Integer

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heshamelaziry: Legendary Member; Posts: 869; Joined: Wed Aug 26, 2009 3:49 pm; Location: California; Thanked: 13 times; Followed by:3 members

Integer

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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Source: Beat The GMAT — Data Sufficiency | Sun Nov 29, 2009 1:33 pm

papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pm; Thanked: 653 times; Followed by:252 members

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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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

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.