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# If n is an integer, then n is divisible by how many positive

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If n is an integer, then n is divisible by how many positive [#permalink]  11 Aug 2007, 21:03
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19. If n is an integer, then n is divisible by how many positive integers?
(1) n is the product of two different prime numbers.
(2) n and 2^3 are each divisible by the same number of positive integers

pls explain y OA is D .
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Re: DS Section 5 Q19 [#permalink]  11 Aug 2007, 21:14
crazy123 wrote:
19. If n is an integer, then n is divisible by how many positive integers?
(1) n is the product of two different prime numbers.
(2) n and 2^3 are each divisible by the same number of positive integers

pls explain y OA is D .

The question wants you to find how many factors/divisors for n.

(1) We know that prime numbers have two factors 1 and itself. So the product of two prime numbers will always yield four divisors. You can test this with several numbers:
2 x 3 = 6 -> 1,2,3,6
5 x 7 = 35 -> 1,5,7,35
since product of two prime #s will always have four factors, SUFFICIENT

(2) 2^3 = 8 : divisors for 8: 1,2,4,8, since 8 and n has the same number, we know that n must also have four factors, SUFFICIENT
Re: DS Section 5 Q19   [#permalink] 11 Aug 2007, 21:14
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