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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]

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02 Jul 2011, 01:10
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Question Stats:

78% (01:23) correct 22% (00:43) wrong based on 31 sessions

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

(1) n and 3^4 are divisible by the same number of positive numbers.
(2) n is the product of 2 and an odd prime number.
[Reveal] Spoiler: OA

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Re: n divisible by how many positive integers [#permalink]

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02 Jul 2011, 01:55
(1) says :

3^4 has (3+1) = 4 factors

Hence n also has 4 factors

Sufficient.

(2) says :

n = 2 * K, where k is an odd prime number

So n has (1+1) * (1+1) = 2*2 = 4 factors

Sufficient

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Re: n divisible by how many positive integers [#permalink]

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02 Jul 2011, 02:03
vinayrsm wrote:
If n is an integer, then n is divisible by how many positive integers?

(1) n and 3^4 are divisible by the same number of positive numbers.
(2) n is the product of 2 and an odd prime number.

St1 and St2 are contradicting each other. St1 says n has 5 positive factors; St2 says n has 4 positive factors. If we ignore this discrepancy, both statements are sufficient because we get a definite number of +ve factors for n.

Ans: "D"
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Re: n divisible by how many positive integers [#permalink]

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02 Jul 2011, 02:08
Yes, you're right. I was in slight hurry and read 4 as 3
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Re: n divisible by how many positive integers [#permalink]

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02 Jul 2011, 02:47
Hi Subhash & Fluke,

I want to get confirmation that "statements contradict" eachother - thats the reason behind posting this question. I was wondering whether I am missing something here.

Great. thanks both!
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Re: n divisible by how many positive integers [#permalink]

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02 Jul 2011, 02:59
vinayrsm wrote:
If n is an integer, then n is divisible by how many positive integers?

(1) n and 3^4 are divisible by the same number of positive numbers.
(2) n is the product of 2 and an odd prime number.

Whats the source? looks like the 2 statements contradict each other and this never happens on real GMAT.

st:1- n has 5 factors. ( unless there is a typo and it reads as 3^3)
S :2- n has 4 factors.

has to be D
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Re: n divisible by how many positive integers [#permalink]

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04 Jul 2011, 02:21
subhashghosh wrote:
(1) says :

3^4 has (3+1) = 4 factors

Hence n also has 4 factors

Sufficient.

(2) says :

n = 2 * K, where k is an odd prime number

So n has (1+1) * (1+1) = 2*2 = 4 factors

Sufficient

from Statement 1
$$3^4$$ has 5 factors as below
1, $$3^1$$,$$3^2$$,$$3^3$$,$$3^4$$

hence sufficient

from Statement 1
n = 2 * K, where k is an odd prime number
has 4 factors as below
1, 2, k,2*k
Sufficient

hope this helps....
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Re: n divisible by how many positive integers   [#permalink] 04 Jul 2011, 02:21
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