Mathematics · Quantitative Aptitude

Number Sums and Series

287 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

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.

Multiple choice maths numbers and place value forming numbers formation of greatest and smallest numbers identifying the largest and smallest numbers with given digits

Find the sum of smallest three digit even number and greatest three-digit odd number using the digits $6, 2, 3$

  1. $859$
  2. $958$
  3. $598$
  4. $985$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
The three digit numbers that can be formed using the digits $6,2,3$ are $623,632,263,236,362,326$ in which the odd numbers are $623,263$ and the even numbers are $632,236,362,326$.

The smallest even number is $236$ and the greatest odd number is $623$ and their sum can be determined as:

$236+623=859$

Hence, the sum of smallest three digit even number and greatest three-digit odd number using the digits $6,2,3$ is $859$.
Multiple choice maths tenths and hundredths more money decimal fractions in the units of currency, length, weight, capacity understanding tenth and hundredth part of a number

A certain sum consists of $x$ pounds $y$ shillings, and it is half of $y$ pounds $x$ shillings; find the sum.

  1. Pounds $6$. $13s$.
  2. Pounds $6$. $25s$.
  3. Pounds $7$. $13s$.
  4. Pounds $7$. $25s$.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the sum be 20x + y = 1/2 * (20y + x). Solving this: 40x + 2y = 20y + x, which simplifies to 39x = 18y, or 13x = 6y. For integer values, x=6 and y=13. The sum is 6 pounds and 13 shillings.

Multiple choice maths numbers and place value face value of digit large numbers general form of number

What is the sum of all integers between $50$ and $350$ which have $1$ as the units digit?

  1. $5880$
  2. $5985$
  3. $6230$
  4. $6800$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The sequence $51+61+71...+341$ is an arithmetic progression.

$\Rightarrow$  To find the sum of n terms of an AP we use the formula.
$\Rightarrow$  Here, $n=30,\,a=51$ and $d=10$.
$\therefore$   $S _n=\dfrac{n}{2}[2a+(n-1)d]$

$\therefore$   $S _n=\dfrac{30}{2}[2\times 51+(30-1)10]$

$\therefore$   $S _n=15[102+290]$
$\therefore$   $S _n=15\times 392$
$\therefore$   $S _n=5880$