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PS tricky question. Can someone explain?

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by madhavi » Wed Oct 24, 2007 1:56 am
35. 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 gabriel » Wed Oct 24, 2007 4:15 am
the answer should be A none...

if x=y then the value of 2x/y = 2 but we need it to be > 2, so this cannot be true ..

if y = 1 then 2x/y becomes a composite integer , this cannot be true either

if x and y are prime then 2x/y will not be an integer ... so the answer should be A .. None ..
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by ldoolitt » Wed Oct 24, 2007 10:23 am
I would say A.

I and II have been ruled out by posters above.

III. A counter example

x = 6 (a non prime)
y = 4 (a non prime)

2x / y = 2 * 6 / 4 = 3, a prime.

Thus, x and y needn't be prime integers for 2x/y to be a prime integer. It could be true (take y=2, x=3) but it need not necessarily be true.

Thus A.
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