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What is the number of factors of X

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What is the number of factors of X [#permalink] New post   04 Sep 2016, 04:16
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64% (01:25) correct 36% (01:49) wrong based on 94 sessions
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What is the number of factors of X?
A) X=P*Q; P and Q have exactly one common prime factor
B) P and Q each have exactly three factors
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C
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What is the number of factors of X [#permalink] New post   04 Sep 2016, 05:51
The question may have some typos: the fact X=P*Q should not be in the 1st statement. It should be the common fact.
Obviously the 1st (or the 2nd) statement alone is not sufficient.
When they are combined, we can get something:
* The 2nd statement implies that both P and Q are square of prime numbers.
* When we combine it with the 1st statement, these numbers must be the same.
Therefore X=p^4 where p is a prime. So X has 5 factors.
The answer should be C
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Re: What is the number of factors of X [#permalink] New post   04 Sep 2016, 06:12
anurag16 wrote:
What is the number of factors of X?
A) X=P*Q; P and Q have exactly one common prime factor
B) P and Q each have exactly three factors


The number of factors of perfect square is odd and all other positive integers have even number of factors.

Stat 1: X=P*Q; P and Q have exactly one common prime factor...here we are not sure if the P and Q are odd or even...Insufficient.

Stat 2: P and Q each have exactly three factors...i.e. they are perfect squares numbers...but we don't have relation with X from this statement...Insufficient.

Both : X = P*Q...when P and Q are perfect square then X will be ...then we get Odd number of factors...Sufficient..

Option C.
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What is the number of factors of X [#permalink] New post   04 Sep 2016, 10:13
from 1 & 2: we know that X=P*Q ; P and Q share a common prime number as factor ; P and Q are perfect squares and has just 3 factors each.

Assume 'n' be the prime factor that is common
we can say that P=Q=n^2 since P and Q have a common prime factor and also have 3 factors each
Therefore X=n^2*n^2=n^4

No. of factors =4+1=5
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Re: What is the number of factors of X [#permalink] New post   29 Sep 2017, 10:50
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Re: What is the number of factors of X [#permalink]
29 Sep 2017, 10:50
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