Quantitative Aptitude

Number System and Simplification

585 Questions

Number system and simplification questions assess mathematical proficiency in handling fractions, decimals, and complex algebraic expressions. Test takers must simplify surds, calculate reciprocals, and solve intricate number pattern equations. This foundational quantitative aptitude topic is critical for achieving high scores in SSC and banking exams.

Fraction simplificationDecimal operationsSurds and indicesPercentage calculationsComplex number algebra

Number System and Simplification Questions

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

$\displaystyle (0.34\overline{67}+0.13\overline{33})$ is equal to 

  1. $\displaystyle 0.\overline{48}$

  2. 0.4803
  3. $\displaystyle 0.48\overline{01}$
  4. $\displaystyle 0.4\overline{8}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\displaystyle 0.34\overline{67}+0.13\overline{33}=\frac{3467-34}{9900}+\frac{1333-13}{9900}$


= $\displaystyle \frac{3433}{9900}+\frac{1320}{9900}=\frac{4753}{9900}$

= $\displaystyle \frac{4801-48}{9900}=0.4801 $

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

The value of $\displaystyle 0.\overline{2}+0.\overline{3}+0.\overline{4}+0.\overline{9}+0.\overline{39}$ is 

  1. $\displaystyle 0.\overline{57}$
  2. $\displaystyle 1\frac{20}{33}$
  3. $\displaystyle 2\frac{1}{3}$
  4. $\displaystyle 2\frac{13}{33}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\displaystyle 0.\overline{2}+0.\overline{3}+0.\overline{4}+0.\overline{9}+0.\overline{39}$


= $\displaystyle \frac{2}{9}+\frac{3}{9}+\frac{4}{9}+\frac{9}{9}+\frac{39}{99}$

= $\displaystyle \frac{22+33+44+99+39}{99}$

= $\displaystyle \frac{237}{99}=2\frac{13}{33}$

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

Simplify $\displaystyle :0.\overline{4}+0.\overline{61}+0.\overline{11}-0.\overline{36}$

  1. $\displaystyle 0.\overline{83}$
  2. $\displaystyle 0.\overline{87}$
  3. $\displaystyle 0.\overline{80}$
  4. $\displaystyle 0.\overline{85}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\displaystyle :0.\overline{4}+0.\overline{61}+0.\overline{11}-0.\overline{36}=\frac{4}{9}+\frac{61}{99}+\frac{11}{99}-\frac{36}{99}=\frac{4}{9}+\frac{72}{99}-\frac{36}{99}$


$\displaystyle=\frac{4}{9}+\frac{36}{99}=\frac{44}{99}+\frac{36}{99}=\frac{80}{99}=0.\overline{80}$

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

The value of $\displaystyle \frac{0.25\times0.25-0.24\times0.24}{0.49}=?$

  1. $0.0006$
  2. $0.49$
  3. $0.01$
  4. $0.1$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given, $\displaystyle \frac {0.25\times0.25-0.24\times0.24}{0.49}$

Using the identity $a^2 - b^2 = (a+b)(a-b)$
$\therefore \displaystyle 0.25\times 0.25 - 0.24\times 0.24 = (0.25+0.24)(0.252-0.24) = (0.49)(0.01)$

Thus, $\displaystyle \frac {0.25\times0.25-0.24\times0.24}{0.49} = \frac {0.49\times 0.01}{0.49}$ = $0.01$

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

$\displaystyle \frac{42.31-26.43}{42.31+26.43}\div \frac{423.1-264.3}{4.231+2.643}$  is equal to 

  1. $\displaystyle 10^{-2}$
  2. $\displaystyle 10^{-1}$

  3. 10
  4. $\displaystyle 10^{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\displaystyle \frac{42.31-26.43}{42.31+26.43}\div \frac{423.1-264.3}{4.231+2.643}$

$=\displaystyle \frac{15.88}{68.74}\div \frac{158.8}{6.874}$
$=\displaystyle \frac{15.88}{68.74}\times \frac{6.874}{158.8}=\frac{1588}{6874}\times \frac{68.74}{1588}$
= $\displaystyle \frac{68.74}{6874}=\frac{6874}{687400}=\frac{1}{100}=0.01$

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

Which pair of operations will make the equation below true when inserted into the blank spaces in the order shown? $\displaystyle 2\frac{3}{10} $      $1.5$  _  $2=1.8$

  1. $-$ and $+$
  2. $\displaystyle \times $ and $+$
  3. $+$ and $-$
  4. $\displaystyle \times $and $-$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let us first write the mixed fraction $2\dfrac {3}{10}$ in decimals as follows:


$2\dfrac { 3 }{ 10 } =\dfrac { (2\times 10)+3 }{ 10 } =\dfrac { 20+3 }{ 10 } =\dfrac { 23 }{ 10 } =2.3$

Therefore, $2\dfrac {3}{10}=2.3$

Now, add $1.5$ to $2.3$ then we get,

$2.3+1.5=3.8$

Now subtract $2$ from $3.8$ as follows:

$3.8-2=1.8$

Therefore, we have $2.3+1.5-2=1.8$

Hence, $2\dfrac { 3 }{ 10 } +1.5-2=1.8$

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

The simplification of $\displaystyle3\overline{36}-2.\overline{05}+1\overline{33}$ is equal to

  1. 2.6

  2. 2.64
  3. $\displaystyle 2.\overline{61}$
  4. $\displaystyle 2.\overline{64}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\displaystyle 3.\overline{36}-2.\overline{05}+1.\overline{33}$


= $\displaystyle 3+0.\overline{36}-\left ( 2+0.\overline{05} \right )+1+0.\overline{33}$

= $\displaystyle 3+\frac{36}{99}-2-\frac{5}{99}+1+\frac{33}{99}$


= $\displaystyle 2+\frac{64}{99}=2+0.\overline{64}=2.\overline{64}$