Number prop

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yellowho: Master | Next Rank: 500 Posts; Posts: 233; Joined: Wed Aug 22, 2007 3:51 pmFollowed by: 2 members; Location: New York; Thanked: 7 times

by yellowho » Fri Jan 28, 2011 9:27 pm

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

(A) One
(B) Two
(C) Three
(D) Four
(E) Five

I had 5. OA is 2. It didn't say different. How is everyone else interpreting this question.

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Source: Beat The GMAT — Data Sufficiency | Fri Jan 28, 2011 9:27 pm

schumi_gmat: Master | Next Rank: 500 Posts; Posts: 377; Joined: Wed Sep 03, 2008 9:30 amFollowed by: 2 members; Thanked: 15 times

by schumi_gmat » Fri Jan 28, 2011 11:49 pm

96 = 2^5 * 3

10p/96 = 2*5*p/96

for above equation to be an integer p = 2^4 *3

There are 2 prime factors - 2 and 3

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sat Jan 29, 2011 12:41 am

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

(A) One
(B) Two
(C) Three
(D) Four
(E) Five

10p/96 = 5p/48 ---> An integer

For 5p/48 to be integer, p has to be a multiple of 48 = (2^4)*(3)

Hence, p must have at least 2 prime factors, i.e. 2 and 3.

The correct answer is B.

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prachich1987: Legendary Member; Posts: 752; Joined: Sun Sep 12, 2010 2:47 amFollowed by: 10 members; Thanked: 20 times; GMAT Score:700

by prachich1987 » Thu Feb 03, 2011 3:09 am

Anurag@Gurome wrote: 10p/96 = 5p/48 ---> An integer

For 5p/48 to be integer, p has to be a multiple of 48 = (2^4)*(3)

Hence, p must have at least 2 prime factors, i.e. 2 and 3.

The correct answer is B.

The question is not asking us to find DISTINCT prime factors.
It is just asking us to find prime factors.
The minimum no. of prime factors should be 5.

Can you please explain.

Thanks!
Prachi

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