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Help with This Question

by niladri17 » Wed Jun 08, 2016 5:11 am
If n is an integer, then n is divisible by how many positive integers?
(1) n is the product of a prime number and a non-prime positive integer.
(2) n and 20 are each divisible by the same number of positive integers.

Suggest answer please
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Source: — Data Sufficiency |
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by MartyMurray » Wed Jun 08, 2016 8:28 pm
Statement 1: n is the product of a prime number and a non-prime positive integer.

Look at two extreme cases.

n = 3 The factors of n are 3, prime, and 1, non prime. Answer: 2

n = 3000 Two of the factors of n are 3, prime, and 1000, non prime. n has many factors. Answer: Way more than 2.

Two different answers.

Insufficient.

Statement 2: n and 20 are each divisible by the same number of positive integers.

Since you can determine by how many positive integers 20 is divisible, you can determine by how many n is divisible.

Sufficient.

The correct answer is B.
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by niladri17 » Wed Jun 08, 2016 8:43 pm
Thanks Marty !!!
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by Matt@VeritasPrep » Fri Jun 10, 2016 9:54 am
The biggest takeaway here is that you don't even need to bother unpacking S2: since it will give you a unique answer (the number of factors of 20), it's sufficient! (Not a big deal on this problem, since finding the factors of 20 is pretty trivial, but it'd be a big deal if the number were 13,122, or something.)
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