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# If N is an odd integer between 2 and 30, how many distinct

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Senior Manager
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If N is an odd integer between 2 and 30, how many distinct [#permalink]  24 Jul 2007, 21:40
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If N is an odd integer between 2 and 30, how many distinct prime factors does it have?

3 is not a factor of N
5 is not a factor of N
Director
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Re: DS: odd couple [#permalink]  24 Jul 2007, 22:34
ArvGMAT wrote:
If N is an odd integer between 2 and 30, how many distinct prime factors does it have?

3 is not a factor of N
5 is not a factor of N

stat1: any number N b/w 2 & 30 that is not a multiple of 3 has only one prime factor. suff

stat2: if N= 3 then 1 prime factor; if N=21 then 2 prime factors. insuff
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Re: DS: odd couple [#permalink]  25 Jul 2007, 00:16
GK_Gmat wrote:
ArvGMAT wrote:
If N is an odd integer between 2 and 30, how many distinct prime factors does it have?

3 is not a factor of N
5 is not a factor of N

stat1: any number N b/w 2 & 30 that is not a multiple of 3 has only one prime factor. suff

stat2: if N= 3 then 1 prime factor; if N=21 then 2 prime factors. insuff

For... St A... I first thought u missed 25... everything else was a prime number... then realized 5*5 still means only one prime factor and 25 is not a prime factor.

Playing mind games
Senior Manager
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A is OA

I made the mistake of selecting C then realized that the only # that is a multiple of 5 is 15 and 25. 15 has 3 as a multiple so we can eliminate it and 25 has only 5 as a factor.
Senior Manager
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C, both needed.

with 1 & 2 combined we see that prime numbers fit.
Senior Manager
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ArvGMAT wrote:
A is OA

I made the mistake of selecting C then realized that the only # that is a multiple of 5 is 15 and 25. 15 has 3 as a multiple so we can eliminate it and 25 has only 5 as a factor.

Crap. I fell for it.
Current Student
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Yeah Its A...

If N is an ODD integer between 2 and 30..lets list em out

3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29...

1) if 3 is not a factor of N..then its clear 15, 21 and 27 are out...which leaves us with 1 DISTINCT prime factor only... Sufficient

2) if 5 is not a factor then ..7 and 3 could still be factors or 29 which is a prime can be a factor...so insufficient..

A it is..
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St1:
If 3 is not a factor of N, then N will be odd and have only one distinct prime factor.

St2:
If 5 is not a factor of N, then N could be 33, (2 distinct primes), N could be 9 (just 1 prime). Insufficient.

Ans A
Director
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That was tricky.. i alomst went for C. the word prime factors in the question makes all the difference.
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