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by mehaksal » Sat Aug 25, 2012 4:56 am
If y ≠ 3 and 2x/y is a prime integer greater than 2, which of the following must be true?
I. x = y
II. y = 1
III. x and y are prime integers.
(A) None (B) I only (C) II only (D) III only (E) I and II
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by vk_vinayak » Sat Aug 25, 2012 5:12 am
mehaksal wrote:If y ≠ 3 and 2x/y is a prime integer greater than 2, which of the following must be true?
I. x = y
II. y = 1
III. x and y are prime integers.
(A) None (B) I only (C) II only (D) III only (E) I and II
2x/y is a prime integer greater than 2 => 2x/y is an odd integer.

Any prime number greater than 2 is an odd integer.

I). If x=y, then 2x/y becomes 2. FALSE
II) If y=1, then 2X needs to be prime integer, which is never possible. FALSE
III) If x and Y are prime integers, then x/y is not an integer. Therefore, for 2x/y to be an integer, y must be 2, and x must be a prime integer greater than 2. TRUE

Eg: 2 * 17/2 = 17 or 2*3/2 = 3.

Ans: D
- VK

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by neelgandham » Sat Aug 25, 2012 5:37 am
Since, VK already proved that statement I and II are not must-be-true statements, I will show you how statement III is also not a must-be-true condition.

If y ≠ 3 and 2x/y is a prime integer greater than 2, which of the following must be true?
III. x and y are prime integers.

If x = 17 and y = 2 then 2x/y = 17 (A prime number greater than 2) and x,y are prime numbers.
If x = 14 and y = 4 then 2x/y = 28/4 = 7 (A prime number greater than 2) and x,y are NOT prime numbers. Hence, statement III is also not a must-be-true condition.

So, the answer to this question should be A and not D
Anil Gandham
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by mehaksal » Sun Aug 26, 2012 8:48 pm
neelgandham...very well pointed out...but I generally tend to ignore such cases :(
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