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# For any integer P greater than 1, P! denotes the product of all the in

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Manager
Joined: 02 Jun 2015
Posts: 190
Location: Ghana
For any integer P greater than 1, P! denotes the product of all the in  [#permalink]

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20 Jul 2017, 03:05
1
00:00

Difficulty:

85% (hard)

Question Stats:

41% (01:46) correct 59% (01:41) wrong based on 17 sessions

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For any integer P greater than 1, P! denotes the product of all the integers from 1 to P, inclusive. In how many ways can 9! be expressed as a product of 2 positive integers?

A) 36
B) 72
C) 79
D) 80
E) 160

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Intern
Joined: 03 Jun 2017
Posts: 15
Re: For any integer P greater than 1, P! denotes the product of all the in  [#permalink]

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20 Jul 2017, 03:09
1
9! Can be expanded to be written as 3^4 x 2^7 x 7 x 5

Number of ways to express is a product of 2 factors is simply

(8*5*2*2)/2 = 80

D for me

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Math Expert
Joined: 02 Aug 2009
Posts: 7686
Re: For any integer P greater than 1, P! denotes the product of all the in  [#permalink]

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20 Jul 2017, 03:12
1
1
duahsolo wrote:
For any integer P greater than 1, P! denotes the product of all the integers from 1 to P, inclusive. In how many ways can 9! be expressed as a product of 2 positive integers?

A) 36
B) 72
C) 79
D) 80
E) 160

Hi..
First factorise 9!..
1*2*3*4*5*6*7*8*9=$$2^7*3^4*5^1*7^1$$
So Number of factors=(7+1)(4+1)(1+1)(1+1)=8*5*2*2=160..
But set of two will EQUAL to 9!..
So Number of sets = $$\frac{160}{2}$$=80

D

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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Re: For any integer P greater than 1, P! denotes the product of all the in   [#permalink] 20 Jul 2017, 03:12
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