Hi folks,

I am going over my Veritas GMAT app for iPhone, and came across a question that I thought Veritas did not answer correctly.

The question is: If x>0 and y>0, is (x-a)/(y-a) < (x/y)?
(1) x>y
(2) a>0

According to Veritas, the answer is C, but I think it should be E. Veritas' explanation is as follows:

I. Pick numbers to see whether we can answer the question Yes or No. If x = 4, y= 3, and a = 2, then:

(4-2)/(3-2)= 2/1; 2/1 > 4/3 - (No)

If x = 3, y = 4, and a = 2, then:

(4+2)/(3+2)= 6/5; 6/5 < 4/3 - (Yes)

Not Sufficient

II. Pick numbers to see if we can answer the question Yes or No. The first set of numbers we picked satisfied these conditions and answered the question No.

If x = 3, y = 4, and a = 2, then:

(3-2)/(4-2)= 1/2; 1/2 < 4/3 - Yes

Not Sufficient.

Together. If we combine the statements, we know x > y and a > 0. The first set of numbers we picked satisfied these conditions and answered the question No. There are no solutions that satisfy the conditions x > y and a > 0 and answer the question Yes.

Therefore, we know if x > y and a > 0, then we know the answer to "is (x-a)/(y-a) < (x/y)?" is No. Sufficient.

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However, by my calculation/reasoning, if we were to use the first set of numbers, but change a from 2 to 6, you will have 2/3 on the left hand side, which is indeed smaller than 4/3.

So the answer should be E, if my reasoning above is correct.

I'd be grateful for any views/help from the forum.

Thanks!