Question: If \(10^{50} - 74\) is written as an integer in base 10 notation, what is the sum of the digits in that integer?

1. 424
2. 433
3. 440
4. 449
5. 467

Answer:
Solution with Explanation:
Approach Solution (1):

Based 10 notations, or decimal notation, is just a way of writing a number using 10 digits: 1, 2, 3, 4, 5, 6, 7, 8, and 0 (usual way), in contrast, for example, to binary numeral system (base-2 number system) notation.

\(10^{50}\) has 51 digits: 1 followed by 50 zeroes;

\(10^{50} - 74\) has 50 digits: 48 9’s and 26 in the end;
So, the sum of the digit of \(10^{50} - 74\) equals to 48 * 9 + 2 + 6 = 440

Correct Option: C

Approach Solution (2):

\(10^3-74\)= 1,000 – 74 = 926 (1 nine)
\(10^4-74\)= 10,000 – 74 =9926 (2 nines)
\(10^5-74\)= 100,000 – 74 = 99926 (3 nines)
\(10^6-74\)= 1,000,000 = 999926 (4 nines)
.
.
.
In general, we can see that \(10^n-74\) will feature n – 2 9’s followed by 26
So, \(10^{50}-74\) will feature 48 9’s followed by 26

This means the sum of the digits = 48 (9) + 2 + 6 = 432 + 2 + 6 = 440

Correct Option: C

Approach Solution (3):

\(10^x-74\)--- last 2 digits are always 2, 6
\(10^2-74\)= 26
\(10^3-74\)= 926
\(10^4-74\)= 9926 and so on…
If x > 1,

The sum of the digits --- (x – 2) * 9 + 2 + 6
Hence, (50 – 2) * 9 + 8 = 440

Correct Option: C

“If\(10^{50}-74\)is written as an integer in base 10 notation, what is the sum of the digits in that integer?”- 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.

Suggested GMAT Problem Solving Samples

• How many Terminating Zeroes does 200! Have? GMAT Problem Solving
• 1511−151014=? GMAT Problem Solving
• If g is an integer what is the value of(−1)g4−1(−1)g4−1? 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 P2−QR=10P2−QR=10 ,Q2+PR=10Q2+PR=10 ,R2+PQ=10R2+PQ=10 GMAT Problem Solving
• If 298=256L+N298=256L+N , Where L and N are Integers and 0≤N≤40≤N≤4 , What is the Value of N? GMAT Problem Solving
• How Many 5-Letter Words can be Formed Using the Letters of the English Alphabet that Contain 2 Different Vowels 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
• 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 Full of Water. GMAT Problem Solving
• How Many Multiples of 7 are there Between 21 and 343, Exclusive? 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
• What is the Remainder when 333^222 is Divided by 7? GMAT Problem Solving
• In a College of 300 Students, Every Student Reads 5 Newspapers and every Newspaper is Read by 60 Students 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 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 √(x2+6x+9)(x2+6x+9) - √(y2−2y+1)(y2−2y+1)? GMAT Problem Solving
• A Cube Of Side 7 cm Is Coloured On Pair of Opposite Faces By Red, Green and Yellow Shades GMAT Problem Solving
• Given f(x) = x/(x + 1), For What Value k Does f(f(k)) = 2/3 ? GMAT Problem Solving
• Which of the Following Expressions CANNOT have a Negative Value? GMAT Problem Solving
• The Figure Shown Above Consists of a Shaded 9-Sided Polygon GMAT Problem Solving
• A list of measurements in increasing order is 4, 5, 6, 8, 10 and x GMAT Problem Solving
• Rahul Can Finish a Job in 30 Days GMAT Problem Solving
• The Price of Raw Materials Has Gone up by 15% GMAT Problem Solving
• In a Class of 100 Students 70 Passed in Physics, 62 Passed in Mathematics, GMAT Problem Solving
• If x and y Are Positive Odd Integers, And Both Numbers Have An Odd Number Of Positive Divisors GMAT Problem Solving
• Copper Pipe Costs x Cents Per Foot in 8-Foot Lengths GMAT Problem Solving
• Find The Smallest Positive 4-Digit Number Which, When Increased by 8, is Divisible by 12, 18, 30, and 45 GMAT Problem Solving
• How Much Pure Alcohol Should Be Added To 400 ml of a 15% Solution To Make The Strength Of The Solution 32%? GMAT Problem Solving
• If n = 3, What is The Value of 2^2n+1? GMAT Problem Solving
• The First Five Numbers in a Regular Sequence are 4, 10, 22, 46, and 94 GMAT Problem Solving
• The Volume of a Sphere With Radius r is (4/3)*pi*r^3 and the Surface Area is 4*pi*r^2 GMAT Problem Solving
• Which of the Following is Equal to 5^17×4^9? GMAT Problem Solving
• In a Shooting Competition, Probability of A Hitting Target is 2/5, by B is 2/3 and C is 3/5 GMAT Problem Solving
• The Sides of a Quadrilateral Taken in Order are 16,16,14 and 10 GMAT Problem Solving
• If 80 Lamps Can Be Lighted, 5 Hours Per Day For 10 Days GMAT Problem Solving
• If denotes the area of a circle with diameter d, then which of the following is equal to <4>*<6> GMAT Problem Solving
• If @ x=x^2/2x^2-2 , What is the Units Digit of @ (@4)? GMAT Problem Solving 
• What is the product of all possible solutions of the equation |x+2|- 5|x+2| = -6? GMAT Problem Solving 
• Metropolis Corporation has 4 Shareholders GMAT Problem Solving 
• What is the number of integers from 1 to 1000, inclusive that are not divisible by 11 or by 35? GMAT Problem Solving 
• If m is Three Times n, and if 2n + 3 is 20% of 25, What is the value of m? GMAT Problem Solving 
• If Ben Were to Lose the Championship, Mike would be the Winner GMAT Problem Solving 
• A Train Travelling at a Certain Constant Speed takes 30 seconds GMAT Problem Solving 
• A circle with a radius R is inscribed into a square with a side K GMAT Problem Solving 
• The square of \(5^\sqrt2)\ =? GMAT Problem Solving 
• A farm has chickens, cows and sheep GMAT Problem Solving