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by heshamelaziry » Sun Nov 29, 2009 1:33 pm
Is q an integer ?

A- q + 6 is an integer

B- 2q is even

[spoiler]OA is D. Why B is Sufficient? I think that 2 * 1/24 = 1/12 is even number but not an integer; is 1/12 not even ? when it says even, does this mean an integer ? [/spoiler]
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by papgust » Sun Nov 29, 2009 9:33 pm
1/12 is not an even number. It is a positive proper fraction. Fractions cannot be odd or even.

Again, 2q can be negative or positive even numbers (integers). But we are not concerned whether it is negative or positive. The question only asks "Is q an integer?" Whether its positive or negative, this will be sufficient.
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by Stuart@KaplanGMAT » Mon Nov 30, 2009 12:06 am
heshamelaziry wrote:Is q an integer ?

A- q + 6 is an integer

B- 2q is even

[spoiler]OA is D. Why B is Sufficient? I think that 2 * 1/24 = 1/12 is even number but not an integer; is 1/12 not even ? when it says even, does this mean an integer ? [/spoiler]
As papgust notes, 1/12 is not even; only integers are odd or even.

We can rewrite B as an equation:

2q = even

and, just like any other equation, we can divide both sides by 2 to get:

q = even/2

Since every even number is divisible by 2 (that's the definition of an even number), q must be an integer.
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