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Numbers Set - Answer contridicts - Need expert advise please

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by svd.kumar » Sat Jun 23, 2012 8:09 pm
Q) K is a set of numbers such that

a) if x is in K, then -x is in K, and
b) if each 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

IMO is D

But OA is C

I still think my answer is correct. Please advise.
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by Anurag@Gurome » Sat Jun 23, 2012 10:07 pm
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.

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.
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by sandeep_thaparianz » Sun Jun 24, 2012 4:09 am
Agree with C
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by svd.kumar » Sun Jun 24, 2012 6:28 am
Thanks Anurag,

My point here is

Option 1 alone is sufficeient to tell whether 12 is in Set K or not right? All intengers which are multiples of 2 only in set, so 12 is not in Set K.

Similarly for Option 2 alone is sufficent to tell that all integers which are multiples of 3 only in set, so 12 is not in set K.

Why can't answer be D, with both statements alone are sufficent.
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by Anurag@Gurome » Sun Jun 24, 2012 6:31 am
"2 is in K" doesn't mean only 2 is in K. 3 or 6 or 12 or etc may be in K.

Hope that helps.
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