GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Aug 2019, 15:48 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. ### Request Expert Reply # If p is a positive integer and 10p/96 is an integer

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern  Joined: 17 Dec 2012
Posts: 28
If p is a positive integer and 10p/96 is an integer  [#permalink]

### Show Tags

1
3 00:00

Difficulty:   25% (medium)

Question Stats: 69% (01:18) correct 31% (01:33) wrong based on 250 sessions

### HideShow timer Statistics

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
Math Expert V
Joined: 02 Sep 2009
Posts: 57155
Re: If p is a positive integer and 10p/96 is an integer  [#permalink]

### Show Tags

1
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.
_________________
Intern  Joined: 17 Dec 2012
Posts: 28
Re: If p is a positive integer and 10p/96 is an integer  [#permalink]

### Show Tags

1
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. and thanks again
Math Expert V
Joined: 02 Sep 2009
Posts: 57155
Re: If p is a positive integer and 10p/96 is an integer  [#permalink]

### Show Tags

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. 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.
_________________
Intern  Joined: 17 Dec 2012
Posts: 28
Re: If p is a positive integer and 10p/96 is an integer  [#permalink]

### Show Tags

1
Your assertion has such remedial effect to us novices. I must accept it is much more than just placebo. Thanks dude.
Manager  Joined: 22 Feb 2009
Posts: 158
Re: If p is a positive integer and 10p/96 is an integer  [#permalink]

### Show Tags

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 _________________
.........................................................................
+1 Kudos please, if you like my post
Director  G
Joined: 02 Sep 2016
Posts: 655
Re: If p is a positive integer and 10p/96 is an integer  [#permalink]

### Show Tags

96= 2^5*3^1

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

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

Two prime factors.
_________________
Help me make my explanation better by providing a logical feedback.

If you liked the post, HIT KUDOS !!

Don't quit.............Do it.
Intern  B
Joined: 18 Jul 2018
Posts: 36
Re: If p is a positive integer and 10p/96 is an integer  [#permalink]

### Show Tags

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. 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.
Math Expert V
Joined: 02 Sep 2009
Posts: 57155
Re: If p is a positive integer and 10p/96 is an integer  [#permalink]

### Show Tags

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. 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.
_________________
GMAT Club Legend  D
Joined: 18 Aug 2017
Posts: 4491
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If p is a positive integer and 10p/96 is an integer  [#permalink]

### Show Tags

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
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 7399
Location: United States (CA)
Re: If p is a positive integer and 10p/96 is an integer  [#permalink]

### Show Tags

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
_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: If p is a positive integer and 10p/96 is an integer   [#permalink] 27 Jan 2019, 19:36
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

#### MBA Resources  