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irda
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If p is a positive integer and 10p/96 is an integer 29 Jul 2014, 13:45
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69% (01:20) correct 31% (01:36) wrong based on 309 sessions

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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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If p is a positive integer and 10p/96 is an integer 29 Jul 2014, 13:51
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irda
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
Show more

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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If p is a positive integer and 10p/96 is an integer 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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If p is a positive integer and 10p/96 is an integer 29 Jul 2014, 14:23
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irda
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
Show more

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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If p is a positive integer and 10p/96 is an integer 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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If p is a positive integer and 10p/96 is an integer 29 Jul 2014, 18:49
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Bunuel
irda
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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yeah, it is totally clear :-D
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If p is a positive integer and 10p/96 is an integer 03 Apr 2017, 06:01
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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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If p is a positive integer and 10p/96 is an integer 23 Jan 2019, 02:23
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Bunuel
irda
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.
Show more

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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If p is a positive integer and 10p/96 is an integer 23 Jan 2019, 02:26
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Bunuel
irda
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.
Show more

Yes. I think I answered this above.
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If p is a positive integer and 10p/96 is an integer 23 Jan 2019, 07:25
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irda
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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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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If p is a positive integer and 10p/96 is an integer 27 Jan 2019, 19:36
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irda
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
Show more

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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If p is a positive integer and 10p/96 is an integer 01 Jul 2024, 03:14
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10p/96 = 5p/48.

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

Answer: B
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