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Intern
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How many prime factors does N have? [#permalink]
 06 Oct 2012, 01:31
Question Stats:
33% (02:25) correct
66% (01:21) wrong based on 0 sessions
How many prime factors does N have? (1) N is a factor of 7200 (2) 180 is a factor of N
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Re: how many prime factors n has? [#permalink]
06 Oct 2012, 01:56
First I chose E because I was of the opinion we need to get the count of the different prime factors and I did not know how many times the prime factors would be repeated. Then reworked to come to the opinion that "C" should be right answer. Statement 1 : N is a factor of 7200. Could be 360, 180, 24, 3, 2, 5 etc... There could be different combination of prime factors possible. Statement 2 : 180 is a factor of N. Could be again 180, 360, 1260 etc...There could be different number of prime factors possible. Statement 1 + Statement 2 = i)N is less than or equal to 7200 and greater than or equal to 180. ii)In order to satisfy both statements the number "N" when factorized will contain only 3 prime factors - (2^n)*(3^m)*(5^p)
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Last edited by Pansi on 06 Oct 2012, 01:58, edited 2 times in total.
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Re: how many prime factors n has? [#permalink]
06 Oct 2012, 01:56
shivanigs wrote: Hi,
Request help with the following question.Thanks..
How many prime factors does N have?
1. N is a factor of 7200
2.180 is a factor of N (1) 7200 has plenty of divisors, 1, 2, 3, 4, 6, ... Not sufficient. (2) There are many multiples of 180, so N can be 180, 360, 540,..., 7*180,... Not sufficient. (1) and (2): We can deduce that 7200 = AN, for some integer A. Also, N = 180B, for some integer B. In conclusion, 7200 = 180AB, from which AB = 40. B must be a factor of 40. The prime factors of 180 are 2, 3, and 5. The prime factors of 40 are 2 and 5. In conclusion, the prime factors of N = 180B are 2, 3 and 5 only. Sufficient. Answer C.
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Re: How many prime factors does N have? [#permalink]
06 Oct 2012, 02:17
Wouldn't a real gmat question state that we are looking for the number of distinct prime factors?
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Re: How many prime factors does N have? [#permalink]
06 Oct 2012, 02:27
Zinsch123 wrote: Wouldn't a real gmat question state that we are looking for the number of distinct prime factors? On the GMAT yes, I think so. They are quite pedantic, so almost sure, they would explicitly stress "distinct". But, for example, there is no particular reason to count how many prime factors 32 has. You are either interested in how many (distinct) prime factors a number has, or how many distinct factors it has. I don't think you would count 5 prime factors of 32...
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Re: how many prime factors n has? [#permalink]
06 Oct 2012, 08:21
EvaJager wrote: shivanigs wrote: Hi,
Request help with the following question.Thanks..
How many prime factors does N have?
1. N is a factor of 7200
2.180 is a factor of N (1) 7200 has plenty of divisors, 1, 2, 3, 4, 6, ... Not sufficient. (2) There are many multiples of 180, so N can be 180, 360, 540,..., 7*180,... Not sufficient. (1) and (2): We can deduce that 7200 = AN, for some integer A. Also, N = 180B, for some integer B. In conclusion, 7200 = 180AB, from which AB = 40. B must be a factor of 40. The prime factors of 180 are 2, 3, and 5. The prime factors of 40 are 2 and 5. In conclusion, the prime factors of N = 180B are 2, 3 and 5 only. Sufficient. Answer C. It just occurred to me that I could summarize the the above reasoning for (1) and (2) in the following way: N is a divisor of 7200, which has prime factors 2, 3, and 5. Therefore, N can have at most three prime divisors: 2, 3, and 5. N must not have all of them. Since 180 is a factor of N and has prime factors 2, 3, and 5, necessarily N must have at least the same prime factors, and ALL of them. Therefore, in conclusion, N must have exactly three prime factor: 2, 3, and 5.
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Re: how many prime factors n has?
[#permalink]
06 Oct 2012, 08:21
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