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Re: If x is a positive integer, is x divisible by [#permalink]
13 Jan 2013, 03:11
This post received KUDOS
If \(x\) is a positive integer, is \(x\) divisible by 15?
(1). \(x\) is a multiple of 10 (2). \(x^2\) is a multiple of 12
In my opinion answer must be B. The least perfect square which is a multiple of 12 is 36 and the answer is no. The next is 144 (12^2), again no. Explanation is not clear.
Thanks & Regards Vinni
If x is a positive integer, is x divisible by 15?
(1) x is a multiple of 10 --> if x=10 then the answer is NO but if x=30 then the answer is YES. Not sufficient
(2) x^2 is a multiple of 12 --> the least perfect square which is a multiple of 12 is 36. Hence, the least value of \(x\) is 6 and in this case the answer is NO, but if for example \(x=12*15\) then the answer is YES. Not sufficient.
Notice that from this statement we can deduce that \(x\) must be a multiple of 3 (else how can this prime appear in \(x^2\)?).
(1)+(2) \(x\) is a multiple of both 10 and 3, hence it's a multiple of 30, so \(x\) must be divisible by 15. Sufficient.
Notice that for (2) if x^2=(12*15)^2 (x^2 IS divisible by 12), then x=12*15 and in this case x IS divisible by 15. _________________