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by Brent@GMATPrepNow » Sun Jan 04, 2015 9:29 am
maggiejdyer wrote:How does 12!/10! X 10!/11! x 3!/4! reduce to 12x11/1 x 1/11 x 1/4? Seeing the steps would be helpful.
12!/10! = (12)(11)(10)(9)(8)....(3)(2)(1)/(10)(9)(8)....(3)(2)(1)
= (12)(11) [the blue values cancel out]

10!/11! = (10)(9)(8)....(3)(2)(1)/(11)(10)(9)(8)....(3)(2)(1)
= 1/11 [the blue values cancel out]

3!/4! = (3)(2)(1)/(4)(3)(2)(1)
= 1/4 [the blue values cancel out]

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by [email protected] » Sun Jan 04, 2015 10:38 am
Hi maggiejdyer,

This calculation actually reduces further (and the overall calculation can be reduced using a different set of steps, if you so choose). Here's how:

First, to reduce it further, we have to look at the existing result:

(12)(11)(1/11)(1/4) = (12x11)/(11x4)

Here, the 11s cancel out, leaving us with 12/4, which then reduces to 3
--------------
With the original calculation, we can reduce it in a different set of steps (but with the same math rules):

(12!/10!)((10!/11!)(3!/4!)

In the original calculation, the 10!s cancel be cancelled out first, leaving...

(12!)(1/11!)(3!/4!)

12!/11! = 12.....

(12)(3!/4!)

As noted earlier, 3!/4! = 1/4, so...

12(1/4) = 3

This goes to show that many of the calculations that you will have to do to answer GMAT Quant questions can be done in a variety of ways.

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by GMATinsight » Mon Jan 05, 2015 7:07 am
maggiejdyer wrote:How does 12!/10! X 10!/11! x 3!/4! reduce to 12x11/1 x 1/11 x 1/4? Seeing the steps would be helpful.
12!/10! = 12x11x10!/10! = 12x11

10!/11! = 10!/11x10! = 1/11

3!/4! = 3!/4x3! = 1/4

i.e. 12!/10! X 10!/11! x 3!/4! = (12x11) x (1/11) x (1/4)

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by Matt@VeritasPrep » Mon Jan 05, 2015 10:31 am
Numbers with the same color will cancel out as follows:

12! * 10! * 3!
--------------
10! * 11! * 4!

is really

12! * 3!
--------
11! * 4!

is really

(12*11*10*9*8*7*6*5*4*3*2) * (3*2)
----------------------------------
(11*10*9*8*7*6*5*4*3*2) * (4*3*2)

is really

12/4, or 3.
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