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The value of 12! is closest to:
[#permalink]
Updated on: 06 Feb 2017, 11:17
Updated on: 06 Feb 2017, 11:17
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Difficulty:
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Question Stats:
53% (02:09) correct
47%
(01:59)
wrong
based on 635
sessions
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)
A. (10^6)
B. 3(10^7)
C. 5(10^8)
D. 7(10^9)
E. 9(10^11)
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Joined: 12 Sep 2015
Posts: 6803
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Location: Canada
The value of 12! is closest to:
[#permalink]
06 Feb 2017, 14:45
06 Feb 2017, 14:45
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Top Contributor
gupta87
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)
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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The value of 12! is closest to:
[#permalink]
31 Aug 2019, 14:07
31 Aug 2019, 14:07
1
Kudos
x=1*2*3*4*5*6*7*8*9*10*11*12
x=\(10^4\)*3*4*6*7*8*12
\(x=10^6*3*4*6*7\)
\(x=10^6*72*7\)
\(x≈10^6*500\)
\(x≈5*10^8\)
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
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)
A. (10^6)
B. 3(10^7)
C. 5(10^8)
D. 7(10^9)
E. 9(10^11)
