factorial reductions- help!
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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.
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12!/10! = (12)(11)(10)(9)(8)....(3)(2)(1)/(10)(9)(8)....(3)(2)(1)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)(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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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.
GMAT assassins aren't born, they're made,
Rich
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.
GMAT assassins aren't born, they're made,
Rich
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12!/10! = 12x11x10!/10! = 12x11maggiejdyer 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.
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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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.
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.