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 negative numbers and integers even and odd numbers sum of numbers odd and even numbers

Given that the sum of the odd integers from $1$ to $99$ inclusive is $2500$, what is the sum of the even integers from $2$ to $100$ inclusive?

  1. 2450

  2. 2550

  3. 2460

  4. 22500
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Odd integers $=1,3,5,7,9.....$

Sum of odd integers $=2500$
Even integers $=2,4,6,8,,10......$
In the series of even integers each term is one more than the each term of odd integers.
Hence, there are $50$ terms.
So, the sum of even integers $=$ $2500+50=2550$

Multiple choice maths negative numbers and integers even and odd numbers sum of numbers odd and even numbers

Find three consecutive odd integers such that the sum of first and third integers is same as the second integer when decreased by $9$.

  1. $-9,-7,-5$
  2. $-13,-11,-9$
  3. $-15,-13,-11$
  4. $-11,-9,-7$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let us say the first odd integer be $x$. The second consecutive odd integer would be $x+2$ (zit would not be $x+1$ because that would result in an even integer. The sum of two odd integers is even). The third consecutive odd integer would be $(x+2)+2$ or $x+4$.


Now, it is given that the sum of first and third integers is same as the second integer when decreased by $9$ which means:

$x+(x+4)=(x+2)-9\ \Rightarrow 2x+4=x-7\ \Rightarrow 2x-x=-7-4\ \Rightarrow x=-11$

Therefore, the first odd integer is $-11$ then the second integer is $x+2=-11+2=-9$ and the third integer is $x+4=-11+4=-7$

Hence, the three consecutive odd integers are $-11,-9,-7$.

Multiple choice maths negative numbers and integers even and odd numbers sum of numbers odd and even numbers

Find three consecutive even integers such that the sum of first two integers is same as the sum of third integer and $6$.

  1. $4,6,8$
  2. $6,8,10$
  3. $8,10,12$
  4. $10,12,14$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let us say the first even integer be $x$. The second consecutive even integer would be $x+2$ (zit would not be $x+1$ because that would result in an odd integer. The sum of two even integers is even). The third consecutive even integer would be $(x+2)+2$ or $x+4$.


Now, it is given that the sum of first two integers is same as the sum of the third integer and $6$ which means:

$x+(x+2)=(x+4)+6\ \Rightarrow 2x+2=x+10\ \Rightarrow 2x-x=10-2\ \Rightarrow x=8$

Therefore, the first even integer is $8$ then the second integer is $x+2=8+2=10$ and the third integer is $x+4=8+4=12$

Hence, the three consecutive even integers are $8,10,12$.

Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

The two consecutive multiples of $3$ whose sum is $51$ are __________.

  1. $24, 27$
  2. $20, 31$
  3. $40, 11$
  4. $25, 26$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Lets say $x$ is the multiple of $3$

Next consecutive multiple of $3$ will be $(x+3)$
Given sum is $=51$
$\Rightarrow x+x+3=51$
$\Rightarrow  2x=48$
$\Rightarrow x=24$
Two consecutive multiples of $3$ are $24,27$.

Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

If the sum of four consecutive even integers is $212$, what is the value of the second even integer?

  1. $50$
  2. $51$
  3. $52$
  4. $53$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the four consecutive even numbers be $x, x + 2, x + 4$ and $x + 6$.

Therefore, $x + x + 2 + x + 4 + x + 6 = 212$
$4x + 12 = 212$
$4x = 212 - 12$
$4x = 200$ (Divide both sides by $4$)
$x = 50$
The second number be $x + 2$
So, the second number is $52$.

Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

If the sum of four consecutive odd integers is $400$, what is the value of the first odd integer?

  1. $95$
  2. $96$
  3. $97$
  4. $98$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the four consecutive odd numbers be $x, x + 2, x + 4$ and $x + 6$.
Therefore, $x + x + 2 + x + 4 + x + 6 = 400$
$4x + 12 = 400$
$4x = 400 - 12$
$4x = 388$  (Divide both sides by $4$)
$x = 97$
The first number be $x$ 
So, the first number is $97$.

Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

If the sum of four consecutive integers is $110$, what is the value of the third consecutive integer?

  1. $26$
  2. $27$
  3. $28$
  4. $29$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the four consecutive numbers be $x, x + 1, x + 2$ and $x + 3$.
Therefore, $x + x + 1 + x + 2 + x + 3 = 110$
$4x + 6 = 110$
$4x = 110 - 6$
$4x = 104$   (Divide both sides by $4$)
$x = 26$
The third number be $x + 2$ 
So, the third number is $28$.

Multiple choice maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

The sum of two numbers is $45$ and their difference is $11$. What are the two numbers?

  1. $28$ and $17$
  2. $27$ and $18$
  3. $25$ and $20$
  4. $22$ and $23$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the numbers be $a$ and $b$
Given that 

$a+b=45$ ....(1)
$a-b=11$ ....(2)
Adding these two equations, we get
$2a=56$
$\Rightarrow a=28$
Substituting value of $a$ in equation (1), we get
$28+b=45$
$\Rightarrow b=45-28$
$\Rightarrow b=17$
We get $a = 28$ and $b=17$

Multiple choice maths arithmetic sequences forming an arithmetic progression between two quantities a and b sums arithmetic progression

$\sum{n^3}=$

  1. $(\sum{n})^3$
  2. $(\sum{n})^2$
  3. $(\sum{n})^3+(\sum{n})^2$
  4. $\sum{(n+n^2)}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
We have, $ \sum { { n }^{ 3 } } = { 1 }^{ 3 }+{ 2 }^{ 3 }+....+{ n }^{ 3 } $
The formula to find the sum of cubes of natural numbers is $ ={( \dfrac {n(n+1)}{2} )}^2 $

But sum of first $ n $ natural numbers is$  \sum { { n } } = \dfrac {n(n+1)}{2} $ 

So, $ \sum { { n }^{ 3 } } = { (\sum { { n } })}^2 $
Multiple choice maths vedic mathematics square roots using vedic maths square and square roots using vedic mathematics history of mathematics

When multiplied by itself, which number is equal to $12,345, 678, 987, 654, 321$?

  1. $1,111,111$
  2. $111,111,111$
  3. $11,111,111,111$
  4. $111,111,111,111$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
$(1)^2=1$
$(11)^2=121$
$(111)^2=12321$
$(111, 111, 111)^2=12345678987654321$
Here we can show a pattern for each count of $1$ in $LHS$ is extended the number from $1$ to that Number and reverse that number to the $1$ in $RHS$
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.