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

Suggested GMAT Problem Solving Questions

• If g is an integer what is the value of (-1)^g^4-1? GMAT Problem Solving
• What is the area of the triangle with the following vertices L(1,3) M(5,1) and N(3,5)? GMAT Problem Solving
• If,P^2-QR=10,Q^+PR=10,R^2+PQ=10 and R≠QR≠Q, what is the value of P^2+Q^2+R^2? GMAT Problem Solving
• If y (u-c) = 0 and j (u-k) = 0, which of the following must be true, assuming c < kc < k? GMAT Problem Solving
• If 2^98= 256L+N, where L and N are integers and 0≤N≤4, what is the value of N? GMAT Problem Solving
• If m, p, and t are distinct positive prime numbers, then (m^3)(p)(t) has how many different positive factors greater than 1? GMAT Problem Solving
• How many 5-letter words can be formed using the letters of the English alphabet that contain 2 different vowels and 3 different consonants? GMAT Problem Solving
• If a+b+c = 0 and a^3+b^3+c^3 = 216, what is the value of a∗b∗c ? GMAT Problem Solving
• If a polygon has 44 diagonals, then how many sides are there in the polygon? GMAT Problem Solving
• If (a1 + a2 + a3 + .... +an) = 3(2n+1 - 2), for every n≥1, then a11 equals GMAT Problem Solving
• A chord of a circle is equal to its radius GMAT Problem Solving
• If 4 people are selected from a group of 6 married couples, what is the probability that none of them would be married to each other? GMAT Problem Solving
• If the equation |x|+|y|= 5 encloses a certain region on the graph, what is the area of that region? GMAT Problem Solving
• If x = ¾ and y = ⅖ , what is the value of (x^2+ 6x+ 9) - (y^2-2y+ 1)? GMAT Problem Solving
• (15^11 - 15^10)/14 =? GMAT Problem Solving
• A clock loses a minute every three hours for 4 days and gains 1% in the subsequent 6 days GMAT Problem Solving
• A Container in the Shape of a Right Circular Cylinder is 1/2 GMAT Problem Solving
• How many multiples of 7 are there between 21 and 343, exclusive? GMAT Problem Solving
• How many odd factors does 210 have? GMAT Problem Solving
• How many three-digit integers are not divisible by 3? GMAT Problem Solving