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sanaa.rizwan: Senior | Next Rank: 100 Posts; Posts: 69; Joined: Wed Aug 08, 2012 9:00 amFollowed by: 1 member

by sanaa.rizwan » Mon Apr 08, 2013 5:09 pm

NP: QE DS 70

K is a set of numbers such that

(i) if x is in K, -x is in K, and
(ii) if each of x and y is in K, then xy is in K

is 12 in K

1. 2 is in K
2. 3 is in K

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Source: Beat The GMAT — Data Sufficiency | Mon Apr 08, 2013 5:09 pm

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Anju@Gurome: GMAT Instructor; Posts: 511; Joined: Wed Aug 11, 2010 9:47 amFollowed by: 86 members; Location: Delhi, India; Thanked: 344 times

by Anju@Gurome » Mon Apr 08, 2013 7:19 pm

sanaa.rizwan wrote:K is a set of numbers such that

(i) if x is in K, -x is in K, and
(ii) if each of x and y is in K, then xy is in K

is 12 in K

1. 2 is in K
2. 3 is in K

Statement 1: As 2 is in k, -2 is in K.
Hence, (2)*(-2) = -4 is in K
We can see that extending the logic all the integers which are multiple of 2 only will be in K. But 12 contains a 3, which is not possible to include from this statement.

Not sufficient

Statement 2: Same logic as of statement 1 for 3.

Not sufficient

1 & 2 Together: As 2 and 3 are in K, 2*3 = 6 is in K.
As 2 and 6 are in K, 2*6 = 12 is in K.

Sufficient

The correct answer is C.

Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.

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