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If x is a positive integer and 10^x – 74 in decimal

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by VJesus12 » Sat Feb 10, 2018 2:00 am
If x is a positive integer and 10^x - 74 in decimal notation has digits whose sum is 440, what is the value of x?

A. 40
B. 44
C. 45
D. 46
E. 50

The OA is the option E.

I don't know how to solve this PS question. Experts, can you give me some help? Thanks in advanced. <i class="em em-confused"></i>
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by regor60 » Sat Feb 10, 2018 8:52 am
VJesus12 wrote:If x is a positive integer and 10^x - 74 in decimal notation has digits whose sum is 440, what is the value of x?

A. 40
B. 44
C. 45
D. 46
E. 50

The OA is the option E.

I don't know how to solve this PS question. Experts, can you give me some help? Thanks in advanced. <i class="em em-confused"></i>
Look for a pattern.

10^2 - 74 = 26> digits sum to 8
10^3-74 = 926>digits sum to 17
10^4-74=9926>digits sum to 26

A pattern of increasing by 9 starting with 8.

Subtract 8 from 440 = 432. This represents a certain number of 9s starting from the beginning.

432/9= 48. So 48 steps from the 10^2-74 beginning.

Since the beginning exponent of 10 was 2, 48 steps from there is 50, E
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