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The value of 12! is closest to:

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by [email protected] » Sat Nov 25, 2017 11:55 am
Hi M7MBA,

We're asked to estimate the value of 12! It's worth noting that the 5 answer choices are NOT "close" to one another - each answer is more than 10 TIMES the value of the answer that appears before it. Thus, we need to properly account for all of the 'powers of 10' that appear in 12!

12! = (12)(11)(10)(9)(8)(7)(6)(5)(4)(3)(2)(1)
(12)(8) = 96.... about 10^2
(11)(9) = 99.... about 10^2
(10) = 10 .... 10^1
(7)(5)(3) = 105.... about 10^2
(6)(4)(2)(1) = 48... about (5)(10^1)

Thus, we have... (10^2)(10^2)(10^1)(10^2)(5)(10^1) = about (5)(10^8)

Final Answer: C

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by Brent@GMATPrepNow » Sat Nov 25, 2017 1:34 pm
Here's another question to practice your approximation skills: https://www.beatthegmat.com/the-product- ... 97313.html

Cheers,
Brent
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Re: The value of 12! is closest to:

by Scott@TargetTestPrep » Tue Jan 21, 2020 8:08 am
M7MBA wrote: ↑
Sat Nov 25, 2017 8:29 am
 The value of 12! is closest to:

A. (10^6)
B. 3(10^7)
C. 5(10^8)
D. 7(10^9)
E. 9(10^11)

The OA is C .

How can I get the best approximation here? Experts, is there a fast way?
12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

We have:

10 x 5 x 2 x 1 = 100 = 10^2

12 x 8 = 96 ≈ 100 = 10^2

11 x 9 = 99 ≈ 100 = 10^2

So we are left with 7 x 6 x 4 x 3, which is 42 x 12 ≈ 500 = 5 x 10^2.

Therefore, 12! ≈ 10^2 x 10^2 x 10^2 x 5 x 10^2 = 5 x 10^8.

Answer: C

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