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

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Intern
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If p is a positive integer and 10p/96 is an integer  [#permalink]

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New post 29 Jul 2014, 12:45
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B
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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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Posts: 52344
Re: If p is a positive integer and 10p/96 is an integer  [#permalink]

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New post 29 Jul 2014, 12:51
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1
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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Re: If p is a positive integer and 10p/96 is an integer  [#permalink]

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New post 29 Jul 2014, 13:06
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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]

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New post 29 Jul 2014, 13:23
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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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What are GMAT Club Tests?
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Intern
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Re: If p is a positive integer and 10p/96 is an integer  [#permalink]

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New post 29 Jul 2014, 13:31
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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]

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New post 29 Jul 2014, 17:49
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]

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New post 03 Apr 2017, 05:01
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]

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Re: If p is a positive integer and 10p/96 is an integer &nbs [#permalink] 12 Jan 2019, 21:19
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