The value of 12! is closest to:

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

by M7MBA » 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?

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Source: Beat The GMAT — Problem Solving | Sat Nov 25, 2017 8:29 am

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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

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8155; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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