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The value of 12! is closest to:

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The value of 12! is closest to: [#permalink]

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New post Updated on: 06 Feb 2017, 11:17
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Difficulty:

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Question Stats:

50% (03:12) correct 50% (01:33) wrong based on 190 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)
[Reveal] Spoiler: OA

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.
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The value of 12! is closest to: [#permalink]

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New post 06 Feb 2017, 14:45
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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

Answer: C

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Re: The value of 12! is closest to: [#permalink]

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New post 31 Mar 2018, 12:17
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Re: The value of 12! is closest to:   [#permalink] 31 Mar 2018, 12:17
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