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

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14 Dec 2012, 23:53

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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

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Last edited by daviesj on 15 Dec 2012, 00:30, edited 1 time in total.

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

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15 Dec 2012, 00:30

sorry...edited with right answer...:)
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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

\(x-y=even\) --> 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]

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16 Dec 2012, 04:22

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

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16 Dec 2012, 12:20

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]

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14 Aug 2014, 19:45

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I have a small question. I answered E which is all 3, I got I and II, but for III of course it will be a fraction and fraction is not a prime number so I includded also III as must be true answer choice. Im I wrong or the question has to add something like a integer and non-prime, something on that line. Im sure you got my point. Why I think this is beacuse as I remmeber well there was one OG question saying non even integer, and the correct choice was includong odd numebrs and fractions. so I got confused. I perfectly fine arrive to teh answer but this small ambiguity present in the question take away from me the correct answer.

I have a small question. I answered E which is all 3, I got I and II, but for III of course it will be a fraction and fraction is not a prime number so I includded also III as must be true answer choice. Im I wrong or the question has to add something like a integer and non-prime, something on that line. Im sure you got my point. Why I think this is beacuse as I remmeber well there was one OG question saying non even integer, and the correct choice was includong odd numebrs and fractions. so I got confused. I perfectly fine arrive to teh answer but this small ambiguity present in the question take away from me the correct answer.

Thanks

Non-prime integers are integers which are not prime. Can you please share OG question you are talking about? Thank you.
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