory B. retirement C. may not apply D. forced E. No error. There are no errors in this sentence. |
| A. rode B. down the hill C. breaks D. crosswalk. E. No error. Here option 3 is correct. Breaks is not the correct word as it should be brakes. They sound the same but are completely different words. A break would be to take a pause while brakes are the mechanical devices to slow vehicles down. |
| A. looked over B. have concluded C. your D. candidate E. No error. Here option 3 is correct. The word your should be you're. Be careful. These words sound the same but have entirely different meanings. Your is possessive. You’re is a contraction of you are. |
| A. Clearly B. you're C. falling down D. amusing E. No error. Here option 2 is correct. The word you're should be your. Be careful. These words sound the same but have entirely different meanings. Your is possessive. You’re is a contraction of you are. |
| A. Whose B. responsible C. theft D. ingestion E. No error. Here option 1 is correct. The word whose should be who's. Be careful. These words sound the same but have entirely different meanings. Whose is possessive. Who’s is a contraction of who is. |
| A. who's B. ate C. threatened D. hurt E. No error. Here option 1 is correct. The word who's should be whose. Be careful. These words sound the same but have entirely different meanings. Whose is possessive. Who’s is a contraction of who is. |
| A. Its B. left C. out D. its E. No error. Its and it’s are often used interchangeably—but they are very different beasts. Its signals possession. It’s is a contraction of it is. |
| A. that was B. left out C. had D. it's E. No error. Its and it’s are often used interchangeably—but they are very different beasts. Its signals possession. It’s is a contraction of it is. |
| A. should of B. done C. homework D. before E. No error. People sometimes write should of when they mean should’ve or should have. Unfortunately |
| A. could of B. gone C. claimed D. engagement. E. No error. People sometimes write could of when they mean could’ve or could have. Unfortunately could of is an imaginary phrase. |
| A. found B. he began C. to fall in love D. alot. E. No error. Despite widespread usage, the word alot does not exist. It is a made-up word that is never grammatically correct. Always use the phrase |
| A. wrote B. thank you notes C. fancy D. stationary. E. No error. Here option 4 is correct. The word stationary should be stationery Be careful. These words sound the same but have entirely different meanings. Stationary means immobile. Stationery is fancy writing paper. |
| A. such B. had C. hang D. stationery E. No error. Here option 4 is correct. The word stationery should be stationary Be careful. These words sound the same but have entirely different meanings. Stationary means immobile. Stationery is fancy writing paper. |
| A. such B. principal C. leaders and politicians D. chose E. No error. Here option 2 is correct. The word principal should be principle. Be careful. These words sound the same but have entirely different meanings. |
| A. Principle B. gave C. detention D. tardiness. E. No error. Here option 1 is correct. The word Principle should be Principal Be careful. These words sound the same but have entirely different meanings. |
| A. so good B. have C. never D. lose. E. No error. There are no errors in this sentence. |
| A. lose B. snapped off C. occupant D. fell E. No error. Here option 1 is correct. The word lose should be loose. Be careful. These words sound the same but have entirely different meanings. Loose means movable, unfastened, or promiscuous. To lose something is to misplace it or shake it off. |
| A. tried to B. lose C. sweater D. had given him E. No error. Here option 2 is correct. The word loose should be lose. Be careful. These words sound the same but have entirely different meanings. Loose means movable, unfastened, or promiscuous. To lose something is to misplace it or shake it off. |
| A. was amazed B. illusion C. created by D. mature E. No error. There are no errors in this sentence. |
| A. appraising B. dilapidated C. told D. not to buy. E. No error. There are no errors in this sentence. |
| A. suffered B. once again C. difficulties D. breathing. E. No error. There are no errors in this sentence. |
| A. Conscientious B. completed C. then D. homework. E. No error. There are no errors in this sentence. |
| A. knows B. affected C. still D. can't E. No error. There are no errors in this sentence. Effect is usually a noun. The effect is the result of something. |
| A. effect B. measurable C. improvement D. attributable E. No error. There are no errors in this sentence. Effect is usually a noun. The effect is the result of something. |
| A. grew up B. ostrich C. close D. desert. E. No error. There are no errors in this sentence. |
| A. uneducated B. continue to live C. imminent D. sentence E. No error. There are no errors in this sentence. |
| A. Supporters B. thrilled C. eminent D. threat of execution. E. No error. There are no errors in this sentence. |
| A. crowd's arrival B. seemed C. eminent D. ran out E. No error. Here option 3 is correct. The word eminent should be imminent. Be careful. These words sound the same but have entirely different meanings. An imminent event is one that is just about to happen. An eminent person is one who is well-known and highly regarded. |
| A. imminent B. disguised C. himself D. with E. No error. Here option 1 is correct. The word imminent should be eminent. Be careful. These words sound the same but have entirely different meanings. An imminent event is one that is just about to happen. An eminent person is one who is well-known and highly regarded. |
| A. positively B. effects C. outcome D. applications. E. No error. Here option 2 is correct. The word effects should be affects. Be careful. These words sound the same but have entirely different meanings. Effect is usually a noun. The effect is the result of something. |
| A. Studying B. has had C. profound D. affect E. No error. Here option 4 is correct. The word affect should be effect. Be careful. These words sound the same but have entirely different meanings. Effect is usually a noun. The effect is the result of something. |
| A. loves B. to eat C. fruity D. desert. E. No error. Here option 4 is correct. The word desert should be dessert Be careful. These words sound the same but have entirely different meanings. |
| A. lumbering B. had little C. crossing D. dessert. E. No error. Here option 4 is correct. The word dessert should be desert Be careful. These words sound the same but have entirely different meanings. |
| A. Suddenly B. became C. conscience D. was not alone E. No error. Here option 3 is correct. The word conscience should be conscious. Be careful. These words sound the same but have entirely different meanings. |
| A. he robbed B. conscious C. began to D. bother him. E. No error. Here option 2 is correct. The word conscious should be conscience. Be careful. These words sound the same but have entirely different meanings. |
| A. breath B. gasped C. clutching at D. throat. E. No error. Here option 1 is correct. The word breath should be breathe Be careful. These words sound the same but have entirely different meanings. |
| A. took B. breathe C. jumped off D. diving board. E. No error. Here option 2 is correct. The word breathe should be breath Be careful. These words sound the same but have entirely different meanings. |
| A. provided B. alternate C. mindless D. poorly written E. No error. Here option 2 is correct. The word alternate should be alternative. Be careful. These words sound the same but have entirely different meanings. |
| A. was ousted B. scandal C. alternative D. took his place E. No error. Here option 3 is correct. The word alternative should be alternate Be careful. These words sound the same but have entirely different meanings. |
| A. magician and his assistant B. allusions C. could use D. amuse E. No error. Here option 2 is correct. The word allusions should be illusions. Be careful. These words sound the same but have entirely different meanings. |
| A. was littered B. conspicuous C. illusions D. Shakespeare and Descartes. E. No error. Here option 4 is correct. The word illusions should be allusions. Be careful. These words sound the same but have entirely different meanings. |
| A. recently moved B. brand-new C. in D. Street. E. No error. Here, the answer is option C, because we say, “I live on this street,” rather than, “I live in this street.” There is no specific rule that explains why we use the word on; it’s just something you probably know from years of English-speaking. |
| A. In my family B. to engage C. thus preventing D. to be completed. E. No error. Your ear will help you on gerund questions. The phrase preventing the game to be completed might sound funny to you. This phrase should read thus preventing the game from being completed, changing the infinitive to be to the conjugated form, being. Therefore D is the correct option. |
| A. Of B. I drive C. I like D. best. E. No error. This sentence implies a comparison between two cars. Because only two things are being compared, best is the wrong word. Only when comparing three or more things can you use words like best. Thus D is the best option. |
| A. special B. shows C. quick D. can devour E. No error. This sentence uses the adjective quick to describe the verb devour; the adverb quickly is the right word to use. Therefore C is the correct answer. |
| A. No matter B. careful C. often D. get tangled E. No error. In this sentence, the adjective careful is used improperly to describe the verb flown. Because a verb is being described, careful should be carefully. Thus B is the correct answer. |
| A. paper's B. good C. I'll D. on time. E. No error. A paper can’t go pretty good; it can only go pretty well. In order to describe the verb going, we must use an adverb like well, instead of the adjective good. Thus option B is correct. |
