Mathematics · Quantitative Aptitude

Number Sums and Series

268 Questions

Number sums and series questions test the ability to find patterns and calculate the sum of number sequences. These problems are a staple in the quantitative aptitude sections of various competitive exams. Practice this collection to improve speed and accuracy in solving arithmetic and geometric series problems.

Sum of consecutive integersGeometric series sumsRatio and proportion sumsOdd and even number propertiesRoman numeral calculations

Number Sums and Series Questions

Multiple choice

The sum of four numbers in G.P is 60 and the A.M of the 1st and the last is 18. The numbers are

  1. 4, 8, 16, 32

  2. 4, 16, 8, 32

  3. 16, 8, 4, 20

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the GP be a, ar, ar^2, ar^3. Given a(1+r+r^2+r^3) = 60 and (a+ar^3)/2 = 18, so a+ar^3 = 36. Dividing the sum equation by this gives (1+r+r^2+r^3)/(1+r^3) = 5/3. This leads to 2r^3 - 3r^2 - 3r + 2 = 0, which has r = 2 as a solution. With r = 2, a(1+8) = 36 gives a = 4. The numbers are 4, 8, 16, 32.

Multiple choice

The sum of all odd numbers between 200 and 300 is

  1. 11600

  2. 12490

  3. 12500

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The odd numbers between 200 and 300 are 201, 203, 205, ..., 299. This is an arithmetic progression with first term 201, last term 299, and 50 terms. Sum = n/2 × (first + last) = 50/2 × (201 + 299) = 25 × 500 = 12500.

Multiple choice

You can solve sums with the help of

  1. number keys

  2. calculator

  3. keyboard

  4. mouse
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A calculator is a tool specifically designed to perform mathematical calculations efficiently.

Multiple choice

The sum of mn + 5 - 2 and mn+3 is

  1. 2mn + 6

  2. mn + 6

  3. mn - 6

  4. 2mn - 6

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Two equations upon simplification are mn+3 and mn+3 so there addition will be 2mn + 6)

Multiple choice

The sum of first five multiples of 3 is:

  1. 45

  2. 65

  3. 75

  4. 90
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

3: (a) 45[Soln: Sn = [2a + (n - 1)d]× n/2⇒ S5 = [2×3 + (5 - 1)3)]× 5/2⇒ S5 = [6 + 12] × 5/2 = 18 × 5/2 = 9 × 5 = 45

Multiple choice

A, B and C are three consecutive even numbers (not necessarily in same order). What is the sum of these numbers?i)One-fourth of number is 24ii) The difference between B and C is 4.

  1. Statement 1 ALONE is sufficient, but statement 2 alone is not sufficient to answer the question asked

  2. Statement 2 ALONE is sufficient, but statement 1 alone is not sufficient to answer the question asked.

  3. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient

  4. EACH statement ALONE is sufficient to answer the question asked.

  5. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Combining the statement I and ii,
 A=96 and the value of C can be 96-2 or 96+2.
 Hence we can find the sum of A ,B and C by using both the statements together.

Multiple choice

Express 172 as a sum of two consecutive integers.

  1. Sum of 8 and 9

  2. Sum of 144 and 145

  3. Sum of 200 and 89

  4. Sum of 100 and 189

  5. It is not possible to write 172 as a sum of 2 consecutive integers.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Yes, it is correct. 172  =  (172 - 1) / 2 + (172 + 1) / 2

Multiple choice

The product of two consecutive odd positive integers is 483. The integers are

  1. 21 and 23

  2. 27 and 29

  3. 17 and 19

  4. 31 and 33
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the two consecutive odd positive integers be x and x + 2. x(x + 2) = 483 $\Rightarrow$ x2 + 2x - 483 = 0 x2 + 23 x - 21 x  - 483 = 0 $\Rightarrow$ x (x + 23) - 21 (x + 23) = 0 (x + 23) (x - 21) = 0 x = -23 , x - 21 => x = 21. Since integers are positive, -23 can't be the answer. So, the two integers are 21 and 23.