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12!/(3^4*5!*2^6)=

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12!/(3^4*5!*2^6)=  [#permalink]

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New post 11 Jun 2015, 03:40
1
1
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

87% (01:12) correct 13% (02:18) wrong based on 115 sessions

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Re: 12!/(3^4*5!*2^6)=  [#permalink]

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New post 12 Jun 2015, 00:33
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1
Bunuel wrote:
\(\frac{12!}{(3^4*5!*2^6)}=\)

(A) 2,210
(B) 770
(C) 480
(D) 77
(E) 35


Kudos for a correct solution.


hello all
there is no requirement to carry out lengthy calculations..
since we are racing against time , we should try and use the properties of the numbers we see in front..

here we can easily see numerator 12! consist of prime numbers 7 and 11, which are not being cancelled out by denominator..
so ans has to be a multiple of 77... only B and D are left ..

now 12! also consists of two*5s(one each in 5 and 10).. however the denominator has only one 5 in 5!..
the ans has to be multiple of 77*5.. only B is left ..

ans B 770
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Re: 12!/(3^4*5!*2^6)=  [#permalink]

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New post 11 Jun 2015, 04:03
1
Bunuel wrote:
\(\frac{12!}{(3^4*5!*2^6)}=\)

(A) 2,210
(B) 770
(C) 480
(D) 77
(E) 35


Kudos for a correct solution.



\(\frac{12!}{(3^4*5!*2^6)}=\frac{(12*11*10*9*8*7*6*5!)}{(3^4*5!*2^6)}\)

i.e. \(\frac{12!}{(3^4*5!*2^6)}=\frac{(12*11*10*9*8*7*6)}{(3^4*2^6)}\)

i.e. \(\frac{12!}{(3^4*5!*2^6)}=\frac{(2^2*3*11*2*5*3^2*2^3*7*2*3)}{(3^4*2^6)}\)

i.e. \(\frac{12!}{(3^4*5!*2^6)}=\frac{(2^7*3^4*11*5*7)}{(3^4*2^6)}\)

i.e. \(\frac{12!}{(3^4*5!*2^6)}=\frac{(2*11*5*7)}{(1)}\)

i.e. \(\frac{12!}{(3^4*5!*2^6)}=(770)\)

Answer: Option
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12!/(3^4*5!*2^6)=  [#permalink]

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New post Updated on: 12 Jun 2015, 01:12
1
Bunuel wrote:
\(\frac{12!}{(3^4*5!*2^6)}=\)

(A) 2,210
(B) 770
(C) 480
(D) 77
(E) 35


Kudos for a correct solution.


\(\frac{12!}{(3^4*5!*2^6)}=\)

\(=\frac{12*11*10*9*8*7*6*5*4*3*2}{(3*3*3*3)*(5*4*3*2*1)*(2*2*2*2*2*2)}=\)

\(=\frac{(2*2*3)*11*(2*5)*(3*3)*(2*2*2)*7*(2*3)*5*(2*2)*3*2}{(3*3*3*3)*(5*(2*2)*3*2)*(2*2*2*2*2*2)}=\)

\(=\frac{2^{10}*3^5*11*5^2*7}{3^5*5*2^9}=\)

\(=2*11*5*7=2*11*35=2*385=770=B\)

Originally posted by bluesquare on 12 Jun 2015, 00:18.
Last edited by Bunuel on 12 Jun 2015, 01:12, edited 2 times in total.
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Re: 12!/(3^4*5!*2^6)=  [#permalink]

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New post 15 Jun 2015, 01:28
Bunuel wrote:
\(\frac{12!}{(3^4*5!*2^6)}=\)

(A) 2,210
(B) 770
(C) 480
(D) 77
(E) 35


Kudos for a correct solution.


MANHATTAN GMAT OFFICIAL SOLUTION:

Since 5! and 12! share the common terms (5)(4)(3)(2)(1), these terms can be canceled from both the numerator and denominator. Thus, we can rewrite \(\frac{12!}{(3^4*5!*2^6)}\) as:

\(\frac{12*10*9*8*7*6}{(3^4*2^6)}=\)

We need to cancel the 2's and 3's in the denominator, so we identify these common factors in the numerator.

\(\frac{(2^2*3)*11*(2*5)*(3^2)*(2^3)*7*(2*3)}{(3^4*2^6)}\)

Group the common factors of 2 and 3 in the numerator, then cancel and compute:

\(\frac{(2^7*3^4)*11*5*7}{(3^4*2^6)}=2*11*5*7=770\)

The correct answer is B.

Note: If you do not have time to do all the canceling involved in this problem, you can at least rule out answer choices C (480) and E (35), because the correct answer must be a multiple of 11. The 12! in the numerator is a multiple of 11, and the denominator contains no factors of 11 that would cancel this term. You could use the same argument to eliminate non-multiples of 7; however, the divisibility rule for 7 is complicated, and on typical GMAT problems, testing by long division or inspection will be just as fast. In any event, you could eliminate answer choices C (480) and A (2,210) in this manner.
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Re: 12!/(3^4*5!*2^6)=  [#permalink]

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