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Number properties problem

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by Troika » Mon May 21, 2012 1:22 am
K is a set of numbers such that

i. if x is in K, then -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

OA: C

Source: No. 70.,OG Quant Review, 2nd Edition
The only battle you can loose, is the one you abandon.
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Source: — Data Sufficiency |
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by aneesh.kg » Mon May 21, 2012 2:05 am
HG10 wrote:K is a set of numbers such that

i. if x is in K, then -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

OA: C

Source: No. 70.,OG Quant Review, 2nd Edition
12 = 2*2*3 = (2)*(-2)*(-3)

For 12 to be there in K, we need two 2s and a 3.

Statement(1):
We have a 2 and a (-2) and thus a (-2)*(2) as well. But, we need 3 also. No information on that.
INSUFFICIENT

Statement(2):
We have a 3 and a (-3). But, we need a 2 also. No information on that.
INSUFFICIENT

Let's combine.
The simplest of all is (2)*(-2)*(-3) = 12
SUFFICIENT

[spoiler](C)[/spoiler] is the answer.
Last edited by aneesh.kg on Sat May 26, 2012 7:02 am, edited 1 time in total.
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by Troika » Sat May 26, 2012 6:56 am
Thank you, Aneesh!
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