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Number Properties

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TheSituation
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Number Properties [#permalink] New post  Updated on: 24 May 2010, 21:56
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

71% (00:49) correct 29% (00:51) wrong based on 48 sessions
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If p is a positive integer and 10p/96 is an integer, then the minimum number of unique prime factors p could have is:

A. 1
B. 2
C. 3
D. 4
E. 5

Show Spoiler
B


I'm trying to build a case for A, any opinions?



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Originally posted by TheSituation on 24 May 2010, 19:02.
Last edited by TheSituation on 24 May 2010, 21:56, edited 1 time in total.
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lagomez
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Re: Number Properties [#permalink] New post  24 May 2010, 19:44
TheSituation 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. 1
B. 2
C. 3
D. 4
E. 5

Show Spoiler
B


I'm trying to build a case for A, any opinions?


How did you get 1?

Just set P = 96
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TheSituation
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Re: Number Properties [#permalink] New post  24 May 2010, 22:04
I just took another look at the OE after taking a break for a few hours.

I honestly don't know how it didn't make sense before. I read it and it clicked, just made sense instantly.

For me, this is the most frustrating part of my GMAT prep. After MONTHS of studying quant heavily I will still make stupid mistakes like that. Careless, silly mistakes.
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lagomez
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Re: Number Properties [#permalink] New post  25 May 2010, 06:50
TheSituation wrote:
I just took another look at the OE after taking a break for a few hours.

I honestly don't know how it didn't make sense before. I read it and it clicked, just made sense instantly.

For me, this is the most frustrating part of my GMAT prep. After MONTHS of studying quant heavily I will still make stupid mistakes like that. Careless, silly mistakes.


happens to all of us
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bibha
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Re: Number Properties [#permalink] New post  08 Jun 2010, 05:13
What is the OA? Isn't it B?
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oldstudent
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Re: Number Properties [#permalink] New post  01 Aug 2010, 07:20
The OA is B. 10p/96= 5.2.p/3.2^5 => For 10p/96 to be an integer p should have factors 3, 2^4, so that it gets divided by denominator without leaving any remainder. As the question asks "unique" prime factors-> they are 3 and 2 -> so 2 ->B
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Re: Number Properties [#permalink] New post  01 Aug 2010, 13:20
For a problem like this, plugging in might not necessarily work. You need to narrow down the fraction to simplest possible one and then find prime factors of the denominator to figure this out.

\(\frac{10p}{96} = \frac{5p}{48}\)

\(48 = 2*24 = 2*2*12 = 2*2*2*6 = 2*2*2*2*3 = 2^4*3\)

Thus there are AT least two prime factors to p.
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Re: Number Properties [#permalink] New post  01 Aug 2010, 16:54
My attempt:

10p/96 should resolve to a integer => 5p/48 should resolve to an integer.

Hence p/48 should resolve to a integer.

48 -- > 2^4 * 3.

Hence p should have atleast 2^4*3 for p/48 to resolve to a int.

The unique prime factors in 2^4 * 3 is 2, 3 and hence the answer is B(2).
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helenec
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Re: Number Properties [#permalink] New post  01 Aug 2010, 20:54
If p is a positive integer and 10p/96 is an integer, then the minimum number of unique prime factors p could have is:

1. first you need to reduce the fraction -> 5p/48 int

2. then prime factor the denominator: 48 = 4*2*2*3 = 2^4*3

3. you can see that there is no 5 in denominator so p needs to have at least 2^4*3 to be a multiple of 48

4. notice that if denominator had a 5 -> one 5 would be cancelled



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Re: Number Properties [#permalink]
01 Aug 2010, 20:54
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