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What is the sum of all digits of 2^13*5^7?

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Math Revolution GMAT Instructor
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What is the sum of all digits of 2^13*5^7?  [#permalink]

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New post 03 Aug 2017, 01:31
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A
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E

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  15% (low)

Question Stats:

88% (01:29) correct 12% (02:04) wrong based on 71 sessions

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What is the sum of all digits of \(2^{13}5^7\)?

A. 3
B. 4
C. 6
D. 8
E. 10

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Re: What is the sum of all digits of 2^13*5^7?  [#permalink]

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New post 03 Aug 2017, 01:34
2
5^7 and 2^7 will multiply to become 10^7 .
After that we are left with 2^6 which will be 64 multiplied by 10^7. So sum of digits is 10

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Re: What is the sum of all digits of 2^13*5^7?  [#permalink]

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New post 03 Aug 2017, 04:55
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1
MathRevolution wrote:
What is the sum of all digits of \(2^{13}5^7\)?

A. 3
B. 4
C. 6
D. 8
E. 10


\(2^{13}5^7\)

\(2^6*2^7*5^7\)

\(2^6(2^7*5^7)\)

\(2^6(10^7)\)

\(64(10^7)\)

\(64\) and \(7\) zeros \(= 640000000\)

Sum of all digits \(= 6 + 4 + 0 = 10\)

Answer (E)...


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Re: What is the sum of all digits of 2^13*5^7?  [#permalink]

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New post 06 Aug 2017, 18:17
==> You get \(2^{13}5^7=2^6(2^75^7)=64(10^7)=640,000,000.\) The sum of the 0's at the back always becomes 0, so you get \(6+4=10.\)

The answer is E.
Answer: E
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Re: What is the sum of all digits of 2^13*5^7?  [#permalink]

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New post 09 Aug 2017, 12:53
MathRevolution wrote:
What is the sum of all digits of \(2^{13}5^7\)?

A. 3
B. 4
C. 6
D. 8
E. 10


We can rewrite the given expression as:

2^6 x 2^7 x 5^7

2^6 x 10^7

64 x 10^7
Thus, 2^13 x 5^7 is the number 64 followed by 7 zeros and the sum of the digits is 6 + 4 = 10.

Answer: E
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Re: What is the sum of all digits of 2^13*5^7?   [#permalink] 09 Aug 2017, 12:53
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