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Is X even

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Is X even

by prat_agl » Fri Aug 24, 2012 6:32 am
X is a positive number. Is X Even?

A) 3x is even
B) 5x is even

A- Insufficient if 3X =2, x= 2/3 which is not even. B- insufficient, 5X =2 , X = 2/5 not even.
Taking them together, if 3x is even and 5x is also even then their difference will also be even . i.e, 2x is even which doesn't mean X is even. I was not able to pick any numbers here. If I take any multiple of 15 that will say x is even. But when I took both statements alone, I didn't picked a multiple of 3 or 5. Please suggest what I am missing here.
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by hjafferi » Fri Aug 24, 2012 6:39 am
IMO D

Rule is

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

Since both 3 and 5 are odd and their multiplication is even therefore x old have to be even.
Hence both statements are sufficient.
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by Ian Stewart » Fri Aug 24, 2012 6:58 am
If this were a real GMAT question (it's clearly not) it would ask "is x an even *integer*" to make it clear that the question is not only asking if x is even, but is also asking whether x need be an integer at all. If you know in advance that x is an integer, the answer is D here. If x need not be an integer, the answer is C, since many fractions will satisfy each individual statement.

In any case, you just about got to the answer with your approach, and I thought your approach was interesting, so we can use it to finish answering the question:
prat_agl wrote:
Taking them together, if 3x is even and 5x is also even then their difference will also be even . i.e, 2x is even
Yes, if 5x and 3x are even integers, then their difference, 2x, must also be an even integer. Notice we now know that 3x and 2x are both even integers, so their difference must also be an even integer, which means 3x - 2x = x is an even integer. So the two statements together are sufficient.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by prat_agl » Fri Aug 24, 2012 7:06 am
Thanks Ian.

The only think that I didn't get it why do we need to perform 3x -2x is also even?
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by Ankur87 » Fri Aug 24, 2012 9:33 am
prat_agl wrote:Thanks Ian.

The only think that I didn't get it why do we need to perform 3x -2x is also even?


Hi.. we are doing 5x-3x to show that their difference is even i.e. 2x but we still don't know about x ( if x is even or not... ) because x can be 3,4,5 etc. to show x is even we need to do 3x-2x which shows even - even = even i.e. x is even.
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