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(2^5*5^6)/10000=?

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Math Expert
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Joined: 02 Sep 2009
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(2^5*5^6)/10000=?  [#permalink]

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New post 15 Nov 2016, 08:58
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

91% (01:11) correct 9% (00:47) wrong based on 80 sessions

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Senior Manager
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Joined: 06 Jun 2016
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Location: India
Concentration: Operations, Strategy
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GMAT 1: 600 Q49 V23
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Re: (2^5*5^6)/10000=?  [#permalink]

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New post 15 Nov 2016, 09:06
Bunuel wrote:
(2^5*5^6)/10000=?

A. 0.2
B. 5
C. 25/2
D. 25
E. 50



(2^5*5^6)/(2^4*5^4)= 2*5*5 = 50
E
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Re: (2^5*5^6)/10000=?  [#permalink]

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New post 15 Nov 2016, 09:26
Bunuel wrote:
(2^5*5^6)/10000=?

A. 0.2
B. 5
C. 25/2
D. 25
E. 50


I did it this way:

2*2*2*2*2*5*5*5*5*5*5/10,000. I then factored out 10,000 step-by-step.
10000=5(2000). Cross off a 5 (5 5s remaining from up top)
2000=2(1000). Cross off a 2 (4 2s remaining from up top)
1000=5(200). Cross off a 5 (4 5s remaining from up top)
200=2(100). Cross off a 2 (3 2s remaining from up top)
100=5(20). Cross off a 5 (3 5s remaining from up top)
20=2(10). Cross off a 2 (2 2s remaining from up top)
10=2(5). Cross of a 2 and a 5. That leaves 2 5s and 1 2 remaining up top.
5*5=25*2=50.
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Re: (2^5*5^6)/10000=?  [#permalink]

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New post 15 Nov 2016, 10:05
Bunuel wrote:
(2^5*5^6)/10000=?

A. 0.2
B. 5
C. 25/2
D. 25
E. 50


\(\frac{(2^5*5^6)}{10000}\)

Or, \(\frac{(2^5*5^5*5)}{10^4}\)

Or, \(\frac{(10^5*5)}{10^4}\)

Or, \((10*5)\) = \(50\)

Hence, answer will be (E) \(50\)
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Re: (2^5*5^6)/10000=?  [#permalink]

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New post 16 Nov 2016, 08:11
Bunuel wrote:
(2^5*5^6)/10000=?

A. 0.2
B. 5
C. 25/2
D. 25
E. 50


We can start by breaking 10,000 into prime factors:

10,000 = 100 x 100 = 10 x 10 x 10 x 10 = 2^4 x 5^4

Plugging our prime factors back into the given expression, we have:

(2^5 x 5^6)/(2^4 x 5^4) = 2^1 x 5^2 = 2 x 25 = 50

Answer: E
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Re: (2^5*5^6)/10000=?  [#permalink]

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New post 22 Oct 2018, 19:16
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Re: (2^5*5^6)/10000=?   [#permalink] 22 Oct 2018, 19:16
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