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 maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

The sum of the squares of three numbers which are in the ratio $2 : 3 : 4$ is $725.$ What are these numbers?

  1. $10, 15, 20$
  2. $14, 21, 28$
  3. $20, 15, 30$
  4. $20, 30, 40$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the three numbers be 2x, 3x and 4x.
Given, $(2x)^2 + (3x)^2 + (4x)^2 = 725$
$\Rightarrow 4x^2 + 9x^2 + 16 x^2 = 725 \Rightarrow 29 x^2 = 725$
$\Rightarrow x^2 = 25 \Rightarrow x = 5$
$\therefore$ The numbers are 10, 15 and 20.

Multiple choice maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

The whole number whose sum is $72$ cannot be in the ratio

  1. $\dfrac{5}{7}$
  2. $\dfrac{3}{5}$
  3. $\dfrac{3}{4}$
  4. $\dfrac{4}{5}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The whole number must   be divided by sum of two ratio particularly

A.$5+7=12$
$72$ can be divided by $12$

B.$ 3+5=8$
$72$ can be divided by $8$

C.$ 4+3=7$
$72$ can not be divided by $7$

D.$4+5=9$
$72$ can be divided by $9$

Multiple choice maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

Two number are in the ratio 8 : 3. If the sum of numbers is 143, Find the numbers.

  1. $14,39$
  2. $104,40$
  3. $10,39$
  4. $104,39$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the two numbers be $8x$ and $3x$ respectively

Given that the sum of the numbers is $143$


$\Rightarrow 8x+3x = 143$
$\Rightarrow 11x = 143$
$\Rightarrow x= \dfrac{143}{11}=13 $

We have $x = 13$ then, $8x=8(13)=104, 3x=3(13)=39$

Thus the numbers are $104,39$

Multiple choice maths fundamental concept of ratio and proportion division problem dividing a quantity in a given ratio problems on ratios

The product of two positive integers is $936$. Find the greater number, if the integers are in the ratio $13\,\colon\,18.$ 

  1. $27$
  2. $31$
  3. $36$
  4. $41$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the two positive integers be $13x$ and $18x.$
Their product is $936.$

$\therefore 13x\times 18x=936$

$\Rightarrow x^{2}=\dfrac{936}{13\times 18}=4$

$\Rightarrow x=2$
Then two positive integers are $26$ and $36.$
$\therefore$ The greater number is $36.$

Multiple choice maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

What would be the reciprocal of the sum of the reciprocal of the numbers $\displaystyle \frac{3}{5}$ and $\displaystyle \frac{7}{3}$?

  1. $\displaystyle \frac{1}{42}$
  2. $\displaystyle \frac{21}{44}$
  3. $\displaystyle \frac{4}{5}$
  4. $\displaystyle \frac{36}{55}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Sum of the reciprocals of $\displaystyle \dfrac{3}{5}$ and $\dfrac{7}{3}$
$\displaystyle =\frac{5}{3}+\frac{3}{7}=\frac{35+9}{21}=\frac{44}{21}$
$\displaystyle \therefore $ Required number $\displaystyle =\frac{21}{44} $

Multiple choice maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

A triangular number which is the sum of the square of two consecutive odd numbers is?

  1. $10$
  2. $15$
  3. $21$
  4. $28$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Let the two consecutive odd numbers be $n-2,n$
$(n-2)^2+n\\ n^2+4-4n+n^2\\2n^2+4-4n$
If we put $n=1\\ 2(1)-4+4=2\\n=2\\ 2(4)+4-4=4\\n=3\\2(9)+4-4(3)\\=18+4-12\\=10$
$\therefore $ Triangular no. is $10$
For any other value of $n$ the triangular no. is not in the required options
$\therefore$ we take $n=3$ and triangular no. is $10$
Multiple choice maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

Repeated addition of same number is called _________.

  1. Addition

  2. Subtraction

  3. Multiplication

  4. Division
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Repeated addition is also known as multiplication. If the same number is repeated then in short we can write that in the form of multiplication.
For example : $3+3+3+3+3$

Here $3$ is repeated $5$ times so in short we can write this addition as $3\times 5$ 

Multiple choice maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

The sum of all two digit numbers which when divided by $4$, yield unity as reminder is

  1. $1012$
  2. $1201$
  3. $1212$
  4. $1210$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Sum of all $2$ digit number divided by $4$ yields unity as remainder

$=13+17+21+97$
Series is in $AP$ and total are
$=a+(n-1)d=97$
4413+(n-1)4=97$
$(n-1)4=84$
$n-1=21$
$n=22$ terms
Sum $=\cfrac{n}{2}(2a+(n-1)d)\=\cfrac{22}{2}(26+(21\times4)\=11(26+84)\=11(110)\=1210$
Answer $D$