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 5-digit numbers expanded form introduction to numbers and number systems numbers in general form

What is the sum of $289$ and $410$ in number name form(i.e. in words)? 

  1. Six hundred and ninety two

  2. Six hundred and eighty five

  3. Six hundred and ninety nine

  4. Six hundred and fifty four
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
$\Rightarrow$  The given two numbers are $289$ and $410.$
$\therefore$  $289+410=699$
 Hundreds  Tens  Units
$ 6$  $9$ $ 9$

$\therefore$  In word $699$ can be written as "Six hundred and ninety nine."

Multiple choice maths decimal numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

Sum of $1.8, 16.3$ and $72.985$ is _____ 

  1. $91.85$
  2. $9108.5$
  3. $91.085$
  4. $9.1085$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For obtaining the sum of decimal numbers with different decimal values we expand the decimal values of all the numbers with respect to the number with the highest decimal value. 


Because the number with the largest decimal places is $72.985$ with $3$ decimal places, we expand all numbers up to $3$ decimal places.

$1.800+16.300+72.985=91.085$

So option C is the correct answer.

Multiple choice maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

Express $49$ as the sum of $7$ odd numbers.
Express $121$ as the sum of $11$ odd numbers.

  1. $1+3+5+7+9+11$
    $1+3+5+7+9+11+13+15+19$
  2. $1+3+5+7+9+11+13$
    $1+3+5+7+9+11+13+15+19+21$
  3. $1+3+5+7+9+11$
    $1+3+5+7+9+11+13+15+19+21$
  4. $1+3+5+7+9+11+13$
    $1+3+5+7+9+11+13+15+19$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$49=7^2=$ sum of first $7$ odd numbers.
So, $49=1+3+5+7+9+11+13$.
Similarly, $121=11^2=$ sum of first $11$ odd numbers. 
So, $121=1+3+5+7+9+11+13+15+19+21$

Multiple choice maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

Find the sum of:
$1+3+5+7+9+11+13+15+17+19+21+23$

  1. $11^2$
  2. $12^2$
  3. $10^2$
  4. $13^2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
$S _{n}=\dfrac{n}{2}\left [ 2a+(n-1)d \right ]$
$a =$ First term
$d =$ Common difference
$n =$ number of terms

Given series is an A.P.
with first term $=$ $1$
common difference $=$ $2$
and last term $=$ $23$

Sum $=$ $\dfrac{12}{2}$ $\times$ $(2+11\cdot 2)$ $=$ $12\times12$
Hence, Option B is correct.

Multiple choice maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

What is the series and also find the total of first $100$ consecutive odd numbers?

  1. $1 + 2 + 4 + 6 + 8 + 10 +... 100 = 12000$
  2. $2 + 3 + 4 + 7 + 9 + 11 +...100 = 10000$
  3. $1 + 3 + 5 + 7 + 10 + 11 +....100 = 1000$
  4. $1 + 3 + 5 + 7 + 9 + 11 +...100 = 10000$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Sum of first $100$ consecutive odd numbers $= 1 + 3 + 5 + 7 + 9 + 11 + ....+100 = 10000$
Since, we know the formula for sum of consecutive odd numbers $= n^2$
So, $n = 100$, Sum $= 100^2 = 10000$

Multiple choice maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

Find the sum of two consecutive number for $13^2$.

  1. $84$ and $85$
  2. $83$ and $84$
  3. $86$ and $82$
  4. $81$ and $80$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the two consecutive numbers be, $\dfrac{n^{2} - 1}{2}$ and $\dfrac{n^{2} + 1}{2}$
$13^2= 169$
n = 13
$\dfrac{n^{2} - 1}{2} = \dfrac{13^{2} - 1}{2} = 84$
$\dfrac{n^{2} + 1}{2} = \dfrac{13^{2} + 1}{2} = 85$
So, the sum of two consecutive numbers = 84 + 85 = 169.

Multiple choice maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

Find the sum of two consecutive numbers for $15^2$.

  1. 112 and 113

  2. 113 and 114

  3. 115 and 112

  4. 113 and 115
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the two consecutive numbers be, $\dfrac{n^{2} - 1}{2}$ and $\dfrac{n^{2} + 1}{2}$
$15^2= 225$
n = 15
$\dfrac{n^{2} - 1}{2} = \dfrac{15^{2} - 1}{2} = 112$
$\dfrac{n^{2} + 1}{2} = \dfrac{15^{2} + 1}{2} = 113$
So, the sum of two consecutive numbers = 112 + 113 = 225.