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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 nonprime 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.



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Re: If x and y are positive integers greater than 1 such that x [#permalink]
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15 Dec 2012, 00:10
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]
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15 Dec 2012, 00:30
sorry...edited with right answer... :)
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Re: If x and y are positive integers greater than 1 such that x [#permalink]
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15 Dec 2012, 05:38
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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 nonprime 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 \(xy=even\) > 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 nonprime integers, while III won't be an integer at all. Answer: D. Similar question to practice: ifaandbarepositiveintegerssuchthatabandabare88108.html
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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, 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 nonprime 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 nonprime. 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]
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Re: If x and y are positive integers greater than 1 such that x [#permalink]
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08 Apr 2016, 15:16
Hi Bunuel or any other expert... 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 nonprime, 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



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Re: If x and y are positive integers greater than 1 such that x [#permalink]
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09 Apr 2016, 01:50
kzivrev wrote: Hi Bunuel or any other expert... 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 nonprime, 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 Nonprime integers are integers which are not prime. Can you please share OG question you are talking about? Thank you.
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Re: If x and y are positive integers greater than 1 such that x [#permalink]
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01 Mar 2017, 18:25
Posting official solution of this problem :
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