| A. can't scarcely B. gymnastics C. without D. underneath. E. No error. This is a double negative. Can’t is a fairly obvious negative word, but scarcely is also negative, so the two cannot be used together, therefore option A is the correct answer. |
| A. is definitely B. on the menu C. clam chowder D. best appetizer. E. No error. The best appetizer where? In the nation? In the world? Because the first part of the sentence specifies on the menu, the second part of the sentence must also be specific. In corrected form, this sentence would read, The steak is definitely the best entrée on the menu, and the clam chowder is the best appetizer in the world. Option D is correct. |
| A. drinking wine B. eating cheese C. to go D. party. E. No error. When you see a list like this, be on the alert for an error in parallelism. In this case, the list starts out with two gerunds (drinking, eating) and then switches to an infinitive (to go). Because the list starts out with gerunds, it has to use gerunds all the way through, thus option C is the correct answer. |
| A. was B. would C. have to D. study for E. No error. Was and would do not agree. This is a conditional statement. The sentence should read, If I were queen, I would never have to study for a standardized test, thus option A is the right answer. |
| A. On B. laid C. for an hour D. tan. E. No error. Option B is the correct answer here, because laid is not the correct tense in the context of this sentence. The past tense of to lie is lay, so the sentence should read I lay in the sun. |
| A. as well as B. are C. good D. tonight. E. No errors. The actual subject here is leadoff hitter. Since leadoff hitter is a singular subject, the verb must be singular, too. The presence of the phrase as well as does not make the subject plural. Even though there are two hitters doing well, the leadoff hitter is the only subject of this sentence. Option B is the answer; the sentence should read the leadoff hitter, as well as the cleanup hitter, is getting some good hacks tonight |
| A. Nobody B. even me C. are D. the weekend. E. No error. Nobody is one of those subjects that sounds plural, but is actually singular. It needs to be matched with a singular verb. Look carefully at all seemingly plural subjects; make sure they’re not singular subjects masquerading as plural ones. In this sentence, the answer is option C. The sentence should read Nobody, not even me, is excited about the weekend. |
| A. Neither B. nor C. measure D. hearts. E. No error. Even though there are two card games being discussed, both of those card games are singular nouns (one game of rummy, one game of solitaire), and therefore the verb must be singular. Measure is a plural verb, when it should be a singular one, so option C is the answer. |
| A. while B. if consumed C. is sickening D. for breakfast E. No error. In this sentence, they’ve put the subject (sundaes) at the beginning of the sentence, and the verb (is) not very close. Sometimes it helps to bracket prepositional phrases so you can see what’s really going on. A prepositional phrase is a phrase that begins with a preposition like while, although, which, etc., which does not change the essential meaning of the sentence if removed. Prepositional phrases are often set off by commas. If you get rid of the prepositional phrase here (while good if consumed in moderation), you’re left with sundaes is sickening. That sounds wrong. Thus option C is the right answer. |
| A. Atop B. mass C. whipped cream D. sits E. No error. The answer is option D, sits. Because we’re talking about two maraschino cherries (plural subject) we need to use sit (plural verb). The sentence should read Atop my sundae, a mass of whipped cream and sprinkles, sit two maraschino cherries. Why is this tricky? The subject, maraschino cherries, comes after the verb, sits. With all the singular stuff floating around—one sundae, one mass of whipped cream—it’s easy to assume that the verb should be singular, too. Look out for those backwards constructions. |
| A. Chris B. better C. than D. them E. No error. Here the word are is implied (we use are, which is plural, because in this sentence the pronoun them is plural). Adding are leaves us with Chris is a better pitcher than them are. Again, that sounds wrong, so we know that the sentence should read Chris is a better pitcher than they, and that option D is the right answer. |
| A. her B. which C. because D. I'll win E. No error. In this sentence, I is being compared to her. These two pronouns are in different cases, so one of them must be wrong. Since only her is underlined, it must be wrong, and therefore the right answer. |
| A. she B. had C. and that D. might E. No error. The pronoun she poses a problem in this sentence. Who has a problem with foot odor, Carol or Jane? No one knows, because she is ambiguous. Grammatically and logically, she could refer to Carol or Jane Therefore, option A is the correct answer. |
| A. first begins B. it's C. your D. well. E. No error. This sentence presents a pronoun shift problem. If you start talking about one, you have to keep talking about one for the duration of the sentence. The sentence could read when one first begins to play tennis, it’s important to work on one’s serve or when you first begin to play tennis, it’s important to work on your serve, but the sentence cannot combine one and you.
|
| A. When it B. me C. 'concentration' D. name. E. No error. Although it may sound right, me is actually incorrect in this sentence. If you use me, the phrase means when it comes to me, which isn’t right. You’re doing more than talking about yourself; you’re talking about you and studying. Using my allows you to say when it comes to my studying. Thus option 2 is the answer. |
| A. Her B. her family C. play D. they take a trip E. No error. This passage has a plural subject: Her and her family. You know her and her family is the subject since they are the ones who do the liking in the sentence; they are the performers of the verb. This sentence is tricky because the her in her family acts as an adjective, not a pronoun. Since family is a perfectly acceptable subject noun, that underlined portion is correct. But the initial her is a pronoun, and it is wrong since it is in the objective case rather than the subjective. It should be she. |
| A. For B. up for C. their D. own E. No error. In this sentence, the pronoun their replaces the noun car. This is incorrect, because car is singular, and their is plural. If you were reading carelessly, however, you might assume that since the first part of the sentence contains the plural noun cars, the plural pronoun their is correct. Most students do fine on this kind of are-you-paying-attention pronoun agreement question; just make sure you’re inspecting each pronoun with an eagle eye. |
| A. suddenly B. exodus C. surgical D. had to close E. No error. There are no errors in this sentence. |
| A. precincts B. projectioning C. incumbent D. will defeat E. No error. Here option 2 is incorrect. The word |
| A. was feeling B. that C. to stop eating D. desserts E. No error. There are no errors in this sentence. |
| A. At swimming pools B. will have brought C. thousands of people D. tepid. E. No error. This sentence begins by talking about the past (last summer), but then uses the phrase will have brought, which is not the past tense. We’re talking about a phenomenon of last summer that is now over and done with, and firmly in the past. The phrase will have brought doesn’t fit because it suggests an ongoing phenomenon. Therefore, option B is the correct answer. |
| A. Even though B. vary C. his or her D. to reason E. No error. In this sentence, the problem is with option C, the phrase his or her. The second clause in this sentence begins with the plural noun people; therefore, a plural pronoun must be used to refer to that plural noun. His or her is singular. This is a case in which their is correct, and his or her is incorrect. |
| A. in the classroom B. to forget C. his D. homework E. No error. His does not agree with |
| A. decided B. was going C. he would D. Dance E. No error. There are no errors in this sentence. |
| A. which B. were C. rowdy D. audience E. No error. Option (A) or (B) seem to be the most likely error. Option (A) is which. Sometimes which is mistakenly used instead of that, but here, which is the correct choice. (Quick rule: when there’s a comma, choose which; when there’s no comma, choose that.) You can eliminate (A). What about (B), were? Were is a verb. Subject-verb agreement problems are commonly tested on this section of the test. What is the subject of were? The crowd. Standing between the subject and the verb is a prepositional phrase, which clamored for the play to begin. Get rid of that prepositional phrase for the moment, so you can more easily see whether the subject matches up with the verb. When you eliminate the phrase, you get the crowd were. That doesn’t match. The crowd is a singular subject, and were is a plural verb. (B) is the correct answer. |
| A. principal B. is C. is often D. to be E. No error. The answer to this question is D because the word accused must take the preposition of rather than to. Idiomatically, the preposition of must be followed by a gerund rather than an infinitive, so the verb to be is incorrect. The sentence should read: |
| A. $402.32 B. $412.19 C. $414.85 D. $430.88 E. $432.62 $428.00 - (.06) $428.00 = $402.32. |
| A. .90X B. .99X C. 1x D. 1.01x E. 1.11x The worker starts at x dollars per week. After the pay cut, he receives 90% of his salary. The 10% raise adds 9% to the salary (10% of 90%), so the new salary is 0.99x. |
| A. 3/8 B. 3/4 C. 1.5 D. 3 E. 24 The weights are proportional to the volumes, and the volumes vary as the cubes of their dimensions. If the edges are doubled, the volume becomes 23 = 8 times as large. Thus the weight = 8 X 3 = 24 ounces or 1.5 pounds. |
| A. $0.35 B. $0.45 C. $0.50 D. $0.55 E. $0.75 Buying the candy in single units would cost
30 X $0.13 = $1.38.
The reduced rate is $1.38 a dozen.
