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If n is a positive integer, is n divisible by at least six positive in

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If n is a positive integer, is n divisible by at least six positive in  [#permalink]

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New post 29 Jul 2010, 11:08
1
4
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A
B
C
D
E

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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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Re: If n is a positive integer, is n divisible by at least six positive in  [#permalink]

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New post 29 Jul 2010, 11:42
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1
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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Re: If n is a positive integer, is n divisible by at least six positive in  [#permalink]

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New post 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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Re: If n is a positive integer, is n divisible by at least six positive in  [#permalink]

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New post 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  [#permalink]

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New post 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   [#permalink] 29 Oct 2018, 22:24
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