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 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 calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

If $50$ is subtracted from two-third of a number, the result is equal to sum of $40$ and one-fourth of that number. What is the number? 

  1. $174$
  2. $216$
  3. $246$
  4. $336$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the number be N. According to the problem, (2/3)N - 50 = 40 + (1/4)N. Rearranging terms gives (2/3)N - (1/4)N = 90. Finding a common denominator results in (5/12)N = 90, which means N = 90 * 12 / 5 = 216.

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

The sum of all natural members which multiples of $7$ or $3$ or both and lie between $200$ and $500$ is

  1. $45049$
  2. $40149$
  3. $45149$
  4. $45249$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To find the sum of natural numbers between 200 and 500 that are multiples of 7, 3, or both, we use the principle of inclusion-exclusion. Calculate the sum of multiples of 3 plus the sum of multiples of 7, minus the sum of their least common multiple multiples (21), within the specified range, yielding 45149.

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 $D$

Multiple choice

The sum of first 45 natural numbers is

  1. 1035

  2. 1280

  3. 2070

  4. 2140
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The sum of the first n natural numbers is given by n(n+1)/2. For n=45, the sum is 45 * 46 / 2 = 45 * 23 = 1035.