Author 
Message 
Manager
Joined: 26 Jun 2005
Posts: 122

If x is a positive integer, then how many factors does x [#permalink]
Show Tags
13 Sep 2005, 11:03
This topic is locked. If you want to discuss this question please repost it in the respective forum. 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.
_________________
Chet
Last edited by chet719 on 13 Sep 2005, 11:18, edited 1 time in total.



Senior Manager
Joined: 29 Nov 2004
Posts: 483
Location: Chicago

Re: Data Sufficiency [#permalink]
Show Tags
13 Sep 2005, 11:09
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...
_________________
Fear Mediocrity, Respect Ignorance
Last edited by ranga41 on 13 Sep 2005, 12:31, edited 1 time in total.



Manager
Joined: 26 Jun 2005
Posts: 122

Ranga, I had to edit the question. I accidentally forgot the exponent symbol on the first post.
_________________
Chet



Manager
Joined: 15 Jul 2005
Posts: 105

the answer will still be (d)



Manager
Joined: 06 Aug 2005
Posts: 197

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



Manager
Joined: 26 Jun 2005
Posts: 122

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??
_________________
Chet



Director
Joined: 13 Nov 2003
Posts: 789
Location: BULGARIA

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



Senior Manager
Joined: 30 Oct 2004
Posts: 284

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.
_________________
Vikram



Manager
Joined: 06 Aug 2005
Posts: 197

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.



Intern
Joined: 09 Sep 2005
Posts: 18

(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



Senior Manager
Joined: 30 Oct 2004
Posts: 284

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.
_________________
Vikram



Senior Manager
Joined: 13 Jan 2005
Posts: 331

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



Manager
Joined: 06 Aug 2005
Posts: 197

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



Intern
Joined: 16 Aug 2005
Posts: 25
Location: India

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.
D is the answer.



Senior Manager
Joined: 13 Jan 2005
Posts: 331

I admit my mistake and shudnt have stated that the OA is wrong.
Thanks Richard. I now understand the qn better.
GA



Manager
Joined: 06 Aug 2005
Posts: 197

No problem.
Sorry I am having a grumpy day today.
Didn't mean to be too blunt again ...



Manager
Joined: 17 Aug 2005
Posts: 165

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.










