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2nd Edition - OG - Question 70

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2nd Edition - OG - Question 70

by shanice » Sun Aug 05, 2012 7:56 pm
How do I approach the below question?

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.

Answer is C.

Thank you in advance.
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by alex.gellatly » Sun Aug 05, 2012 9:04 pm
shanice wrote:How do I approach the below question?

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.
This question is just dealing with prime factorization. We want to know if 12 is in K. When you factor 12 down to its prime numbers you get 2*2*3. So... we need to know if 2*2*3 is in K. Now this question makes it a little more complicated with the two conditions which I'll talk about later.

clearly statements 1 and 2 are not sufficient.

Now we're left with either C or E. On first glance we want to say E because we only know that 2*3=6 is in K, and we are looking for 2*2*3=12. However by condition ii we know that if x and y is in k, than xy is in K. That means if 2 and 3 are in K, then 6 is also in K. If 6 is in K and we know that 2 is in K (statement 1), then 2*6=12 must also be in K.

Hope this helps.
A useful website I found that has every quant OG video explanation:

https://www.beatthegmat.com/useful-websi ... tml#475231
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by GMATGuruNY » Mon Aug 06, 2012 3:43 am
I posted a solution here:

https://www.beatthegmat.com/ds-numbers-t116250.html
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