If x and y are positive integers, 2x + y < 29, and y > 4, what is the greatest possible value of x - y?
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.