Problem Solving

BTGmoderatorDC wrote:a, b and c are three distinct integers, greater than 1, such that the product of these integers is 150. If the greatest common divisor of any two numbers, among the three integers, is 1, then what is the sum of all the three integers?

A. 18
B. 22
C. 30
D. 32
E. 54

OA C

Source: e-GMAT

150 = (2)(3)(5)(5)
There are three sets of 3 values (each greater than 1) that have a product of 150:
{2, 3, 25}
{3, 5, 50}
{2, 5, 15}

GIVEN: The greatest common divisor of any two numbers, among the three integers, is 1
The only set that meets this condition is {2, 3, 25}

SUM = 2 + 3 + 25 = 30

Answer: C

Cheers,
Brent

BTGmoderatorDC wrote:a, b and c are three distinct integers, greater than 1, such that the product of these integers is 150. If the greatest common divisor of any two numbers, among the three integers, is 1, then what is the sum of all the three integers?

A. 18
B. 22
C. 30
D. 32
E. 54

OA C

Source: e-GMAT

First, let's prime factorize 150:

150 = 3 x 50 = 3 x 2 x 5^2

Since the three numbers are pairwise relatively prime, they must be 3, 2 and 25. Therefore, the sum is 3 + 2 + 25 = 30.

Answer: C