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What is the sum of the digits of integer x, where x = 4^10 x

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What is the sum of the digits of integer x, where x = 4^10 x [#permalink] New post 05 Nov 2017, 01:34
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71% (02:02) correct 28% (00:31) wrong based on 7 sessions
What is the sum of the digits of integer x, where \(x = 4^{10} * 5^{13}\)?

(A) 13

(B) 11

(C) 10

(D) 8

(E) 5


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[Reveal] Spoiler: OA
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Re: What is the sum of the digits of integer x, where x = 4^10 x [#permalink] New post 05 Nov 2017, 06:23
We can rearrange the expression for x as \(2^7*(2*5)^{13}\) so that \((2*5)^{13}\) is equal to 1 followed by 13 zeros so that when it is multiplied by any number is equal to that number followed by 13 zeros. Then, \(2^7 = 128\) so that multiplied by the power of 10 becomes 128 and 13 zeros. Since we have to sum the digit of this number, we get 1+2+8+13*0 = 11.

Answer B
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Re: What is the sum of the digits of integer x, where x = 4^10 x [#permalink] New post 09 Jan 2018, 10:17
Expert's post
Bunuel wrote:
What is the sum of the digits of integer x, where \(x = 4^{10} * 5^{13}\)?

(A) 13

(B) 11

(C) 10

(D) 8

(E) 5


We can simplify the given equation:

x = 4^10 x 5^13

x = 2^20 x 5^13

x = 2^7 x 2^13 x 5^13

x = 2^7 x 10^13

x = 128 x 10^13

We see that x is the number 128 followed by 13 zeros. Thus, the sum of the digits of x is 1 + 2 + 8 = 11.

Answer: B
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Re: What is the sum of the digits of integer x, where x = 4^10 x   [#permalink] 09 Jan 2018, 10:17
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