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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).
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]
09 Sep 2014, 19:28
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.