Thirty candies is 2.5 dozen, so the cost for 30 candies is
$1.38 X 2.5 = $3.45
The savings with this reduced rate is
$3.90 - $3.45 = $0.45. |
| A. 100% B. 200% C. 300% D. 400% E. 500% If each of the dimensions is doubled, the area of the new rectangle is four times the size of the original one. The increase is 3 times or 300%. |
| A. 52% B. 60% C. 62% D. 69% E. 122% We do not know how many games the Unicorns played but we do know the ratio of games played in the second year to that played in the first year. This is 2:1. Try 50 games in the first year so they won 25 games. In the second year there were 100 games and they won 65 of them. Altogether they won 90 out of 150 games which is simplified to 3/5 or 60%. |
| A. 7 B. 14 C. 21 D. 24 E. 28 A hexagon with 22 inch sides has a perimeter of 6 X 22, or 132 inches.
c = 2πr
132 = 2πr
132 = 2(3.14)r
132 = 6.28 r
21.02 = r |
| A. 110 B. 110.5 C. 112 D. 114.5 E. 115.5 0.10 X 105 = 10.5lbs.
Jones weighs 105 + 10.5 = 115.5 lbs. |
| A. $11.34 B. $12.48 C. $13.66 D. $13.86 E. $14.00 If the gain was 10% of the selling price, then $12.60 was 90%. Therefore, 100% was equal to $14.00. |
| A. 5-12-13 B. 3-4-5 C. 8-15-17 D. 9-40-41 E. 12-15-18 If a triangle is a right triangle, then the squares of two sides will add up to the square o the hypotenuse.
122 = 144.152 = 225.182 = 324.
144 + 225 does not equal 324. |
| A. w - 1 B. w + 1 C. 2w - 1 D. 2w + 1 E. w2 Multiply the equation 2m = 4x by 2
2(2m) = 2(4x)
2m+1 = 8x = sw
Therefore w = m + 1 and m = w - 1. |
| A. x2 - x - 3y B. -3x + y C. x2 + 3y D. -x2 + x - 3y E. -x2 + x + 3y -X2 + 2y - (-y-x)
= -X2 + 2y + x + y
= -X2 + x + 3y |
| A. 7 B. 9 C. 11 D. 13 E. 15 Let x = the first integer
x + 2 = the second integer
x + 4 = the third integer
3(x) = 3 + 2(x + 4)
3x = 3 + 2x + 8
x = +11 |
| A. $47.50 B. $49.80 C. $150.95 D. $234.00 E. $249.00 20 square yards = 180 square feet. At $1.30 per square foot, it will cost $234.00. |
| A. .08 B. .008 C. .0008 D. .00008 E. .000008 The answer is 0.000008. |
| A. 6π B. 8π C. 10π D. 12π E. 14π The area of the circle is (6)2p, or 36π. In the triangle, 1/2 (6)(h) = 36 π
3h = 36π
h = 12π. |
| A. 30 B. 50 C. 80 D. 125 E. 140 The surface area of a cube is made up of 6 equal squares. If each edge of the cube is x, then
6x2 = 150
x2 25
x = 5
Volume = (edge)2 = 53 = 125. |
| A. (3,4) B. (12,18) C. (6,8) D. (9,6) E. (6,9) Add the x values and divide by 2. Add the y values and divide by 2. |
| A. 36 B. 72 C. 125 D. 144 E. 150 The consecutive angles of a parallelogram are supplementary, so
x + 4x = 1800
5x = 1800
x = 150. |
| A. 10 B. 19 C. 21 D. 79 E. 81 If the radii of the two circles have a ratio of 10:9, the areas have a ratio of 100:81. Therefore, the decrease is 19 out of 100, or 19%. |
| A. 15 B. 45 C. 75 D. 95 E. 225 If the sides have a ratio 1:3, the areas have a ratio 1:9. Therefore, the area of the large square is 9(5), or 45. |
| A. acute. B. isosceles. C. obtuse. D. right. E. equilateral. Represent the angles as 2x, 3x, and 7x.
2x + 3x + 7x = 1800
12x = 1800
x = 150. The an angles are 300, 450, and 1050. Since one angle is between 900 and 180 0, the triangle is called an obtuse triangle. |
| A. 12 B. 36 C. 48 D. 92 E. 108 B = 2, E = 5, D = 4, A = 1
so the sum of the letters would be 12. 12 multiplied by 4 (the length of the word) is 48. |
| A. 22 B. 44 C. 66 D. 100 E. 108 D = 4, F = 6, G = 7, H = 8
so the sum of the letters would be 25. 25 multiplied by 4 (the length of the word) is 100. |
| A. -21 B. -18 C. -12 D. 12 E. 18 Notice the phrase, |
| A. x > y B. x < y C. x + y < 0 D. y - x < 0 E. x = -y If x and y are both positive, but x - y is negative, then y must be a greater number than x. |
| A. w > x > y > z B. w > x > z > y C. x > z > y > w D. z < y < x < w E. z < x < y < w The first and third statements declare:
w > x and x > z, therefore w > x > z.
The second statement says that y is less than z, therefore:
w > x > z > y. |
| A. x > 1 B. x > -1 C. x < 1 D. x < -1 E. x = -1 4 - x > 5
-x > 1
Divide by -1 and change the inequality sign.
x < -1 |
| A. -a B. -b C. -(a+b) D. b E. (a - b) If the product of two numbers is > 0 (positive), then either both numbers are positive or both are negative. Since a < 0 (negative), b must also be negative. |
| A. a = c B. a < d C. a + d = b + c D. a + c < b + d E. a + c > b + d If unequal quantities are added to unequal quantities of the same order, the results are unequal in the same order. |
| A. A = B B. A < B C. A > B D. A < x E. B < y Doubles of unequals are unequal in the same order. |
| A. I only. B. II only. C. III only. D. I and III only. E. I, II, and III. The prime factorization of 24 is 233: hence, if 24AB is a perfect square, then AB must have a factor of 2 and a factor of 3. This means, first of all, that both A and B cannot be odd. So I cannot be possible. II also cannot be possible, because if AB were a perfect square and 24AB were also a perfect square, then 24 would be a perfect square, which it is not. If A were 6 and B were 36 24AB would be a perfect square with both A and B divisible by 6, so III is possible. |
| A. 9/25 B. 13/25 C. 1/2 D. 2/5 E. 3/5 Since each person had 5 options, there are 25 possible pairs of numbers. The only way the sum could be odd is if one person picked an odd number and the other picked an even number. Suppose that Jones chose the odd number and White chose the even one. Jones had 3 possible even numbers to choose from, and for each of these White had 2 possible choices, for a total of (3)(2) = 6 possibilities. However, you could have had Jones pick and even number and White pick an odd one. There are also 6 ways to do that. Thus, out of 25 possibilities, 12 have an odd total, and 13 have an even total. The probability of an even total is 13/25. |
| A. -15x24 B. -15x11 C. 15x5 D. 15x11 E. 15x24 5x3(-3x8) = 5 X x3 X (-3) X x8
= 5 X (-3) X x3 X x8
= -15 X x3 + 8
= 15x11 |
| A. 18w8y12 B. 18w6y7 C. 81w6y7 D. 81w8y12 E. 81w8y7 (3w2y3)4 = (3)4 X w(2 X 4) X y(3 X 4)
81 X w8 X y12
= 81w8y12 |
| A. 6x7 B. 6x8 C. 6x9 D. 6x10 E. 6x12 6x3(x2)3=
6 X x3 X (x2)3
6 X x3 X (x2 X 3)
6 X x3 X x6
6X x9
6x9 |
| A. 5:7 B. 5:8 C. 7:8 D. 8:7 E. 7:5 Let there be y caps in the box. Then, there are 2y/5 red caps.
