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Akansha: Senior | Next Rank: 100 Posts; Posts: 56; Joined: Wed Sep 01, 2010 10:04 amFollowed by: 20 members; Thanked: 1 times

by Akansha » Sun May 29, 2011 10:30 am

How many different prime numbers are factors of positive integer n?
a. 4 different prime numbers are factors of 2n
b. 4 different prime numbers are factors of n^2

OA is B

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Source: Beat The GMAT — Data Sufficiency | Sun May 29, 2011 10:30 am

SoCan: Senior | Next Rank: 100 Posts; Posts: 97; Joined: Sun May 15, 2011 9:19 amFollowed by: 1 member; Thanked: 18 times

by SoCan » Sun May 29, 2011 10:55 am

1) n could have 3 or 4 prime factors (multiplying by 2 adds a prime factor if n is odd).
2) Taking the root of a perfect square doesn't change the number of prime factors, it just reduces the length. Since we know n is an integer, n^2 is a perfect square, and n must have the same 4 prime factors. Only 2) is sufficient.

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