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If x and y are positive integers greater than 1 such that x [#permalink]
14 Dec 2012, 22:53

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Question Stats:

51% (02:29) correct
49% (01:23) wrong based on 240 sessions

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

Re: If x and y are positive integers greater than 1 such that x [#permalink]
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.

Re: If x and y are positive integers greater than 1 such that x [#permalink]
16 Dec 2012, 03:22

Ans: 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). _________________

Re: If x and y are positive integers greater than 1 such that x [#permalink]
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.

Re: If x and y are positive integers greater than 1 such that x [#permalink]
14 Aug 2014, 18:45

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