One-fourth of the caps are blue. So, there are y/4 blue caps.
Therefore, number of green caps = y - 2y/5 - y/4 = (20y - 8y - 5y)/20 = 7y/20.
Ratio of green caps to blue caps = (7/20) ÷ (1/4) = (7/20) x 4 = 7/5 or 7:5. |
| A. 218 B. 220 C. 222 D. 226 E. 230 Let the largest of the four consecutive even integers be m. Then,
m + (m - 2) + (m - 4) + (m - 6) = 892 or 4m - 12 = 892.
Thus, m = 904 / 4 = 226.
The four consecutive even integers are 220, 222, 224 and 226. |
| A. 60% B. 75% C. 100% D. 150% E. 250% Let m be your marks in the first quiz.
Then, your marks are 0.4m in the second quiz and m in the third quiz.
Percent Increase
= (Marks in third Quiz - Marks in second quiz) x 100/Marks in second quiz
= (m - 0.4m) x 100 / 0.4m = (0.6/0.4) x 100 = 150. |
| A. $3500 B. $7500 C. $8750 D. $14000 E. $25000 Let the distributed amounts be m, 2m, 3m and 4m. Then,
m + 2m + 3m + 4m = 35000 or 10m = 35000. Thus, m = 3500 or 4m = 14000. |
| A. -8 B. 2 C. 5 D. 8 E. 24 Adding the three equations gives
12x - 4x = 12 + 17 + 11.
So, 8x = 40 or x = 5. |
| A. 1 B. 2 C. 3 D. 4 E. 5 297/3 = 99 ; 99/3 = 33 ; 33/3 = 11. So, n = 3.
Note 297/(33) = 297/27 = 11, whereas 297/(34) = 297/81 = 3.67. |
| A. 36/48 B. 40/64 C. 35/56 D. 0.625 E. 62.50% 36/48 = 6/8 = 3/4 = 0.75, whereas 35/56 = 40/64 = 0.625 = 62.5% = 5/8. |
| A. vt B. 10vt C. vt/6 D. v/6 E. 10v In 10 minutes (1/6 hour), distance traveled = speed x time = v x (1/6) = v/6. |
| A. 3.5 B. 4.5 C. 5 D. 7 E. 9 Adding the equations gives 7y + 7z = 49.
Dividing by 7 gives y + z = 7.
So, Arithmetic Mean = (y + z)/2 = 7/2 = 3.5. |
| A. (p - 1)/15 B. (p - 2)/5 C. (p - 1)/5 D. (p - 2)/15 E. (p + 1)/15 p = q + 1/2 = 3r + 1 = 3(5s + 1/3) + 1. So, p = 15s + 2 or s = (p - 2)/15. |
| A. 7 B. 13 C. 17 D. 19 E. 21 Now, 399/19 = 21 = 3 x 7 (note that 21 is not a prime number).
Since 399 = 3 x 7 x 19, the largest prime factor is 19. |
| A. xz3 B. zx2 C. xz2 D. xz E. All of the above. Given that x = y/z, we know that y = xz.
So, yz = (xz)z = xz2. |
| A. -17/6 B. -6/17 C. 3/34 D. 6/17 E. 17/6 Now, 12 - 27z = 7z or 12 = 27z + 7z = 34z. Thus, z = 12/34 = 6/17. |
| A. 10 B. 12 C. 16 D. 18 E. 24 Let x be the number of eggs Jones bought. Then,
x - x/2 - 3 = x/3 or
x - x/2 - x/3 = x/6 = 3. Thus, x = 6 x 3 = 18. |
| A. p + q - r B. -p + q + r C. p + q + r D. p - q - r E. p - q + r Mr. Jones is presently (q + r) years old.
Therefore, he will be (p + q + r) years old p years from now.
If the problem appears confusing, choose an easy set of numbers,
e.g., p = 7; q = 50 and r = 3.
Then, Mr. Jones was 50 years old 3 years ago.
Therefore, he is 53 and will be 60 years old 7 years from now.
Note that p + q + r = 7 + 50 + 3 = 60. |
| A. (S - 20)/5 B. 5S + 20 C. (S + 20)/5 D. (S + 12)/5 E. 5S - 20 Let the smallest of the five consecutive odd integers be m. Then, m + (m + 2) + (m + 4) + (m + 6) + (m + 8) = S or 5m + 20 = S.
Thus, m = (S - 20)/5.
If you are not at ease with the algebra, another strategy may be adopted.
Choose an easy set of five consecutive odd integers, e.g., 1, 3, 5, 7, 9.
Their sum S = 25. Next, substituting S = 25, evaluate the given choices.
Only (S - 20)/5 = (25 - 20)/5 = 1 (the smallest integer chosen). |
| A. 7% B. 15.5% C. 22.5% D. 25.5% E. 30% Three-fourths is 75%. So, 75% of the fruits are peaches.
Of the remaining 25%, one-tenth are plums. So, 2.5% of the fruits are plums.
Now, 100 - 75 - 2.5 = 22.5. So, 22.5% of the fruits are apples. |
| A. 3πD2/8 B. πD2/16 C. πD2/4 D. 3πD2/16 E. πD2/8 The area of a circle is πD2/4 and the area of a semicircle is πD2/8.
So, the area of the shaded region within the semicircle must be less than πD2/8. The only option is πD2/16. |
| A. 7 B. 19 C. 26 D. 32 E. 57 The arithmetic mean of n numbers is their sum divided by n.
So, (9 + 29 + y) / 3 = 19 or 38 + y = 19 x 3 = 57. Thus, y = 57 - 38 = 19. |
| A. 300cd/t B. 300t/(cd) C. cd/(300T) D. tc/(3d) E. 3tc/d Working Rate = t/(cd) tables per carpenter per day.
Therefore, 10 carpenters will make 10t/(cd) tables per day.
In 30 days, 10 carpenters will make 300t/(cd) tables. If the problem appears confusing, make an intelligent choice of numbers, e.g., t = 600; c = 10 and d = 30.
Then, Working Rate = 600/(10 x 30) = 2 tables per carpenter per day.
Therefore, 10 carpenters will make 20 tables per day (i.e., 10 x 2).
In 30 days, 10 carpenters will make 600 tables (i.e., 30 x 20).
On substituting these values in the given formulae, two of the formulae are possible options:
300t/(cd) = 300 x 600 / (10 x 30) = 600 ; and
3tc/d = 3 x 600 x 10 / 30 = 600. |
| A. 43% B. 57% C. 67% D. 83% E. 86% Percent of false questions = (3/7) x 100 = 42.86.
So, about 43% of the questions are false.
Alternatively, one could reason out without any calculations as follows.
For every 4 true questions, there are 3 false questions. So, there are fewer false questions than true ones, i.e., less than 50% of the questions are false. The only option is 43%. |
| A. 3 B. 5 C. 7 D. 11 E. 13 Now, 1001 is divisible by neither 3 nor 5.
So, let's try to divide by 7. We find 1001 / 7 = 143 = 13 x 11.
Since 1001 = 13 x 11 x 7, the smallest prime factor is 7. |
| A. 5/3 B. 3/5 C. 7/3 D. 3/7 E. 1 Let c be the computer sales in 2007 and p the printer sales in 2007.
Then, the computer sales in 2008 are 1.4c and the printer sales in 2000 are 0.6p.
