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Intern
Joined: 29 Jul 2010
Posts: 2

If n is a positive integer, is n divisible by at least six positive in
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29 Jul 2010, 11:08
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83% (01:06) correct 17% (01:18) wrong based on 83 sessions
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If n is a positive integer, is n divisible by at least six positive integers? (1) n is the product of three different prime numbers (2) n=30
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Joined: 09 Jun 2010
Posts: 1823
Concentration: General Management, Nonprofit

Re: If n is a positive integer, is n divisible by at least six positive in
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29 Jul 2010, 11:42
It's quite simple. I think the confusion arises when you confuse divisibility by integers with divisibility by prime factors.
Statement 1: n is the product of three prime numbers.
Prime numbers are numbers that are only divisible by 1 and by itself. So, for an example's sake, let's consider the following:
n = a*b*c where a, b and c are three different prime numbers. This implicitly tells us that n = a*b*c*1. This means we know that n is divisible by 4 different positive integers now.
But n is also divisible by the following combinations of numbers:
a*b b*c c*a a*b*c
Add to this the original factors:
a b c 1
And you get that n is divisible by at least 8 different positive numbers.
Hence 1 is sufficient.
Statement 2: n = 30
This is even easier. This is a special case of the first statement where a = 2 b =3 and c =5, the first three prime numbers. So the factors are
1 2 3 5 6 15 10 30
So this is also sufficient.
Hence the answer is D.
Hope this helps.



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Joined: 29 Jul 2010
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Re: If n is a positive integer, is n divisible by at least six positive in
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29 Jul 2010, 13:37
Thanks a lot!! I considered 1 as a prime number by mistake. That's why I doubt that statement 1 is sufficient. You're awesome!



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Joined: 30 May 2010
Posts: 165

Re: If n is a positive integer, is n divisible by at least six positive in
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30 Jul 2010, 13:39
Even if you make the mistake that 1 is prime, Statement 1 would still be sufficient. The question asks is n is divisible by at least six positive integers?
n = a * b * 1
Divisible by: a, b, 1, and ab.
To answer the question, "no" n is not divisible by at least six positive integers (4).
Did you maybe make the mistake of thinking not sufficient means "no" to the question?



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Re: If n is a positive integer, is n divisible by at least six positive in
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29 Oct 2018, 22:24
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Re: If n is a positive integer, is n divisible by at least six positive in
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