What is the Sum of Digits in Decimal Notation of Number (10^20) - 16? GMAT Problem Solving

Question: What is the sum of digits in decimal notation of number \(10^{20}-16\)?

1. 156
2. 158
3. 174
4. 176
5. 456

“What is the sum of digits in decimal notation of number \(10^{20}-16\)?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer:

Approach Solution (1):

Sum of digits in \(10^{2}-16\) = 84 = 8 + 4 = 12
Sum of digits  \(10^{3}-16\)= 984 = 9 + 8 + 4 = 9 + 12
Sum of digits \(10^{4}-16\) = 9984 = 9 + 9 + 8 + 4 = 2 * 9 + 12
Sum of digits \(10^{5}-16\)= 99984 = 9 + 9 + 9 + 8 + 4 = 3 * 9 + 12
…
Sum of digits \(10^{20}-16\) = 99---984 = 9 + 9 + 9 + --- + 9 + 8 + 4 = 18 *9 + 12 = 162 + 12 = 174

Correct option: C

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