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 maths square root square root of perfect square finding square root of a number square root of a perfect square

The sum of the squares of $2$ numbers is $156$. If the one number is $5$, the square of the other number is

  1. $81$
  2. $131$
  3. $11$
  4. $123$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Let the two numbers be $x$ and $y$.
$x^{2}$ $+$ $y^{2}$ $\rightarrow$ $156$
${x}$ $\rightarrow$ 5
$x$ $\rightarrow$ $5\times5$ $\rightarrow$ $25$
Substituting, $25$ $+$ $y^{2}$ $\rightarrow$ $156$
 $y^{2}$ $\rightarrow$ $156-25$ $\rightarrow$ $131$
Multiple choice maths operations adding and subtracting numbers using place value addition & subtraction mental additions and subtractions

If the sum of two consecutive odd numbers is 2004, then the smaller of the two numbers could be

  1. 2001

  2. 1001

  3. 1003

  4. 1
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the two consecutive odd numbers are x and x+2
$x+x+2 = 2004$
$x+x+2-2 = 2004 -2 $ (Subtract 2 from both the sides)
$2x = 2002$
$\frac{2x}{2} = \frac{2002}{2}$ (Divide 2 from both the sides)
$x = 1001$
Hence two numbers are 1001 and 1003

Multiple choice maths operations adding and subtracting numbers using place value addition & subtraction mental additions and subtractions

Sum of $2.8, 26.3$ and $62.874$ is ______

  1. $91.974$
  2. $9.1974$
  3. $919.74$
  4. $9197.4$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To add Various numbers with different decimal points we pick the number with the largest decimal point and extend the others to the same decimal point.


In our question,

$2.800+26.300+62.874= 91.974$

So option A is the correct answer.

Multiple choice maths operations adding and subtracting numbers using place value addition & subtraction mental additions and subtractions

The sum of all even natural numbers between $1$ and $31$ is:

  1. $16$
  2. $128$
  3. $240$
  4. $512$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Required sum $=(2+4+6+......+30)$
This is an A.P in which $a=2,d=(4-2)=2$ and $l=30$.
Let the number of terms be $n$. Then,
${t} _{n}=30$ $\Rightarrow$ $a+(n-1)d=30$
$\Rightarrow$ $2+(n-1)\times 2=30$
$\Rightarrow$ $n-1=14$
$\Rightarrow$ $n=15$
$\therefore$ ${S} _{n}=\cfrac{n}{2}(a+l)=\cfrac{15}{2}\times (2+30)=240$

Multiple choice maths average arithmetic mean of ap introduction to averages means

The  Sum of three numbers in AP is $75$, and product of extremities is $609$. The numbrs and AM of 1st two numbers is 

  1. $\{21,25,29\}$, AM $= 23$
  2. $\{13,17,21\}$, AM $= 22$
  3. $\{21,25,29\}$, AM $= 25$
  4. $\{21,22,29\}$, AM $= 23$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the numbers in A.P.  be (a-d), a, (a+d)

$\therefore (a-d)+a+(a+d)=75$
$\Rightarrow a=25$
Also, $(a-d)(a+d)=609$
$\Rightarrow a^{2}-d^{2}=609$
$\Rightarrow 25^{2}-d^{2}=609$
$\therefore d=\pm4$
The numbers are {21,25,29} or {29,25,21}
According to option, we take {21,25,29}
A.M. of 1st two numbers $=\dfrac{21+25}{2}=23$

Multiple choice maths average arithmetic mean of ap introduction to averages means

Sum of $50$ A.M. between $20$ and $30$ is :

  1. $1255$
  2. $1205$
  3. $1250$
  4. $1225$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The sum of n arithmetic means inserted between two numbers a and b is equal to n times the average of a and b. Here, n = 50, a = 20, and b = 30, so the sum is 50 * (20 + 30) / 2 = 50 * 25 = 1250.

Multiple choice maths average arithmetic mean of ap introduction to averages means

The sum of four numbers in AP is $176$. The product of 1st and last is $1855$.  The mean of middle two is 

  1. $42$
  2. $41$
  3. $44$
  4. $53$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Let the numbers in A.P. be  (a-3d), (a-d), (a+d), (a+3d)
$\therefore (a-3d)+(a-d)+(a+d)+(a+3d)=176$
$\Rightarrow 4a=176$
$\therefore a=44$
$\therefore$ The mean of middle two is:
$=\dfrac{(a-d)+(a+d)}{2}$
$=a=44$                           
Multiple choice maths fraction lowest form of a fraction simplest ratio lowest form of fractions

The number $2.525252$ can be written as a fraction, when reduced to the lowest term, the sum of the numerator and denominator is:

  1. $7$
  2. $29$
  3. $141$
  4. $349$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Let the given number be $x=2.525252....$
multiplying with $100$ on both sides
$\Rightarrow 100x=252.525252...$
$\Rightarrow 100x=250+2.5252...$
$\Rightarrow 100x=250+x\Rightarrow 99x=250$
$\Rightarrow x=\dfrac{250}{99}$
$\therefore$ Sum of numerator and denominator $=25099=349$