Problem Solving

If x and y are integers, what is the least positive number of 24x+15y?
A. 1
B. 3
C. 6
D. 9
E. 12

*An answer will be posted in 2 days.

Max@Math Revolution wrote:If x and y are integers, what is the least positive number of 24x+15y?
A. 1
B. 3
C. 6
D. 9
E. 12

*An answer will be posted in 2 days.

Hmm tricky, looks like the answer is 3.

Max@Math Revolution wrote:If x and y are integers, what is the least positive number of 24x+15y?
A. 1
B. 3
C. 6
D. 9
E. 12

*An answer will be posted in 2 days.

There is a fixed pattern of remainders as you decrease y from -1 by ones, as follows:

9,18,3,12,21,6,15,24 which repeats, so the answer is B

Max@Math Revolution wrote:If x and y are integers, what is the least positive number of 24x+15y?
A. 1
B. 3
C. 6
D. 9
E. 12

24x + 15y = 3(8x + 5y).
Since 24x+5y must be positive, and x and y are integers, the least possible value for 8x+5y = 1.
8x+5y = 1 if x=2 and y=-3, yielding the least possible value for 3(8x + 5y):
3[ (8)(2) + (5)(-3) ] = 3*1 = 3.

The correct answer is B.

Also fine to try the answers, starting with small numbers, which typically uncover the truth on GMAT problems. To get any answers < 15 we need either x or y to be negative, so we'll try one pos, one neg, and see which answers we can make.

If x = 1, y = -1, we'd get 24*1 - 15*1 = 9, so D is possible.

If x = -1, y = 2, we'd get 24*(-1) + 15*2 = 6, so C is possible.

If x = 2, y = -3, we'd get 24*2 - 15*3 = 3, so B is possible.

As the pattern is revealing, we're adding a multiple of 3 (24x) to another multiple of 3 (15y), so the answer MUST be a multiple of 3, making A impossible.

Since we found B, we're done.

Since 24(2)-15(3)=3, B is the correct answer.