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If x and y are different prime numbers, each greater than 2, which of

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If x and y are different prime numbers, each greater than 2, which of [#permalink]

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If x and y are different prime numbers, each greater than 2, which of the following must be true?

I. x+y is an even integer

II. xy is an odd integer

III. (x/y) is not an integer

A. II only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III


Kudos for correct solution.
[Reveal] Spoiler: OA

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If x and y are different prime numbers, each greater than 2, which of [#permalink]

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New post 23 Feb 2016, 02:42
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Bunuel wrote:
If x and y are different prime numbers, each greater than 2, which of the following must be true?

I. x+y is an even integer
II. xy is an odd integer
III. (x/y) is not an integer

A. II only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III

Kudos for correct solution.


This question tests your knowledge about the effect of addition and multiplication on odd and even numbers:
Even + Even = Even
Odd + Even = Odd
Odd + Odd = Even

Even * Even = Even
Odd * Even = Even
Odd * Odd = Odd


Given: x and y are different prime numbers, both greater than 2

Statement I: x+y is an even integer
Since x and y are prime numbers greater than 2, they will be odd
Therefore sum will be even.
Correct

Statement II: xy is an odd integer
Since x and y are prime numbers greater than 2, they will be odd
Therefore multiplication will be odd.
Correct

Statement III: (x/y) is not an integer
Since x and y are prime integers, therefore they will not have any common factor apart from 1
Hence (x/y) will not be an integer
Correct

Hence all three statements I, II and III are correct
Option E
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Re: If x and y are different prime numbers, each greater than 2, which of [#permalink]

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New post 24 Feb 2016, 02:25
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Bunuel wrote:
If x and y are different prime numbers, each greater than 2, which of the following must be true?

I. x+y is an even integer

II. xy is an odd integer

III. (x/y) is not an integer

A. II only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III

Kudos for correct solution.


\(x\) and \(y\) are different prime numbers, each greater than 2.
As 2 is the only even prime number, both \(x\) and \(y\) must be odd.
So, we have three properties that will be useful in solving this question:
1. \(x\) and \(y\) are prime numbers
2. \(x\) and \(y\) are odd numbers
3. \(x\) and \(y\) are different numbers

Now, let us consider each statement.
Statement I: \(x + y\) is an even integer
We know that both \(x\) and \(y\) are odd. We also know that odd + odd = even
hence, \(x + y\) is an even integer.
So, statement I must be true.

Statement II: \(xy\) is an odd integer
We know that both \(x\) and \(y\) are odd. We also know that odd x odd = odd
hence, \(xy\) is an odd integer.
So, statement II must also be true.

Statement III: \(x/y\) is not an integer
This could have been tricky. But we know that \(x\) and \(y\) are different numbers. So, \(x/y\) cannot be 1. We also know that \(x\) and \(y\) are prime numbers. So, \(x\) is definitely not divisible by \(y\).
Hence, \(x/y\) cannot be an integer.
So, statement III must also be true.

Therefore, the correct answer is E.
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Re: If x and y are different prime numbers, each greater than 2, which of [#permalink]

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Re: If x and y are different prime numbers, each greater than 2, which of [#permalink]

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New post 26 May 2017, 02:59
Primes greater than 2 are odd nos.
1. odd+odd= even
2. odd*odd= odd
3. prime/prime= not integer

Hence option E.
Re: If x and y are different prime numbers, each greater than 2, which of   [#permalink] 26 May 2017, 02:59
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