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If x and y are positive integers greater than 1 such that x

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If x and y are positive integers greater than 1 such that x [#permalink] New post 14 Dec 2012, 22:53
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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
(E) I, II and III
[Reveal] Spoiler: OA

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Last edited by daviesj on 14 Dec 2012, 23:30, edited 1 time in total.
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Re: If x and y are positive integers greater than 1 such that x [#permalink] New post 14 Dec 2012, 23:10
Am I missing something over here? If x/y is an positive even integer that means x>y then how y/x is an integer?
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Re: If x and y are positive integers greater than 1 such that x [#permalink] New post 14 Dec 2012, 23:30
sorry...edited with right answer...:):)
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Re: If x and y are positive integers greater than 1 such that x [#permalink] New post 15 Dec 2012, 04:38
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daviesj wrote:
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
(E) I, II and III


x-y=even --> either both even or both odd

\frac{x}{y}=even --> either both even or x is even and y is odd. Also, this statement implies that x>y.

As both statements are true --> both x and y must be even.

As \frac{x}{y} is an even integer and y is even too, then x must be multiple of 4 (x/y=even --> x/even=even --> x=even*even).

So, we have that x>y, x is a multiple of 4 and y is even.

Only I and II will give non-prime integers, while III won't be an integer at all.

Answer: D.

Similar question to practice: if-a-and-b-are-positive-integers-such-that-a-b-and-a-b-are-88108.html
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Re: If x and y are positive integers greater than 1 such that x [#permalink] New post 16 Dec 2012, 03:22
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from the conditions given to us we get x>y and the min value of y can be 2 , therefore x will be a multiple of 4 so both I and ii will always be non-prime but iii will not be an integer. Answer (D).
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Re: If x and y are positive integers greater than 1 such that x [#permalink] New post 16 Dec 2012, 11:20
x - y is an even integer: Therefore, for the equation to hold true, both x and y have to be even.

x/y is an even integer: Therefore, this implies that x has to be greater than y.
We can eliminate option III as y/x will never be an integer (Since x>y)

Statement I, x: x>y, hence x has to greater than 2 and even, therefore divisible by 2 and non-prime.
Statement II, x+y: x+y will be divisible by at least 2 since both x and y are even, hence the sum is non prime.

Thus, option D is the correct answer.
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Re: If x and y are positive integers greater than 1 such that x [#permalink] New post 12 Jun 2013, 04:25
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Re: If x and y are positive integers greater than 1 such that x [#permalink] New post 14 Aug 2014, 18:45
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Re: If x and y are positive integers greater than 1 such that x   [#permalink] 14 Aug 2014, 18:45
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