Ratio of printer sales to computer sales in 2008 = 0.6p/1.4c.
Ratio of printer sales to computer sales in 2007= p/c.
Dividing the above two ratios, we get 0.6/1.4 = 6/14 = 3/7. |
| A. PE/T B. T/PE C. TE/P D. P/TE E. TPE The office requires PE sheets per month.
Therefore, the T sheets of paper will last T/PE months.
If the problem appears confusing, choose an easy set of numbers, e.g., P = 30; E = 10 and T = 600.
Then, the office requires 300 sheets (i.e., 30 x 10) per month.
Therefore, the 600 sheets of paper will last 2 months (i.e., 600/300). |
| A. 85 B. 115 C. 195 D. 275 E. 385 The arithmetic mean of n numbers is their sum divided by n.
So, (3 + 5 + 7 + y) / 4 = 100 or 15 + y = 100 x 4 = 400.
Thus, y = 400 - 15 = 385.
Given that 3, 5 and 7 are small numbers and the average 100 is relatively large, it is possible to guess the answer as 385. |
| A. z = 4.5 B. z < 4.5 C. z = 6 D. z > 4.5 E. z > 6 The given inequality can be simplified as follows.
2z2 + 5z - 15 - 2z2 + 5z - 30 > 0
10z - 45 > 0 or 10z > 45 or z > 4.5 |
| A. 0.80% B. 1.00% C. 1.25% D. 1.50% E. 2.50% Percent Commission = (0.40/50) x 100 = 40/50 = 0.8.
Alternatively, 1% of $50 is 50 cents. Since the commission is 40 cents, it is less than 1%. So, the only option is 0.8%. |
| A. 10 B. 25 C. 75 D. 125 E. 1500 Now, (2.5/100) z = (75/100) 50. So, z = (75/2.5) 50 = (750/25) 50 = 1500.
Alternatively, 75 is 30 times 2.5. So, z must be 30 times 50.Of the given options, only 1500 is large enough. |
| A. $9 000 B. $10 000 C. $12 000 D. $17 000 E. $27 000 If $45,000 is divided equally among the three, then each will get $15,000. Since the prize money is to be divided unequally, the largest prize will be more than $15,000. The only option is $27,000. |
| A. 3cd/40 B. 7cd/100 C. cd/750 D. 15cd/100 E. cd/100 Manufacturing Cost = (d dolls/hour) (c cents/doll)
= cd cents/hour = cd/100 $/hr.
Now, 7 hours and 30 minutes = 7 1/2 hours = 15/2 hours.
Total Manufacturing Cost = (cd/100 $/hr) (15/2 hr) = 15cd/200 $ = 3cd/40 $. |
| A. This cannot be determined. B. 8/9 C. 2/3 D. 1/9 E. 1/3 Let b be the side of the square and d the length of its diagonal. Then, by Pythagoras theorem, d2 = b2 + b2 = 2 b2. Since the diagonal of the larger square is 3 times that of the small square, the side of the larger square is 3 times the side of the small square. If b is the side of the small shaded square, then its area = b2. Now, 3b is the side of the larger square and its area = 9b2.
Thus, unshaded area = 8b2 and fraction of the area of the larger square unshaded = 8/9. |
| A. 0.75P B. 0.8P C. 1.2P D. 1.25P E. 1.4P Let the car's price in 2006 be x dollars.
Then, a 20% price decrease implies the price in 2008 was (1 - 0.2)x.
So, P=0.8x = 4x/5 or x = 5P/4 = 1.25P. |
| A. 40/50 B. 80/100 C. 40% D. 400/500 E. 0.8 40% = 40/100 = 4/10 = 2/5, whereas 400/500 = 40/50 = 80/100 = 0.8 = 4/5. |
| A. -25 B. -10 C. 0 D. 10 E. 25 The arithmetic mean of n numbers is their sum divided by n.
So, Sum of five numbers / 5 = -5 or Sum of five numbers = -25.
Now, Sum of three numbers + 50 = -25 or Sum of three numbers = -75.
Thus, Average = Sum of three numbers / 3 = -75/3 = -25.
Here is an alternative strategy:
Given that the average of all the five numbers is negative (-5), their sum is negative. Given that the sum of two of them is 50 (positive), the sum and average of the other three must be negative. So, the only options are -10 and -25.
Check for -10: Average of five numbers = (50 + 3 (-10))/5 = 4. So, incorrect.
Check for -25: Average of five numbers = (50 + 3 (-25))/5 = -5. So, correct. |
| A. 235 B. 239 C. 241 D. 243 E. 245 Let the smallest of the four consecutive odd integers be m. Then, m + (m + 2) + (m + 4) + (m + 6) = 968 or 4m + 12 = 968.
Thus, m = 956 / 4 = 239.
The four consecutive odd integers are 239, 241, 243 and 245. |
| A. 8 - 2π B. 32 - 8π C. 16 - 4π D. 4 - π E. 1 - π/4 Consider one-fourth of the square with half a semicircle as shown in the figure.
Area of one-fourth of the square = 1 x 1 = 1.
Area of half a semicircle = Area of circle / 4 = π(radius)2/4 = π(1)2/4 = π/4.
Area of shaded portion in figure alongside = 1 - π/4.
There are eight such shaded portions in the complete square.
So, total area of shaded region in the complete square = 8 - 2π. |
| A. 1.40% B. 14% C. 0.09% D. 0.014% E. 0.14% 2% of 7 = (2/100) x 7 = 14/100 = 0.14. So, 2% of 7% = 0.14%. |
| A. 63 B. 105 C. 109 D. 122 E. 125 Jones has 7 times as many crayons as White and 3 times as many as Brown. So, the number of crayons Jones has must be a multiple of 21 (i.e., 7 x 3).
Therefore, 140 and 120 are not possible options.
Also, if Jones has 147 crayons, then White will have 21 crayons; but, White has less than 21 crayons.
So, the maximum number of crayons that Jones can have is 105. |
| A. 14 B. 21 C. 28 D. 35 E. 42 Let White be y years old. So, Jones is 7y years old now.
Ten years from now, White will be (y + 10) and Jones will be (7y + 10).
So, 7y + 10 = 3 (y + 10) = 3y + 30.
