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prime factors

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by grandh01 » Wed Sep 19, 2012 1:25 pm
If m=kp, where k and m are different positive integers,
then does m have more than 5 prime factors?

1) k has 5 different prime factors
2) p has 5 different prime factors

OA IS E
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Source: — Data Sufficiency |

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by Ian Stewart » Wed Sep 19, 2012 3:11 pm
The question should probably say "distinct prime factors".

Using both statements, it could be that k = (2)(3)(5)(7)(11), and p = (2)(3)(5)(7)(13), in which case m would have more than 5 prime factors (it would be divisible by the six primes 2, 3, 5, 7, 11 and 13). Or it could be that the prime factors of k and p are exactly identical, so say k = (2)(3)(5)(7)(11) and p = (2^2)(3)(5)(7)(11), in which case m has only five prime factors. All we can say for sure is that the number of distinct prime factors of m is somewhere between 5 and 10, inclusive. So the answer is E.
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by SmartAssJun » Thu Sep 20, 2012 6:42 pm
grandh01 wrote:If m=kp, where k and m are different positive integers,
then does m have more than 5 prime factors?

1) k has 5 different prime factors
2) p has 5 different prime factors

OA IS E
You don't know if k and p have common prime factors, so even both data together may not be sufficient. hence E
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by abhirup1711 » Sun Sep 23, 2012 1:08 am
Does the question mean 5 different prime factors. If so then answer is E but if not then isn't it not D?
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by Ian Stewart » Sun Sep 23, 2012 11:02 am
abhirup1711 wrote:Does the question mean 5 different prime factors. If so then answer is E but if not then isn't it not D?
You should take the question to mean "distinct prime factors", though a real GMAT question would include the word "distinct". If you are asked "how many prime factors does 25 have", the answer is one, not two; 25 has three factors, 1, 5 and 25, and only one of these factors is prime. There is no logical reason to count the '5' twice.
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