The numbers in which of the following pairs do NOT have a

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Sun Jun 30, 2019 9:26 am

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The numbers in which of the following pairs do NOT have a pair of distinct prime divisors in common?

A. 10 and 20
B. 12 and 18
C. 24 and 32
D. 21 and 63
E. 22 and 88

[spoiler]OA=C[/spoiler]

Source: GMAT Paper Test

Source: Beat The GMAT — Problem Solving | Sun Jun 30, 2019 9:26 am

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Mon Jul 01, 2019 6:35 am

32 = 2^5 has only one prime divisor, so it could never have a "pair" of distinct prime divisors in common with any other number. So the answer is C.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Tue Jul 02, 2019 5:42 pm

Gmat_mission wrote:The numbers in which of the following pairs do NOT have a pair of distinct prime divisors in common?

A. 10 and 20
B. 12 and 18
C. 24 and 32
D. 21 and 63
E. 22 and 88

[spoiler]OA=C[/spoiler]

Source: GMAT Paper Test

We see that 10 and 20 have prime factors 5 and 2 in common, and 12 and 18 have prime factors 2 and 3 in common, but 24 and 32 have only a 2 in common, so they do not have a pair of distinct prime factors in common.

Answer: C

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