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If x and y are two different prime numbers, which of the

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If x and y are two different prime numbers, which of the [#permalink] New post 08 Jun 2012, 08:14
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 14 Jul 2012, 03:08, edited 1 time in total.
Edited the question and added the OA.
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Re: If x and y are two different prime numbers, which of the [#permalink] New post 08 Jun 2012, 08:29
Expert's post
sarb wrote:
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;

Hope it's clear.
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Re: If x and y are two different prime numbers, which of the [#permalink] New post 13 Jul 2012, 08:43
solved in 00:22

Ans : E

followed this strategy

Odd*odd = odd
even*odd=even
odd+odd=even
even+even=even
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If x and y are two distinct prime numbers, which of the following cann [#permalink] New post 09 Sep 2014, 17:24
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
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Last edited by PareshGmat on 09 Sep 2014, 20:37, edited 2 times in total.
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Re: If x and y are two distinct prime numbers, which of the following cann [#permalink] New post 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.

Hope this helps! Good luck studying!

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Re: If x and y are two distinct prime numbers, which of the following cann [#permalink] New post 09 Sep 2014, 20:05
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PareshGmat wrote:
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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If x and y are two distinct prime numbers, which of the following cann [#permalink] New post 09 Sep 2014, 20:37
PareshGmat wrote:
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



After reading this problem, things came to my mind are prime numbers, even numbers & odd numbers. However the last option E clicked over.

Dividing a prime number with another would never yield an integer. Had it been, the number would had been excluded from prime numbers, isn't it? :)

So selected option = E

Believe me, did not do any calculation, number plugging......
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If x and y are two distinct prime numbers, which of the following cann   [#permalink] 09 Sep 2014, 20:37
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