If x and y are integers, is the value of x(y + 1) even? : GMAT Data Sufficiency (DS)
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# If x and y are integers, is the value of x(y + 1) even?

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If x and y are integers, is the value of x(y + 1) even? [#permalink]

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16 Mar 2013, 02:52
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If x and y are integers, is the value of x(y + 1) even?

(1) x and y are prime numbers.
(2) y > 7

[Reveal] Spoiler:
Why is the answer C I'm getting E aren't there multiple cases when the statements are combined?
[Reveal] Spoiler: OA

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Last edited by Bunuel on 16 Mar 2013, 02:56, edited 1 time in total.
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Re: If x and y are integers, is the value of x(y + 1) even? [#permalink]

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16 Mar 2013, 03:02
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fozzzy wrote:
If x and y are integers, is the value of x(y + 1) even?

(1) x and y are prime numbers.
(2) y > 7

Why is the answer C I'm getting E aren't there multiple cases when the statements are combined?

Please hide OA under the spoiler.

If x and y are integers, is the value of x(y + 1) even?

x(y + 1) will be even if x is even or/and y is odd.

(1) x and y are prime numbers. If x is ANY odd prime and y is an even prime, so 2, then x(y + 1) = odd*(even+1) = odd*odd=odd but in all other cases x(y + 1) = even. Not sufficient.

(2) y > 7. Clearly insufficient.

(1)+(2) Since y = prime > 7, then y = odd, thus x(y + 1) = x(odd + 1) = x*even = even. Sufficient.

Hope it's clear.
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Re: If x and y are integers, is the value of x(y + 1) even? [#permalink]

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16 Mar 2013, 05:27
Thanks missed the prime part silly error. I don't know how to insert the second spoiler... I'll do that next time around.
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Re: If x and y are integers, is the value of x(y + 1) even? [#permalink]

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16 Mar 2013, 05:36
fozzzy wrote:
Thanks missed the prime part silly error. I don't know how to insert the second spoiler... I'll do that next time around.

Hey
One quick point here all primes except 2, when 1 is added will give an even number.
Statement provides a clue for the above, So when it is greater than 7 the constraint of 2 is avoided.....and hence the answer is C

Consider Kudos if my post helps.

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Re: If x and y are integers, is the value of x(y + 1) even? [#permalink]

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21 Oct 2014, 08:27
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Re: If x and y are integers, is the value of x(y + 1) even? [#permalink]

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20 Sep 2016, 22:54
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Re: If x and y are integers, is the value of x(y + 1) even? [#permalink]

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28 Sep 2016, 15:27
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fozzzy wrote:
If x and y are integers, is the value of x(y + 1) even?

(1) x and y are prime numbers.
(2) y > 7

Having scanned the two statements, I can see that this question is ultimately testing whether or not we recognize that ALL prime numbers are odd EXCEPT for 2 (which is even).

Target question: Is x(y+1) an even number?

Statement 1: x and y are prime numbers.
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 2 and y = 3, in which case x(y+1) is EVEN
Case b: x = 3 and y = 2, in which case x(y+1) is ODD
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y > 7
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 2 and y = 8, in which case x(y+1) is EVEN
Case b: x = 3 and y = 8, in which case x(y+1) is ODD
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
If y is a prime number and y > 7, we know that y MUST BE ODD
If y is odd, then y+1 must be EVEN
This means that x(y+1) = x(some EVEN integer) = EVEN
So, x(y+1) is definitely even
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

[Reveal] Spoiler:
C

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Re: If x and y are integers, is the value of x(y + 1) even?   [#permalink] 28 Sep 2016, 15:27
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# If x and y are integers, is the value of x(y + 1) even?

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