Thus, 4y = 20 or y = 5. White is 5 years old and Jones is 35 years old now. |
| A. I and II only. B. II and III only. C. III only. D. I only. E. II only. Adding the equations gives 2x = 15 or x = 7.5. So, x > 5 (II is true). Substituting x = 7.5 gives z - y = 2.5. So, z > y (I is false). There are no further conditions on y. So, III is not necessarily true. |
| A. 242/5 B. 86/85 C. 65/31 D. 70/17 E. 5/267 |
| A. -1 B. 11/5 C. 11/3 D. 11/7 E. 1 |
| A. -9x5 B. x7 C. -20x7 D. -20x9 E. -9 x 7 |
| A. 37 degrees. B. 87 degrees. C. 135 degrees. D. 145 degrees. E. 151 degrees. Since there's no note that says otherwise, we know the figure is drawn to scale. Using visual estimation, we can determine that x > 90. However, a theorem from geometry states that "an exterior angle of a triangle is equal to the sum of the two remote interior angles." So x = 50 + 95, x = 145. Even if you didn't remember the theorem, you know that the sum of the angles of a triangle is 180 degrees. Obviously, then, the unlabeled angle of the triangle must equal 180 - (50 + 95) or 35 degrees. You should also know that angle x and the unlabeled angle in the triangle are supplementary - that is, together they also equal 180 degrees. Therefore, angle x must equal 180 - 35 or 145 degrees. |
| A. Offering total knee arthoplasty. B. Implanting hydroxyapatite- coated Unix knee prostheses. C. Through appropriate patient selection. D. Via the correct choice of implant geometry. E. Having the patient rest for a minimum of 5 years. In lines 9 through 11 the author states that "We address this issue in the current study, which is based on a prospective series of 125 hydroxyapatite- coated Unix knee prostheses implanted consecutively" |
| A. Less technical then a total knee arthroplasty but will still need to do a TKA. B. Appropriate patient selection. C. Choice of implant geometry. D. It does not provide a long-term solution for arthritis. E. It requires careful surgical technique. In lines 7 through 9 the author states that "A fundamental issue surrounding UKA is whether hydroxyapatite-coated unicompartmental components can provide a long-term solution to unicondylar arthritis." |
| A. Open an additional reverse osmosis plant. B. Advertise in all newspapers. C. Heighten public awareness. D. Pass a bill demanding water conservation. E. Practice what they preach. In the first sentence the Bermuda Environmental and Sustainability Taskforce warns the campaign must lead by example. In other words the government should practice what they preach in regards to this campaign. |
| A. Pass a bill limiting water consumption. B. Advertise publicly that all should conserve water. C. Build a reverse Osmosis plant. D. Build up rainwater supplies. E. All of the above. The article states that the government is committed to ensuring the availability of water on the island and that they will promote this commitment publicly through various forms of media and presentations. They do not mention anything about passing a bill limiting consumption nor do they describe a plan to build additional rainwater supplies even though that is the current method for providing fresh water on the island. The article mentions a reverse osmosis plant but say it compliments the current plan. |
| A. At the original meeting. B. The next day. C. Before November 15th. D. On November 15th. E. After November 15th. The author states that the reason why the agreement wasn't signed was because it needed to be voted on by New Caledonia's Congress. There will be a special meeting to vote on this agreement on November 15th and as the author reports on line 7 and 8 that the Congress is expected to sign the agreement. Therefore after New Caledonia's Congress has its vote then the Presidents will sign the agreement. This will no doubt be after November 15th. |
| A. New Caledonia’s President refused. B. French Polynesia’s President refused. C. New Caledonia Congress needed pass a vote. D. French Polynesia’s Congress needed pass a vote. E. The agreement wasn’t complete. In lines 5 through 7 the author states that "the two presidents did not sign a |
| A. Scientific knowledge. B. For meat. C. For oil. D. To continue a tradition. E. All of the above. The author states the argument that these countries make is for tradition. He also writes that that Japan argues it is done for novelty meat and scientific knowledge. The question asked about all of the countries and not just Japan though. |
| A. Eco-tourism. B. Hunting. C. Coal firing. D. Steam engines. E. Powering mills with whale oil. The author states that nature or eco-tourism is harmless to whales and that what watching is resource friendly. |
| A. It is the only airport that flies trips into Antarctica. B. It is close to Antarctica. C. It brings many tourists into the country. D. It helps supply the cruise industry. E. It is the southernmost international airport. In lines 8 and 9 the author states that "it is the southernmost international airport in the world." Option 2 is a possibility but it says it is close to Antarctica and not the closest. There are other airports close to Antarctica. thus option 5 is the best answer. |
| A. End of the world. B. Earth’s last Frontier. C. Fin del Mundo. D. Pretty little city. E. Supplier to cruise ships. In lines 7 and 8 the author states that "Arriving at Ushuaia's airport, at the self-proclaimed Fin del Mundo" |
| A. Children. B. Women. C. Men. D. Men and women under 30 years old. E. Men and women over 50 years old. In line 5 the author states that "the symptoms can be more severe in men." |
| A. Age. B. Sunburn. C. Family history. D. A skin mite. E. Bacteria from stomach ulcers. A sunburn is not a contributing factor for developing rosacea. The article suggest that children rarely get rosacea so we can say that age is a factor. In lines 12 and 14 the author states that "Some other contributing factors to the development of rosacea include family history, a type of skin mite that is sometimes found in hair follicles, and bacteria associated with stomach ulcers called H-Pylori." |
| A. Lower heart rate. B. Increased heart rate. C. Suffered heart attacks. D. Developed heart failure. E. All of the above. In lines 8 and 9 the author states that "Participants treated with beta-blockers achieved lower heart rates than did other patients." |
| A. Low blood pressure. B. High blood pressure. C. Heart failure. D. Heart attack. E. Stroke. In lines 5 and 6 the author states that "study suggests beta-blockers do not help people suffering from hypertension." Hypertension is another word for high blook pressure as seen in line 7. |
| A. Navy. B. Coast Guard. C. Marines. D. Air force. E. Army. In lines 6 and 7 the author states that "the lead author who is an active duty pediatrician in the U.S. Air Force" |
| A. 42. B. Less than 200. C. 200. D. 1800. E. More than 1800. In line 7 the author states that "The study, which was small and included fewer than 200 children..." |
| A. Prairies. B. Turf. C. Plants. D. Roots. E. Food. In line 2 the author states that "Grasses are like most plants" |
| A. Makes food for its roots. B. Feel stress. C. Become tightly woven. D. Become like plants. E. Become denser. In lines 8 - 9 the author states that "cutting a lawn is stressful for the grass." |
| A. Leash. B. Fur hat. C. Glove. D. Crown. E. Steps. In line 2 - 3 the author states "calfskin gauntlet has been shared by ancient Persian kings, knights of medieval France, and nomads in present-day Mongolia". Another word for gauntlet is glove. |
| A. Turkey. B. Pheasant. C. Raptor. D. Falcon. E. Eagle. In the first line the speaker who gives the author instructions is referred to as a falconer. We must then assume that the bird of prey is a falcon. |
| A. Large population. B. Cultural differences from the West. C. Fast growing economy. D. Growing cities. E. Foreign companies wishing to do business in china. In the first sentence the author states options 1, 3, and 4 as being important towards the growth of China. Option 5 is never directly stated but it is assumed to be true as the meat of this article is about the pains foreign firms face while doing business in China. Nothing is mentioned about cultural differences limiting the growth of China's power. |
| A. Government red tape. B. Cultural differences. C. Low staff turnover. D. Poorly trained managers. E. Worldwide recession. In lines 4-5, the author states 'the key challenge remains the management of people to achieve world-class operations.' |
| A. Patience and hard work. B. Passion and hard work. C. Practice and hard work. D. Exercise and hard work. E. Coaching and hard work. While option 3, practice and hard work sounds correct the author actually states one needs 'to develop an effective spike so be patient and put in the hard work' |
| A. To make a kill. B. Jumping and hitting. C. A smooth flowing action. D. Hard work. E. Making contact with an open hand. In line 3 and 4 the author states 'spiking is simply the action of jumping into the
air and hitting the ball downwards into your opponent’s side of the
court' |
| A. To help hosts prepare for a festive party. B. To give directions on how to make a simple cocktail. C. To introduce a festive cocktail. D. To use festive language. E. All of the above. All of the options fit the purpose of the passage. |
