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lenagmat: Senior | Next Rank: 100 Posts; Posts: 45; Joined: Sun Oct 16, 2011 2:21 pm; Followed by:1 members

Numbers.

by lenagmat » Wed May 09, 2012 11:59 am

Is x an integer?

(1) x/2 is an integer
(2) 2x is an integer

I used a fraction (1/2) in A to prove that X is not an integer but OA is different.

OA is A.

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Source: Beat The GMAT — Data Sufficiency | Wed May 09, 2012 11:59 am

aneesh.kg: Master | Next Rank: 500 Posts; Posts: 385; Joined: Mon Apr 16, 2012 8:40 am; Location: Pune, India; Thanked: 186 times; Followed by:29 members

by aneesh.kg » Wed May 09, 2012 12:06 pm

Hi,
In Statement(1), x/2 is given to be an integer so you should substitute integer values for x/2. If you do that, x will always be an integer. x/2 = 1 gives us x = 2. x/2 = 53 gives us x = 106.
What you did, however, is that you substituted an integer value for x (but that's the question: Is x an integer or not?) and evaluated what was given to you. There is a difference between what is given and what is being asked. This is a very common mistake.

Statement (1):
Given: x/2 = Integer
x = 2*Integer
so, x has to be an integer (an even integer).
SUFFICIENT

Statement(2)
Given: 2x = Integer
x = Integer/2
so, x is an integer only when the Integer is even. If it's odd, then x is a fraction (1/2, 3/2, etc.).
INSUFFICIENT

[spoiler](A)[/spoiler] is the answer

Aneesh Bangia
GMAT Math Coach
[email protected]

GMATPad:
Facebook Page: https://www.facebook.com/GMATPad

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GMAT/MBA Expert

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Wed May 09, 2012 4:51 pm

lenagmat wrote:Is x an integer?

(1) x/2 is an integer
(2) 2x is an integer

I used a fraction (1/2) in A to prove that X is not an integer but OA is different.

OA is A.

(1) x/2 is an integer.
For x/2 to be an integer, x must be an integer.
x/2 = integer implies x = 2 * integer = integer, which means x is an even integer; SUFFICIENT.

(2) 2x is an integer.
If x = 1/2, then 2x = 2 * (1/2) = 1, which is an integer. But here x is not an integer.
If x = 1, then 2x = 2 * 1 = 2, which is an integer. Here x is an integer.
No definite answer; NOT sufficient.

The correct answer is A.

Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

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