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Please help out on this

by Baton » Mon Feb 16, 2015 3:14 pm
If x and y are integers, is x (y+1) an even number?
1). x, and y are prime numbers. 2). y>7

I am struggling to understand why statement 1 ALONE is not sufficient- according to answer choices I am looking at.

Here is my approach:

x=2, y=2, then 2(3)= 6 = Even
x=2, y=3, then 2(4)=8 = Even
x=11, y=13, then 11(14)= 154 = even. So it seems this product will always be even.

My choice is A but the explanation says the ans is C.
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Source: — Data Sufficiency |

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by [email protected] » Mon Feb 16, 2015 3:25 pm
Hi Baton,

When dealing with Fact 1, you hit MOST of the examples that you needed to hit, but you still missed one:

In each of the 3 options you listed, one (or more) of the terms was EVEN, which is why the product of each was EVEN.

Can you come up with an example in which BOTH of the terms are ODD? That example is why Fact 1 is INSUFFICIENT.

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by Baton » Mon Feb 16, 2015 3:30 pm
Oh yeah, you're right Rich. I just thought of x=3, y=2 then it becomes 3(3)= odd. Thanks for the pointer!
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by [email protected] » Mon Feb 16, 2015 3:39 pm
Hi Baton,

When you see Quant questions that include Number Property "vocabulary" (re: odd, even, positive, negative, etc.), it often helps to take a moment to think about how those rules "work."

Here, the question asks us, in real basic terms, to multiply 2 integers together - and it asks if the result is EVEN?

Using Number Property rules, you might jot the following on your pad:

(even)(even) = even
(even)(odd) = even
(odd)(even) = even
(odd)(odd) = odd

Now you have a series of 'reference points' to TEST, instead of randomly selecting values for X and Y.

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by Brent@GMATPrepNow » Tue Feb 17, 2015 10:57 am
If x and y are integers, is x(y+1) an even number?
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 = C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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