M7MBA wrote: ↑

Thu Oct 29, 2020 12:25 pm

If \(n\) is the least of three different integers greater than \(1,\) what is the value of \(n?\)

(1) The product of the three integers is \(90.\)

(2) One of the integers is twice one of the other two integers.

Answer: C

Source: Official Guide

Solution:

We need to determine the value of n given that n is the least of three distinct integers greater than 1.

Statement One Alone:

Since 90 = 2 x 5 x 9 = 3 x 5 x 6, we see that n can be either 2 or 3. Statement one alone is not sufficient.

Statement Two Alone:

This does not tell us anything about n. Statement two alone is not sufficient.

Statements One and Two Together:

From statement one, we see that 90 = 2 x 5 x 9 or 90 = 3 x 5 x 6. These two multiplications are the only ways that 90 can be expressed as a product of three distinct integers each greater than 1. From statement two, we see that only for the product 3 x 5 x 6 do we have one integer that is twice another integer. Therefore, n must be 3 since it’s the least of the three integers.

Answer: C