| A. In order to maintain the passage's festive theme. B. She thinks that Halloween is an evil holiday. C. She thinks party hosts should do all they can to maintain the festive theme. D. She thinks party goers should maintain a healthy weight. E. She thinks party cocktails are too basic in design. Throughout the entire passage she uses descriptive language that maintains the holiday theme of Halloween. In using the word exorcism she wishes to showcase that one should get rid of such |
| A. Swimming instructors. B. Through parental supervision. C. Everyone learned on their own without any assistance. D. By following their peers. E. No one swam as they grew up in the desert. In the last sentence the author states 'One neighborhood kid would learn something, then the others would try it and so on.' Thus they learned through peer exposure. |
| A. There were no swimming instructors. B. There were no swimming pools. C. She lived in the desert with no ocean to swim in. D. Swimming was such a common activity it was necessary to learn. E. She didn't know how to swim. We see the answer in the sentence 'We learned to swim because we had no choice not to!' Thus swimming was such a common activity that one had to learn to do it in order to be social. |
| A. Most of the world has traveled to London and Australia. B. It has always been easy to travel between London and Australia. C. London and Australia are both part of the British commonwealth. D. London and Australia are very far from each other. E. There are 2 daily flights between London and Australia. The author has selected London and Australia as they are very far from each other and anyone who has seen a globe can recognize that without commercial air travel such a trip would be difficult and timely. |
| A. Showcases how society has benefited from the invention of airlines. B. Showcases how airlines have benefited from society. C. Showcases how airplanes have benefited from being invented. D. Showcases how society overuses air travel. E. Showcases a revolution for companies. The word exploitation showcases how society has benefited from the invention of airlines. |
| A. ease .. trumped B. simplicity .. augmented C. realization .. pinned D. complexity .. glorified. E. expediency .. lightened Simplicity and augmented both agree with all parts of this sentence. |
| A. accordingly B. consequently C. surprisingly D. subsequently E. ludicrously The word |
| A. identify .. endemic B. confuse .. infection C. integrate .. epiphytotic D. differentiate .. pandemic E. initiate .. disease The first blank must be differentiate as the sentence requires it in order to show that the two influenza versions are different. |
| A. intrinsically B. immanently C. explicitly D. categorically E. specially Immanently is the best option as it basically means inherent. |
| A. calculating .. merit B. fanatical . . strengths C. unyielding . . speciousness D. arrogant. . restraint E. timid .. grievances |
| A. gestured towards B. reported on C. differed on D. agreed on E. avoided |
| A. gratifying B. servitude C. anomalous D. accessible E. plentiful |
| A. relaxing B. honor C. prevention D. solace E. urgency Solace means relief and best fits this sentence. |
| A. lament B. rejoice C. beware D. satirize E. notate The word lament best fits this sentence. |
| A. unanimity B. rectitude C. acclamation D. provocative E. modesty The word modesty best fits this sentence. |
| A. expedite B. quality C. unheralded D. appraised E. encouraging Unheralded means unappreciated or unnoticed. |
| A. small .. sobriety B. wry .. confusion C. prominent .. caucus D. dry .. jargon E. incorrigible .. paucity Wry means dry or twisted humor and confusion would certainly be a potential unintended effect from this speaking style. |
| A. founded them leaning towards B. found themselves leaning towards C. have founded themselves to lean towards D. find themselves to leaning towards E. are found them to lean towards 'found themselves leaning towards' agrees with the sentence best. |
| A. she knew he be upset B. she was known he was upset C. she knew he would be upset D. she is going to know he is upset E. she knows he be upset |
| A. he did buy the biggest pumpkin B. he bought the biggest pumpkin C. he would buy the biggest pumpkin D. he is having bought the biggest pumpkin E. he buy the biggest pumpkin "he would buy the biggest pumpkin" is the best fit for this sentence. |
| A. Witnessing his estranged mother B. Witnessing her estranged mother C. The witness estranged his mother D. Witnessed his estranged mother E. Witnessed her estranged mother Witnessing his estranged mother best agrees with the sentence. |
| A. the opening act begin B. the opening act begun C. the opening act is beginning D. the opening act had begun E. the opening act begins had begun agrees with the sentence. |
| A. 0.1 B. 0.2 C. 0.3 D. 0.4 E. 0.5 Let the weight of the empty container = w
(2 - w) = weight of the cookies; and one quarter of the cookies weigh (2 - w)/4
One quarter of the cookies + container = 0.8 = w + (2 - w)/4
Multiply through by 4; 3.2 = 4w + 2 - w
1.2 = 3w; w = 0.4 |
| A. 5 B. 10 C. 15 D. 20 E. 25 The symbol ¤ tells us what to do to x and y. We then follow these directions for the actual values for x and y given in the problem.
Hence, (2 √5)2 - (0)2 = 4.5 =20 |
| A. 10 B. 12 C. 14 D. 15 E. 16 Total new volume is 10 pints. The first solution contributes 0.2 x 6 pints alcohol, and the second contributes 0.1 x 4. Total alcohol = 1.6. Percentage alcohol = (1.6 / 10) x 100 = 16 |
| A. (0, 3) B. (0, 4) C. (3, 4) D. (3, 0) E. (4, 0) Rearrange the equation to fit the form y = mx + c, where c is the intercept on the y-axis. At this point x = 0.
4y = 12 – 5x; y = -5/4 x + 12/4; 12/4 = c = 3 |
| A. 2d/T B. 2 T/d C. 2d + ½ T D. 2(d + ½ T) E. T/d Rate (R) is directly proportional to d. We write this as R = k.d, where k is a constant.
Rate is inversely proportional to T. We write this as R = k. 1/T, where k is a constant.
In the combined expression, d must appear in the numerator and T in the denominator. |
| A. 8 B. 16 C. 32 D. 64 E. 128 Work backwards. If one person got off at stop 7, as the bus approached the stop there must have been two people on board. As it approached the previous stop (no. 6) there were four on board. Approaching stop 5, there were 8. Approaching stop 4, there were 16 on board. Approaching stop 3, there were 32. Approaching stop 2, there were 64. As stop 2 was the first stop at which people got off there must have been a total of 64 people who boarded at the first stop. (One must assume that there were no people on the bus before the first official stop.) |
| A. -1.05 B. -1 C. -0.1 D. 1.05 E. 1.5 0.089 to the nearest tenth = 0.1
1.135 to the nearest tenth = 1.1
0.1 - 1.1 = -1 |
| A. 25% B. 50% C. 100% D. 125% E. 140% If the diameter of the old lid is 100, the diameter of the new lid will be 150.
This gives a ratio of 2 : 3
The areas of the lids will be in the ratio (2)2 : (3)2 . or 4 : 9
This represents an increase in area of 5units for every 4 units
5/4 is equivalent to 125%. |
| A. 4 B. 5 C. 7 D. 9 E. 12 This is a quadratic equation. To find n we multiply the last terms in each bracket together (2 times -5) = -10
To find ‘a’ we multiply the first terms in each bracket together (3x times 2x) = 6x2, So a = 6.
Thus a - n = 16
To find k we multiply the first term in the first bracket by the second term in the second bracket and add the result to the product of the second term in the first bracket and the first term in the second. (-15x + 4x) = -11x. So k = -11
16 - 11 = 5 |
| A. 1.5 B. 2 C. 3 D. 3.5 E. 5 Start constructing the sequence until you see the pattern
1...5...(average of 1 and 5 = 3)...(average of 1, 5, and 3 = 3)...(average of 1,5,3 and 3 = 3)
now you can see that all subsequent terms will be 3. |
| A. 38 B. 312 C. 316 D. 324 E. 332
The ¤ symbol tells us what operation to carry out on x and y
Carry out the same procedure on 3 and 4 first. So 38 is the result.
Now carry out the procedure on 38 and 2. So (38)4 is the result, which is equivalent to 332 |
| A. 5x + 14y B. 5x + 16y C. 5x + 5y D. 6x + 4y E. 3x + 12y Step one 2x + 5y
Step two 3(2x + 5y) = 6x + 15y
Step three (6x + 15y) - (x +y) = 6x + 15y - x - y (Notice that last minus sign!)
This gives 5x + 14y |
| A. both x and y are integers. B. x is an integer. C. either x or y is negative. D. y / x is an integer. E. x = ny where n is an integer. You can eliminate answer choices by selecting numbers.
For example, in option A, x and y could both be equal fractions and x/y would be an integer.
For the same reason option B does not have to be correct.
There is no reason for either of them to be negative.
Option D does not need to be correct. Consider x/y = 6/3. Then y/x = 3/6, which is a fraction not an integer.
But rearranging x/y = n, we get x = ny which is therefore always true. |
| A. 259 B. 950 C. 1040 D. 1145 E. 1155 The weight will be 250g plus (1.55 - 0.65)/0.10 units of 100g
250 + 900 = 1150
This is the maximum weight that can be sent at that price. But, weights exceeding
250 + 800 will also get charged this amount (that is what the ‘part thereof’ implies).
Hence a package weighing 1145 will be charged $1.55. |
| A. 1 B. 2 C. 4 D. 6 E. 8 Look for the pattern in the last digits in all the powers of 2.
The series starts out 2...4...8...16...32....64...128..256...
Already the pattern is clear; the last digits repeat in a pattern 2,4,8,6,2,4,8,6, etc.
