a, b and c are three distinct integers, greater than 1, such

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

a, b and c are three distinct integers, greater than 1, such

by BTGmoderatorDC » Tue Jun 11, 2019 9:58 pm

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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

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Source: Beat The GMAT — Problem Solving | Tue Jun 11, 2019 9:58 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Wed Jun 12, 2019 4:50 am

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

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Fri Jun 14, 2019 2:40 pm

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

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