GMAT Practice Question: If m is an integer and m=10^{32}-32, what is the sum of the digits of m ?
Question
If m is an integer and m=10^{32}-32, what is the sum of the digits of m ?
- 257
- 264
- 275
- 284
- 292
Topics: exponents, sums of digits
Solution
Step 1
We subtract 32 from ten raised to the thirty-second power, which causes a chain of borrowings. The result has thirty nines, then a 6 and an 8.
m = 10^{32} - 32 = 99999...9968
Step 2
We then sum these digits by adding thirty 9s, 6, and 8.
\text{sum of digits} = 30\times9 + 6 + 8 = 270 + 14 = 284
Answer
284
