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# If x is a positive integer, then how many factors does x

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If x is a positive integer, then how many factors does x [#permalink]  13 Sep 2005, 10:03
If x is a positive integer, then how many factors does x have?

(1) x is divisible by one more positive integer than 3^4 is.

(2) x is the product of three different prime numbers.

Couldn't understand the OA so I thought I would ask all of you.
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Last edited by chet719 on 13 Sep 2005, 10:18, edited 1 time in total.
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Re: Data Sufficiency [#permalink]  13 Sep 2005, 10:09
Edited
I still select D, it is one of those question where both conditions give diff answers

COndition 1, 3^4 has 5 factors

Conditon 2, if x is a product of 3 prime number, it has 8 factors, the three prime numbers, the number got by multiplying among them, 1 and itself...
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Last edited by ranga41 on 13 Sep 2005, 11:31, edited 1 time in total.
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Ranga, I had to edit the question. I accidentally forgot the exponent symbol on the first post.
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Chet

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the answer will still be (d)
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3^4 has five factors, 1,3,9,27,81.
So one more than that is six.

If x = pqr
then x has eight factors 1,p,q,r,pq,pr,qr,pqr
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The OA is D, but the question I have is regarding statement 1. Statement 1 says that X is divisible by 1 more positive integer than 3^4. Doesn't that mean that the other integer could be....say "10" which could add two additional "factors" to X? In the end we are looking for the number of factors, not the number of integers...right??
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Absolutely agree with you Chets, make sense for the ans to be B)
A) is not suff. for the reasons you have mentioned in your post
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Actually the question stem says.. 1 more positive integer than 3^4 IS.
3^4 is divisible by all its factors. I/e 5, one more than 5 IS 6.
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richardj wrote:
3^4 has five factors, 1,3,9,27,81.
So one more than that is six.

If x = pqr
then x has eight factors 1,p,q,r,pq,pr,qr,pqr

I stand my reply of a couple of days ago.

What slightly concerns me is that even though I believe that D is the correct answer and both answers are sufficient, the two answers given are different above - 6 and 8. So that makes me concerned that something has gone wrong in the question setting.
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(1) x is divisible by one more positive integer than 3^4 is.

Which means X= 3^4 * M

But M could have any number of factors. So (1) is insuf.

(2) Is suff
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richardj wrote:
richardj wrote:
3^4 has five factors, 1,3,9,27,81.
So one more than that is six.

If x = pqr
then x has eight factors 1,p,q,r,pq,pr,qr,pqr

I stand my reply of a couple of days ago.

What slightly concerns me is that even though I believe that D is the correct answer and both answers are sufficient, the two answers given are different above - 6 and 8. So that makes me concerned that something has gone wrong in the question setting.

I agree. One of those cases where each statement gives a different answer yet satisfies the sufficiency.
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The OA is wrong. It has to be only. The formula to calculate the number of factors/divisors of a number is (p+1)(q+1).... where p, q are exponents of the prime factors

In A, we do not know if the positive integer is a prime number or not.

3^4 X 5^1 - in this case the # of factors is 10
3^4 X 2^4 - in this case the # of factors is 25

So only B can provide the value.

GA
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gandy_achar wrote:
The OA is wrong. It has to be only. The formula to calculate the number of factors/divisors of a number is (p+1)(q+1).... where p, q are exponents of the prime factors

In A, we do not know if the positive integer is a prime number or not.

3^4 X 5^1 - in this case the # of factors is 10
3^4 X 2^4 - in this case the # of factors is 25

So only B can provide the value.

GA

It always concerns me when people say the OA is wrong, because usually the OA is right and they are wrong.

If (1) is true then x can't possibly be prime.

All we know is that it has one more factor than 3^4 has.
That is sufficient.

Your formula is correct that 3^4 has 5 factors.
But actually we don't even need to know that, we just need to know that it can be determined, and hence the number of factors of x.

x is not a multiple of 3^4.

x = p^2 * q, where p and q are distinct primes
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gandy wrote:

The OA is wrong. It has to be only. The formula to calculate the number of factors/divisors of a number is (p+1)(q+1).... where p, q are exponents of the prime factors

In A, we do not know if the positive integer is a prime number or not.

3^4 X 5^1 - in this case the # of factors is 10
3^4 X 2^4 - in this case the # of factors is 25

If x is 3^4* 5^1, then x is divisible by 10 positive integers- 4 more than 3^4 not 1 as question states.

and moreover, it is not necessary that x can be of the form 3^4*M. The question just says x is divisible by ONE more positive integer than 3^4.

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I admit my mistake and shudnt have stated that the OA is wrong.

Thanks Richard. I now understand the qn better.

GA
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No problem.

Sorry I am having a grumpy day today.
Didn't mean to be too blunt again ...
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I have a problem with this question because the number of factors differs for each stem.

in (1), 3^4 has 5 factors (1,3,9,27,81) --> 1 more than 5 is 6
in (2), there are 8 factors of x.

I guess I would have answered D but I would have wasted time trying to get the number of factors to be equal, when in fact they don't.
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