Every power that is a multiple of 4 will end in a 6 . 320 is a multiple of 4. |
| A. p /mn B. npm C. mn / p D. np / m E. mp / n Choose sensible numbers to work the problem out. Then go back to letters.
So if 100 liters are needed per month, 20 households will need 100 x 20 liters per month.
1000 liters will last 1000/ 100 x 20 months. Putting the letters back = p/mn |
| A. 1 B. 2 C. 3 D. 4 E. 5 The smallest value will be obtained by giving x the smallest possible value while y gets the largest possible value. The smallest value for x = 7. Thus y will have to be less than or equal to 3 (so that x + y <11), but we want the largest value of y which is 3.
The difference, x - y will be 4. |
| A. 30% B. 35% C. 40% D. 45% E. 60% Let the original price of the jeans be 100. After the first reduction the price will be 75.
This new price is then reduced by 20% = 0.8 x 75 = 60
60 represents a reduction of 40 percent on the original. |
| A. 5 B. 10 C. 12 D. 15 E. 20 Adding we get 4x + 4y = 20
Therefore 2x + 2y = 10. |
| A. 4 B. 6 C. 8 D. 10 E. 12 Average speed = total distance / total time
Total distance covered = 6 miles; total time = 45 minutes = 0.75 hours
Average speed = 6/ 0.75 = 8 miles/hour |
| A. 360 B. 180 C. 90 D. 75 E. 60 The hour hand moves from pointing to 12 to pointing to half way between 2 and 3. The angle covered between each hour marking on the clock is 360/12 = 30. Since the hand has covered 2.5 of these divisions the angle moved through is 75. |
| A. -1.6 B. -0.6 C. 0 D. 0.6 E. 1.6 First you must realize that the absolute value signs lead to the conclusion that x = 4x – 3 and also –x = 4x – 3
So when we solve these equations we get x = 1 and x = 3/5 = 0.6 but since 1 is not an option above the answer is 0.6. |
| A. stay the same. B. double. C. increase to more than double. D. increase four fold. E. decrease. Pick a number that satisfies the rules that x and y are greater than 0. So for example you could choose 25 for y.
The value of x before doubling is then 25 - 50/25 = 23
The value after doubling y will be 50 - 50/50 = 49, which is more than double. |
| A. 2/10 B. 1/25 C. 1/50 D. 1/500 E. 1/5000 0.127 expressed as a fraction = 127/1000
1/8 can also be expressed as (1 x 125) / (8 x 125) = 125/1000
The difference is 2/1000, which is 1/500 |
| A. A only. B. B only. C. A and B only. D. B and C only. E. A, B, or C. You should not assume that Alphatown, Betaville and Carroty City are on a straight line. Make a diagram with Alphatown and Betaville marked 4 miles apart. Draw a circle centered on Betaville, with radius 5. Carroty City could be anywhere on this circle. The minimum distance will be 1, and maximum 9, but anywhere in between is possible. |
| A. 10 B. 12 C. 14 D. 18 E. 22 The smallest value for n such that 5n is a square is 5.
75np can now be written as 75 x 5 x p.
This gives prime factors.... 3 x 5 x 5 x 5 x p
To make the expression a perfect cube, p will have to have factors 3 x 3 , and hence p =9
n + p = 5 + 9 = 14 |
| A. 3 inches. B. 5 inches. C. 8 inches. D. 10 inches. E. 12 inches. If after each bounce it reaches 2/5 of the previous height, then after the second bounce it will reach 2/5 x 125. After the third it will reach 2/5 x 2/5 x 125. After the fourth it will reach 2/5 x 2/5 x 2/5 x 125. This cancels down to 2 x 2 x 2 = 8. |
| A. f(-1) B. f(0) C. f(1) D. f(3) E. f(4) The easiest way to solve this is to substitute the answer options in the expression and see which has the greatest value.
(-1 + 2) / (-1-2) = -2 / 2 = -1;
(0 + 2) / (0-2) = 2/ -2 = -1;
(1 + 2) / (1-2) = 3/-1 = -3;
(3 + 2) / (3-2) = 5/1 = 5;
(4+ 2) / (4-2) = 6/2 = 3 |
| A. 3 B. 6 C. 9 D. 12 E. 15 If two sets of four consecutive integers have one integer in common, the total in the combined set is 7 and we can write the sets as
n + (n + 1) + (n + 2) + (n + 3 ) and
(n + 3) + (n + 4) + (n + 5) + (n + 6)
Each term in the second set is 3 more than the equivalent term in the first set. Since there are four terms the total of the differences will be 4 x 3 = 12. |
| A. 1π B. 2π C. 5π D. 7π E. 10π The diagonal of a rectangle is the diameter of a circle. The diagonal is the hypotenuse of a 3,4,5 triangle, and is therefore, 5.
Circumference = π.diameter = 5π |
| A. 5 : 1 B. 10 : 3 C. 15 : 2 D. 20 : 3 E. 25 : 2 French coins are common to both ratios. Multiply both ratios by factors such that the French coins are represented by the same number.
Mexico : French = 5 : 2, and French : German = 5 : 1. Multiply the first by 5, and the second by 2.
Now Mexico : French = 25 : 10, and French : German = 10 : 2
Therefore the two ratios can be combined and Mexico : German = 25 : 2 |
| A. 10 B. 20 C. 30 D. 40 E. 50 The marked angle, ABC must be more than 90 degrees because it is the external angle of triangle BDC, and must be equal to the sum of angles BDC (90) and DCB.
Also ABC is not a straight line and must be less than 180.
Therefore 90 < 5x < 180
The only value of x which satisfies this relation is 20. |
| A. 8120 B. 830 C. 230 D. 232 E. 236 All four terms are identical therefore we have 4 (230).
But 4 = 22, and so we can write 22. 230
Which is equivalent to 232 |
| A. 5 - 2√6 B. 5 - √6 C. 1 - 2√6 D. 1 - √3 E. 1 - √2 Expand as for (a + b)2.
(√2 - √3)(√2 - √3) = 2 - 2(√2 + √3) + 3 = 5 - 2 √6 |
| A. 50 B. 25 C. 0 D. -25 E. -50 If x = -5, then (x² – 50) = 25 – 50 = -25
But the sign │x│ means the absolute value of x (the distance between the number and zero on the number line). Absolute values are always positive.
│-25 │ = 25 |
| A. 11 B. 17 C. 24 D. 28 E. 29 You could solve this by drawing a Venn diagram. A simpler way is to realize that you can subtract the number of students taking both languages from the numbers taking French to find the number taking only French. Likewise find those taking only Spanish. Then we have:Total = only French + only Spanish + both + neither
78 = (41-9) + (22-9) + 9 + neither.
Not enrolled students = 24 |
| A. 18 B. 24 C. 36 D. 42 E. 48 If you double the sides of a cube, the ratio of the surface areas of the old and new cubes will be 1: 4. The ratio of the volumes of the old and new cubes will be 1: 8. Weight is proportional to volume. So, If the first weighs 6 pounds, the second weighs 6x8 pounds =48. |
| A. 90 B. 95 C. 100 D. 105 E. 110 You could add up all the multiples of 10 (10 + 20 + 30 ....+190), and divide by the number of terms (19). Or you could realize that the average of an evenly spaced series of numbers is equal to the value of the middle term (or the average of the two middle terms if there are an even number of terms). The middle term out of 19 is the tenth term in the series = 100. |
| A. 300 B. 3000 C. 7200 D. 18000 E. 21000 If an object travels at 5 feet per second it covers 5x60 feet in one minute, and 5x60x60 feet in one hour. Answer = 18000 |
| A. 3 B. 4.5 C. 7.5 D. 9 E. 14 If we take AE as the base of triangle AEC, then the height is CD. The height of the triangle is therefore, 9 (given). To find the base we need to see that triangles AEB and CDE are similar. The ratio AB: CD, is therefore equal to the ratio AE: ED. The given information shows that the ratio is 3:9, or 1:3. Now dividing AD (4) in this ratio gives us AE as 1. The area of AEC = ½ base x height =1/2 x 9 = 4.5 |
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