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MGMAT Advanced quant - Hybrid problem

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by bubbliiiiiiii » Mon Aug 31, 2015 10:37 pm
If x and y are positive integers greater than 1 such that x − y and are both even integers, which of the following numbers must be non-prime integers?

I. x
II. x + y
III. y/x

(A) I only (B) II only (C) III only (D) I and II only (E) I, II and III

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OA D. Why not E?

IMO, III always results in a positive fraction and thus is not prime always. Please let me know what am I missing.
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by GMATGuruNY » Tue Sep 01, 2015 3:10 am
If x and y are positive integers greater than 1 such that x - y and x/y are both even integers, which of the following numbers must be non-prime integers?

I. x
II. x + y
III. y/x

(A) I only (B) II only (C) III only (D) I and II only (E) I, II and III
The problem should read as shown above.
bubbliiiiiiii wrote: IMO, III always results in a positive fraction and thus is not prime always. Please let me know what am I missing.
III: y/x
If x=4 and y=2, then y/x = 2/4 = 1/2.
Since 1/2 is not a non-prime INTEGER, III does not have to be true.
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by Max@Math Revolution » Wed Sep 02, 2015 9:31 pm
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.


If x and y are positive integers greater than 1 such that x - y and x/y are both even integers, which of the following numbers must be non-prime integers?

I. x
II. x + y
III. y/x

(A) I only (B) II only (C) III only (D) I and II only (E) I, II and III
==> x/y=even, x=y*even=even, x-y=even,even-y=even, y=even-even=even therefore x=y=even. Since x/y=x/even=even, x=even*even=a multiple of 4. Therefore, x=4n, y=2m(n,m are integers).

I. x ==> x=4n=multiple of 4, therefore is not a prime number
II. x + y ==> x+y=4n+2m=2(2n+m)=even, therefore it is not a prime number.
III. y/x ==> y/x=2m/4n=m/2n is NOT integer therefore it is not a prime number (since we need non-prime integers)

Therefore the answer is D.


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