DS problem a trick problem?

[Rastis]

I thought for sure I got this question correctly when I did it but apparently I was incredibly wrong. I chose D.

If x is a positive number, is x an even integer?

(1) 3x is an even integer.

(2) 5x is an even integer.

[GMATGuruNY]

If x is a positive number, is x an even integer?

(1) 3x is an even integer.

(2) 5x is an even integer.

Statement 1: 3x is even.
It's possible that x = 2, which is an even integer.
It's possible that x = 2/3, which is not an even integer.
INSUFFICIENT.

Statement 2: 5x is even.
It's possible that x = 2, which is an even integer.
It's possible that x = 2/5, which is not an even integer.
INSUFFICIENT.

Statements 1 and 2 combined:
5x-3x = even - even = even.
Since 5x-3x = 2x, 2x is even.
3x-2x = even - even = even.
Since 3x-2x=x, x is even.
SUFFICIENT.

The correct answer is C.

[Rastis]

The problem I'm having is that is says "3x is an even integer" so when I read that I think it means "3 times a certain number = an even integer." Is that not correct?

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Hi Rastis,

This questions should probably be in the DS Forum, but I'll answer it anyway. The "key" to it is to realize that the prompt does NOT state that X is an integer; it says that X is a POSITIVE NUMBER (so it might be an integer, but it might be a fraction). We're asked if X is an even integer. This is a YES/NO question.

Fact 1: 3X is an even integer

Let's TEST Values....

If X = 2/3, then 3(2/3) = 2 and the answer to the question is NO (2/3 is not an even integer)
If X = 2, then 3(2) = 6 and the answer to the question is YES (2 is an even integer)
Fact 1 is INSUFFICIENT

Fact 2: 5X is an even integer

If X = 2/5, then 5(2/5) = 2 and the answer to the question is NO
If X = 2, then 5(2) = 10 and the answer to the question is YES
Fact 2 is INSUFFICIENT

Combined, we know that:
3X is an even integer
5X is an even integer

If X = 2, then the answer to the question is YES.
None of the fractional examples fits for both (3X and 5X), so there are no fractional possibilities. Therefore, X MUST be an even integer and the answer to the question is ALWAYS YES.
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

[GMATGuruNY]

The problem I'm having is that is says "3x is an even integer" so when I read that I think it means "3 times a certain number = an even integer." Is that not correct?

Correct.
In statement 1, 3x can be equal to ANY EVEN INTEGER.

Options for 3x:
3x = 2, 4, 6, 8, 10, 12...
Dividing every value by 3, we get:
x = 2/3, 4/3, 2, 8/3, 10/3, 4...

Any of the values in red will make 3x even.
If x=2/3, then 3x = 3(2/3) = 2.
If x=4/3, then 3x = 3(4/3) = 4.
If x=2, then 3x = 3*2 = 6.
Since x can be equal to any of the values in red, statement 1 is not sufficient to determine whether x is an integer.

[pooja181]

here take 3x= 2,4, 6 so x could be 2/3 or 2 , so eleminate a

same for b , 5x= 2 6 , 8 and 10 ,again x= 2/5 or 10/5 i.r 2
eliminate b,

come with c, 5x even integer
so left with 2x as even integer ,so x must even