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# If y ≠ 3 and 2x/y is a prime integer greater than 2, which o

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If y ≠ 3 and 2x/y is a prime integer greater than 2, which o [#permalink]

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24 Sep 2011, 14:39
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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-y-3-and-2x-y-is-a-prime-integer-greater-than-2-which-106226.html
[Reveal] Spoiler: OA

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Re: If y ≠ 3 and 2x/y is a prime integer greater than 2, which o [#permalink]

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24 Sep 2011, 16:44
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given 2x/y is prime and greater than 2.

=> 2x/y could be any of the following
3,5,7....
=> 2x/y is odd and prime (as 2 is the only even prime number and its not in this set)

1. x = y , can't be true

if x=y , 2x/y = 2 which is not odd and prime.

2. y=1. can't be true.

if y=1,2x/y = 2x = even which is not odd & prime.

3. x and y are prime integers, need not be true.

lets say 2x/y = 3 and say y=2 prime
=>x = 6/2 = 3 prime
satisfies the given condition here.

but when 2x/y = 3 and y=5 prime

=> x = 15/2 not prime

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Re: If y ≠ 3 and 2x/y is a prime integer greater than 2, which o [#permalink]

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24 Sep 2011, 17:09
maheshsrini wrote:
If y not= 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

I. x = y. Not true AS 2x/y will become 2

II. y = 1
III. x and y are prime integers.
x=26; y=4; Falsifies both II & III, without violating any of the conditions.

Ans: "A"
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Re: If y ≠ 3 and 2x/y is a prime integer greater than 2, which o [#permalink]

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24 Sep 2011, 19:19
I found this problem in the web and did not find the OA. My approach was the same and wanted to confirm the answer.
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Re: If y ≠ 3 and 2x/y is a prime integer greater than 2, which o [#permalink]

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24 Sep 2011, 20:42
"A" from my side as well. No option satisfy the criteria.

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Re: If y ≠ 3 and 2x/y is a prime integer greater than 2, which o [#permalink]

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26 Jul 2014, 19:29
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Re: If y ≠ 3 and 2x/y is a prime integer greater than 2, which o [#permalink]

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27 Jul 2014, 02:10
maheshsrini 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

Note that we are asked "which of the following MUST be true", not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.

So we should try to make the listed statements not true for some x and y (which satisfy y≠3 and 2x/y=prime>2).

I. x = y --> not true: x=3 and y=2 (2x/y=3=prime>2);

II. y=1 --> not necessarily true: x=3 and y=2 (2x/y=3=prime>2);

III. x and y are prime integers --> not necessarily true: x=10 and y=4 (2x/y=5=prime>2).

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-y-3-and-2x-y-is-a-prime-integer-greater-than-2-which-106226.html
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Re: If y ≠ 3 and 2x/y is a prime integer greater than 2, which o   [#permalink] 27 Jul 2014, 02:10
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