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Re: If x and y are integers, is the value of x(y + 1) even?
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16 Mar 2013, 04:02

2

1

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.

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

Re: If x and y are integers, is the value of x(y + 1) even?
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28 Sep 2016, 16:27

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Top Contributor

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

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

Since the question does not say positive or negative integers,but just says "integers". Can we assume that st2 is insufficient because "x" can be negative?

Or in gmat does "integers" mean we should test positive only?

Since the question does not say positive or negative integers,but just says "integers". Can we assume that st2 is insufficient because "x" can be negative?

Or in gmat does "integers" mean we should test positive only?

Hi,

Negative or positive does not influence whether the outcome would be odd or even, since we have both negative odd/even and positive odd/even numbers.

Statement 2 says Y>7, it does not say whether Y is odd or even (also no info is given about X), If y=8 & X=odd, then product is odd and If Y=9 and X=odd, Product is even. Since we get both odd and even numbers based on st-2, it is insufficient.

In ''GMAT'', i generally check for both positive and negative numbers if the question stem says ''integers''.

Since the question does not say positive or negative integers,but just says "integers". Can we assume that st2 is insufficient because "x" can be negative?

Or in gmat does "integers" mean we should test positive only?

Hi,

Negative or positive does not influence whether the outcome would be odd or even, since we have both negative odd/even and positive odd/even numbers.

Statement 2 says Y>7, it does not say whether Y is odd or even (also no info is given about X), If y=8 & X=odd, then product is odd and If Y=9 and X=odd, Product is even. Since we get both odd and even numbers based on st-2, it is insufficient.

In ''GMAT'', i generally check for both positive and negative numbers if the question stem says ''integers''.

Thanks

Hey!

Thanks! I assumed that even/odds can only be for 0 and positive numbers!

Since the question does not say positive or negative integers,but just says "integers". Can we assume that st2 is insufficient because "x" can be negative?

Or in gmat does "integers" mean we should test positive only?

Hi,

Integers mean both positive and negative integers and both negative and positive integers. Also, even integers can be both positive and negative.

0 is even but neither positive nor negative.
_________________

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

#1 x=2 ,y=3 yes even x=3,y=2 not even not sufficient #2 value of x missing not sufficient from 1& 2 irrespective of value of x if x& y are both prime no and y>7 ie its always odd so x ( odd+1) ; even integer IMO C