factors

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CITI29: Senior | Next Rank: 100 Posts; Posts: 93; Joined: Tue Mar 18, 2008 9:28 am; Thanked: 2 times

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: Beat The GMAT — Problem Solving | Wed Jul 23, 2008 7:55 pm

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

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?

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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CITI29: Senior | Next Rank: 100 Posts; Posts: 93; Joined: Tue Mar 18, 2008 9:28 am; Thanked: 2 times

by CITI29 » Wed Jul 23, 2008 8:19 pm

Source- 'Gmat Math difficult questions'--file I downloaded from this forum

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

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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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

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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