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factors

Expert replies
by CITI29 » Wed Jul 23, 2008 7:55 pm
For all integers p, f is the number of distinct factors of p that are divisible by 3 or 2. If p = 36, what is the value of f ?

4
5
6
7
8

I thot the ans is 8, but it says 7..pls explain
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Source: — Problem Solving |

Re: factors

by Stuart@KaplanGMAT » Wed Jul 23, 2008 8:16 pm
CITI29 wrote:For all integers p, f is the number of distinct factors of p that are divisible by 3 or 2. If p = 36, what is the value of f ?

4
5
6
7
8

I thot the ans is 8, but it says 7..pls explain
The factors of 36 are:

1, 36
2, 18
3, 12
4, 9
6

The factors that are divisible by 2 or 3 are:

2, 3, 4, 6, 9, 12, 18, 36

Looks like 8 to me. What's the source?
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by CITI29 » Wed Jul 23, 2008 8:19 pm
Source- 'Gmat Math difficult questions'--file I downloaded from this forum
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by Stuart@KaplanGMAT » Thu Jul 24, 2008 11:12 am
CITI29 wrote:Source- 'Gmat Math difficult questions'--file I downloaded from this forum
Well, that's a non-official (or necessarily trustworthy) source, so there's a good chance that it's just wrong. Maybe the person who made up the question forgot to include 36.
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by Ian Stewart » Thu Jul 24, 2008 5:19 pm
Stuart Kovinsky wrote:
CITI29 wrote:Source- 'Gmat Math difficult questions'--file I downloaded from this forum
Well, that's a non-official (or necessarily trustworthy) source, so there's a good chance that it's just wrong.
Not just a good chance- a 100% chance, at least on this question. The answer is 8, as described above. Or you can prime factorize: 36 = 2^2 * 3^2. and notice that 36 has 9 divisors (add one to the powers, and multiply: 3*3 = 9). All of these divisors will be divisible by 2 or 3 with the exception of 1, so the answer is 8.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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