Primes

[selango]

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

OA later

[kvcpk]

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.

2x/y is prime >2
2x>2y
x>y
Hence I is false

if y =1
2x is a prime integer >2
2x cannot be prime except when x=1. But x cannot be 1 because 2x>2.
II is not true.


x and y are prime integers.
If x and y are both prime, then x/y is not an integer, except when both are equal.
But both cant be equal.
Hence both x and y cant be prime.
III is also not true.

pick A

[vipin85]

x and y are prime integers.
If x and y are both prime, then x/y is not an integer, except when both are equal.
But both cant be equal.
Hence both x and y cant be prime.
III is also not true.

pick A

x/y may not be an integer if both x and y are prime, but 2x/y can be an integer if y=2. And 2 is a prime integer which means x and y are both prime integers.

Answer Choice: D

[kvcpk]

x/y may not be an integer if both x and y are prime, but 2x/y can be an integer if y=2. And 2 is a prime integer which means x and y are both prime integers.

Answer Choice: D

The question says MUST BE TRUE. Even if the x and y are composite, we can get a prime integer for 2x/y.
Hence I think III is wrong.