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If p is a positive integer and 10p/96 is an integer

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irda
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If p is a positive integer and 10p/96 is an integer [#permalink] New post   29 Jul 2014, 13:45
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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
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B
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Bunuel
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Re: If p is a positive integer and 10p/96 is an integer [#permalink] New post   29 Jul 2014, 13:51
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irda 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.

The least positive value of p for which 5p/48 is an integer is 48 = 2^3*3. Hence the minimum number of prime factors p could have is two, namely 2 and 3.

Answer: B

Hope it's clear.
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irda
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Re: If p is a positive integer and 10p/96 is an integer [#permalink] New post   29 Jul 2014, 14:06
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Bunuel,

Thanks. The logic behind the question is unacceptable per my chain of thoughts. I am definitely wrong as both your answer and the answer from the source match, but how can we state the value of unique prime numbers as the value of minimum prime numbers.

Does not minimum number of prime indicate the total number of prime numbers that must be in the numerator? The question does not say unique prime.

can you please help dispel my confusion. It is painful to override my flawed logic , if so.

8-) and thanks again
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Re: If p is a positive integer and 10p/96 is an integer [#permalink] New post   29 Jul 2014, 14:23
Expert Reply
irda wrote:
Bunuel,

Thanks. The logic behind the question is unacceptable per my chain of thoughts. I am definitely wrong as both your answer and the answer from the source match, but how can we state the value of unique prime numbers as the value of minimum prime numbers.

Does not minimum number of prime indicate the total number of prime numbers that must be in the numerator? The question does not say unique prime.

can you please help dispel my confusion. It is painful to override my flawed logic , if so.

8-) and thanks again


I see your point but usually the number of prime factors means the number of unique prime factors. For example, we say that 8 has one prime factor - 2, not three primes 2, 2, and 2. Though on the real test, I think, this would be explicitly stated.
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Re: If p is a positive integer and 10p/96 is an integer [#permalink] New post   29 Jul 2014, 14:31
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Your assertion has such remedial effect to us novices. I must accept it is much more than just placebo. Thanks dude.
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Re: If p is a positive integer and 10p/96 is an integer [#permalink] New post   29 Jul 2014, 18:49
Bunuel wrote:
irda 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.

The least positive value of p for which 5p/48 is an integer is 48 = 2^3*3. Hence the minimum number of prime factors p could have is two, namely 2 and 3.

Answer: B

Hope it's clear.


yeah, it is totally clear :-D
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Re: If p is a positive integer and 10p/96 is an integer [#permalink] New post   03 Apr 2017, 06:01
96= 2^5*3^1

(2*5*p)/2^5*3

Therefore p= 2^4*3^1 (At least)

Two prime factors.
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Re: If p is a positive integer and 10p/96 is an integer [#permalink] New post   23 Jan 2019, 02:23
Bunuel wrote:
irda wrote:
Bunuel,

Thanks. The logic behind the question is unacceptable per my chain of thoughts. I am definitely wrong as both your answer and the answer from the source match, but how can we state the value of unique prime numbers as the value of minimum prime numbers.

Does not minimum number of prime indicate the total number of prime numbers that must be in the numerator? The question does not say unique prime.

can you please help dispel my confusion. It is painful to override my flawed logic , if so.

8-) and thanks again


I see your point but usually the number of prime factors means the number of unique prime factors. For example, we say that 8 has one prime factor - 2, not three primes 2, 2, and 2. Though on the real test, I think, this would be explicitly stated.


Hi Bunuel, thanks for your answer!

So should we always consider "number of prime factors" as "nunber of unique primes"...? I am a bit confused as those2 terms are totally 2 different concepts.
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Re: If p is a positive integer and 10p/96 is an integer [#permalink] New post   23 Jan 2019, 02:26
Expert Reply
iac00 wrote:
Bunuel wrote:
irda wrote:
Bunuel,

Thanks. The logic behind the question is unacceptable per my chain of thoughts. I am definitely wrong as both your answer and the answer from the source match, but how can we state the value of unique prime numbers as the value of minimum prime numbers.

Does not minimum number of prime indicate the total number of prime numbers that must be in the numerator? The question does not say unique prime.

can you please help dispel my confusion. It is painful to override my flawed logic , if so.

8-) and thanks again


I see your point but usually the number of prime factors means the number of unique prime factors. For example, we say that 8 has one prime factor - 2, not three primes 2, 2, and 2. Though on the real test, I think, this would be explicitly stated.


Hi Bunuel, thanks for your answer!

So should we always consider "number of prime factors" as "nunber of unique primes"...? I am a bit confused as those2 terms are totally 2 different concepts.


Yes. I think I answered this above.
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Re: If p is a positive integer and 10p/96 is an integer [#permalink] New post   23 Jan 2019, 07:25
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irda 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
96= 2^ 5*3^1

or say
5p/48
or 5p/2^4 *3

so p has to have atleast 2 factors of 2 & 3 ; IMO B
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Re: If p is a positive integer and 10p/96 is an integer [#permalink] New post   27 Jan 2019, 19:36
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irda 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


Simplifying we have:

10p/96 = 5p/48

In order for 5p/48 to be an integer, then p must be a multiple of 48. Since 48 = 2^4 x 3, we see that the minimum number of prime factors of p is 2.

Answer: B
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Re: If p is a positive integer and 10p/96 is an integer [#permalink] New post   18 May 2022, 04:14
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Re: If p is a positive integer and 10p/96 is an integer [#permalink]
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