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The value of 12! is closest to:

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Intern
Joined: 19 Jul 2016
Posts: 49
The value of 12! is closest to:  [#permalink]

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Updated on: 06 Feb 2017, 11:17
26
00:00

Difficulty:

85% (hard)

Question Stats:

47% (02:01) correct 53% (02:00) wrong based on 232 sessions

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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)

Originally posted by gupta87 on 06 Feb 2017, 11:15.
Last edited by Bunuel on 06 Feb 2017, 11:17, edited 1 time in total.
Edited the question.
CEO
Joined: 12 Sep 2015
Posts: 3966
The value of 12! is closest to:  [#permalink]

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06 Feb 2017, 14:45
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Top Contributor
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gupta87 wrote:
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)

12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

Let's look for groups of numbers that yield a product that's a power of 10.

NOTE: the answer choices are pretty spread apart, so we can be somewhat aggressive with this strategy.

12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 (11 x 9 = 99, which is very close to 100). So...
12 x 100 x 10 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 (12 x 8 = 96, which is very close to 100). So...
100 x 100 x 10 x 7 x 6 x 5 x 4 x 3 x 2 x 1 (7 x 5 x 3 = 105, which is very close to 100). So...
100 x 100 x 10 x 100 x 6 x 4 x 2 x 1 (6 x 4 x 2 x 1 = 48, which is close to 50). So...
100 x 100 x 10 x 100 x 50
10² x 10² x 10 x 10² x 5 x 10
≈ 5 x 10^8

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General Discussion
Director
Joined: 19 Oct 2018
Posts: 878
Location: India
The value of 12! is closest to:  [#permalink]

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31 Aug 2019, 14:07
x=1*2*3*4*5*6*7*8*9*10*11*12
x=$$10^4$$*3*4*6*7*8*12
$$x=10^6*3*4*6*7$$
$$x=10^6*72*7$$
$$x≈10^6*500$$
$$x≈5*10^8$$

gupta87 wrote:
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 value of 12! is closest to:   [#permalink] 31 Aug 2019, 14:07
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