Mathematics · Quantitative Aptitude

Number Operations and Properties

896 Questions

Improve your quantitative aptitude with these number operations and properties questions. The topics range from basic subtraction and division to highest common factor and roman numerals. Regular practice of these fundamentals builds speed for exams.

Basic arithmetic operationsHCF and number propertiesRoman numeral calculationsNumber series evaluation

Number Operations and Properties Questions

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

A number is multiplied by half of itself and then $32$ is added to the product, if the final result is $130$, then find the original number.

  1. $4$
  2. $7$
  3. $5$
  4. $14$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the number be $x$

According to given question, we have
$x\times  \dfrac{x}{2} +32=130$

$\Rightarrow \dfrac{x^2}{2}=98$
$\Rightarrow x^2=196$
$\Rightarrow x=14$

Therefore, the number is $14$.

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 difference of two numbers is $72$ and the quotient obtained by dividing one by the other is $3$. Find the numbers.

  1. $36$ $and$ $108$
  2. $16$ $and$ $88$
  3. $63$ $and$ $135$
  4. $\text{none}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$Let\>the\>numbers\>be\>x\>and\>y,\>then\>x-y=72\\and\>(\frac{x}{y})=3\\or\>x\>=\>3y\\\therefore\>3y-y=72\\2y=72\\\therefore\>y=36,\>then\>x\>=\>108$

Multiple choice maths length, mass and capacity problems on measurement choosing and converting between units conversion between different units

Convert the following into tons :
$670$ quintal

  1. $6700$ tons
  2. $670$ tons
  3. $67$ tons
  4. $6.7$ tons
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

We know that


$1$  $ton =10$  $quintal$

$1$  $quintal =\dfrac1{10}$  $ton$

Given That, we have to convert $670$  $quintal$  to   $tons$

$670$  $quintals =\dfrac{1}{10} \times 670$  $tons$

                    $ =\dfrac{670}{10} $  $tons$

                   $=67$  $tons$

So, option $C$ is correct

Multiple choice maths ratio, proportion and unitary method more on proportion terms related to proportion proportion

Mark the correct alternative of the following.
If $343$ is the third proportional of $a$ and $b,$ where $a : b=1 : 7$, then the values of $a+b$ is?

  1. $14$
  2. $24$
  3. $56$
  4. $63$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$a : b = b : 343$


$\dfrac{a}{b} = \dfrac{b}{343}$


$\dfrac{1}{7} = \dfrac{b}{343}$

$b = \dfrac{343}{7}$

$b = 49$

$\dfrac{a}{b} = \dfrac{1}{7}$

$\dfrac{a}{49} = \dfrac{1}{7}$

$a = \dfrac{49}{7} = 7$

$a + b = 49 + 7 = 56$

Multiple choice maths ratio, proportion and unitary method more on proportion terms related to proportion proportion

If the first three terms of a proportion are $3,5$ and $21$ respectively, then its fourth term is

  1. $21$
  2. $35$
  3. $15$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given, the first three terms of a proportion are $3,5$ and $21$ respectively.

Let the fourth number be $'x'$,

So, Numbers proportion are $3, 5, 21, x$

According to proportionality,

Product of means $=$ Product of extremes

$3 : 5 :: 21 : x$

$\dfrac{3}{5} = \dfrac{21}{x}$

Cross multiply,

$3 \times x = 21 \times 5$

$3x = 105$

$x = 35$

Therefore, The required fourth number is $35$

Multiple choice maths ratio, proportion and unitary method more on proportion terms related to proportion proportion

Find the fourth proportional in $5, \sqrt{75}, \sqrt{48}$

  1. $15$
  2. $45$
  3. $12$
  4. $121$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In $ a:b::c:d;   d $ is the fourth proportional.

In, $ 5: \sqrt {75} :: \sqrt {48} :d $, product of extremes $ = $ product of means

$  5 \times d = \sqrt {75} \times  \sqrt {48} $
$ d = \dfrac{\sqrt {75} \times  \sqrt {48}}{5} = \dfrac{5\sqrt {3} \times 4\sqrt {3}}{5} = 4 \times 3 = 12 $

Multiple choice maths ratio, proportion and unitary method more on proportion terms related to proportion proportion

 The third proportion between $12$ and $192$

  1. $48$
  2. $18$
  3. $68$
  4. $58$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If a : b :: b : c, then we say that a, b, c are in continued

proportion, and c is the third proportional of a and b.





Here, $ {b}^{2} = ac $ or $ b = \sqrt {ac} $





So, for $ 12, 192 $, the third proportional is $ b = \sqrt {12 \times 192} = \sqrt {4

\times 3 \times 64 \times 3} = 2 \times 3 \times 8 = 48 $