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chloeholding
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ANOTHER number properties question 06 Apr 2011, 16:30
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Having a lot of trouble with these number properties questions...

QUESTION: If p is a positive integer and 10p / 96 is an integer, then the minimum number of prime factors p could have is?

My method was to simplify 10p / 96 to 5p / 48 and then since 5 is not a factor of 48 conclude that p must be a multiple of 48 for the result to be an integer. And if p is a multiple of 48 the minimum it can be is 48, and in that case it must have the prime factors 2 and 3. Is that reasoning sound? I'm really fumbling around with the number properties questions, they all seem different and I struggle with each one :-(



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ravsg
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ANOTHER number properties question 06 Apr 2011, 16:40
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Your explanation looks reasonable to me
Min value of p
=>(10 * 48)/96=5 is an integer
=> p = 48
=> p=2^4*3
So two prime number, 2 and 3
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Spidy001
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ANOTHER number properties question 06 Apr 2011, 18:50
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minimum number of primes = 2

(i.e 2 , 3)
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IanStewart
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ANOTHER number properties question 07 Apr 2011, 19:54
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chloeholding
Having a lot of trouble with these number properties questions...

QUESTION: If p is a positive integer and 10p / 96 is an integer, then the minimum number of prime factors p could have is?

My method was to simplify 10p / 96 to 5p / 48 and then since 5 is not a factor of 48 conclude that p must be a multiple of 48 for the result to be an integer. And if p is a multiple of 48 the minimum it can be is 48, and in that case it must have the prime factors 2 and 3. Is that reasoning sound? I'm really fumbling around with the number properties questions, they all seem different and I struggle with each one :-(
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Yes, your reasoning is perfect here. Number Theory is naturally going to seem more difficult than the other GMAT topics, since it's conceptual, you likely didn't study it before in any depth, and as you say, the questions are often very different one from the next, at least on the surface. Still, once you understand the importance of prime factorization and have a good approach to remainders questions, you have the conceptual foundation you'll need, and from your explanation above, it sounds like you're well on your way to getting there. Number Theory is often an important topic on the GMAT, so the time you're spending on it is likely to be worthwhile.



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
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Thank you for understanding, and happy exploring!
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