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If x is an integer, then x is divisible by how many positive

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by BTGmoderatorDC » Sun Jan 05, 2020 7:44 pm
If x is an integer, then x is divisible by how many positive integers?

(1) x is the product of three distinct prime numbers.

(2) x and 2187 each have the same number of factors.




OA D


Source: e-GMAT
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Sun Jan 05, 2020 8:54 pm
BTGmoderatorDC wrote:If x is an integer, then x is divisible by how many positive integers?

(1) x is the product of three distinct prime numbers.

(2) x and 2187 each have the same number of factors.

OA D

Source: e-GMAT
Let's take each statement one by one.

(1) x is the product of three distinct prime numbers.

Say x = p*q*r, where p, q and r are prime numbers. The factors of pqr are 1, p, q, r, pq, pr, qr and pqr. There are 8 factors. Sufficient.

(2) x and 2187 each have the same number of factors.

Since 2187 is a constant, we can certainly find out its number of factors. There is no need to find out since we are sure that it's a unique value. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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