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If x and y are two different prime numbers, which of the following cannot be true?

A. xy is odd. B. x + y is even. C. x + y is odd. D. xy is even. E. x/y is an integer

A prime number is a positive integer with exactly two distinct positive divisors: 1 and itself. So, a prime number cannot be a multiple of another prime number. Which makes option E not possible (x/y=integer means that x is a multiple of y).

Answer: E.

All other options are possible: A. xy is odd --> x=3 and y=5; B. x + y is even --> x=3 and y=5; C. x + y is odd --> x=2 and y=3; D. xy is even --> x=2 and y=3;

Re: If x and y are two distinct prime numbers, which of the following cann [#permalink]

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09 Sep 2014, 18:28

Hi PareshGmat,

The best way to attack this question is to Plug-In simple prime numbers to prove the answer choices. Don't forget that 2 is the first prime number, and also the only even one. As a refresher, the definition of a prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

(A) x*y is odd. Let's choose x=3, y=5, so x*y = 15.

(B) x*y is even. Let's choose x=2, y=3, so x*y = 10.

(C) x-y is odd. Let's choose x=3, y=2, so x-y = 1.

(D) x-y is even. Let's choose x=5, y=3, so x-y = 2.

Thus, E is the only answer choice left, and must be the answer.

If x and y are two distinct prime numbers, which of the following cannot be true?

A. xy is odd. B. xy is even. C. x - y is odd. D. x - y is even. E. \(\frac{x^2}{y}\) is an integer

Whenever you come across prime numbers and the terms odd and even in a question, you must think of 2 - the only even prime number. All other prime numbers are odd.

A. xy is odd. If both x and y are odd, xy can be odd.

B. xy is even. If one of x and y is 2 and the other is some other odd prime number, xy will be even.

C. x - y is odd. If x is odd and y is 2, x-y will be odd.

D. x - y is even. If both x and y are odd, x-y will be even.

So all these are possible. Then answer must be (E). Logically, if x is prime and y is a different prime number, x^2 cannot be divisible by y.
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