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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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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, 03:56, 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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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.

Answer: C.

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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New post 16 Mar 2013, 06:27
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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New post 16 Mar 2013, 06:36
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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Re: If x and y are integers, is the value of x(y + 1) even? [#permalink]

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

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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

Answer:
[Reveal] Spoiler:
C


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

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New post 13 Jul 2017, 00:41
In my opinion, this type of problem is super easy if you really understand what you're being asked, and then re-frame the question to be more straightforward.

Original Question: Is x(y+1) even?

For x(y+1) to be even, either "x", or "y+1" must be even. So we're really asking, "Is either "x" or "y+1" even?

Well, we can simplify that even further. If "y+1" is even, then "y" is odd. So the new question becomes:


"Do we know whether either "x" is even, or "y" is odd?


A.) x and y are prime numbers.

Remember that "2" is a prime number, so "x" could be the even number 2, or it could be the odd number 3,or 5, or 7, etc. Same goes for "y".

This is not enough information to answer the question: "Do we know whether either "x" is even, or "y" is odd?

INSUFFICIENT.


B.) y > 7

This tells us nothing about "x," and it does not tell us whether "y" is even or odd. (There are many even and odd numbers greater than 7. For example, 8 is even, and 9 is odd.)

This is not enough information to answer the question: "Do we know whether either "x" is even, or "y" is odd?

INSUFFICIENT.


C.) If we know that "x" and "y" are prime, AND we know that "y" is greater than 7, then we know that "y" is NOT 2, and therefore "y" is odd. (every prime number above 2 is odd). Since we know that "y" is odd...

This is enough to answer the question "Do we know whether either "x" is even, or "y" is odd?

SUFFICIENT.

Answer is C.

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Re: If x and y are integers, is the value of x(y + 1) even?   [#permalink] 13 Jul 2017, 00:41
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