Quantitative Aptitude

Number System and Simplification

548 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 part number dividing fractions division of a fractions division of a fraction

What is the simplified value of $\displaystyle \frac{\frac{1}{3}\div \frac{1}{3}\times\frac{1}{3}}{\frac{1}{3}\div \frac{1}{3}of\frac{1}{3}}-\frac{1}{9}?$

  1. $0$
  2. $2$
  3. $\dfrac{1}{9}$
  4. $\dfrac{2}{9}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

(Using BODMAS)
$\displaystyle \frac{\frac{1}{3}\div \frac{1}{3}\times \frac{1}{3}}{\frac{1}{3}\div \frac{1}{3}of\frac{1}{3}}-\frac{1}{9}=\frac{\frac{1}{3}\times \frac{3}{1}\times \frac{1}{3}}{\frac{1}{3}\div \frac{1}{9}}-\frac{1}{9}$
$\displaystyle =\frac{1\times \frac{1}{3}}{\frac{1}{3}\times \frac{9}{1}}-\frac{1}{9}=\frac{1}{3\times 3}-\frac{1}{9}=\frac{1}{9}-\frac{1}{9}=0$

Multiple choice maths part number dividing fractions division of a fractions division of a fraction

If we multiply a fraction by itself and divide the product by its reciprocal the fraction thus 
obtained is $\displaystyle 18\frac{26}{27}$. The original fraction is 

  1. $\displaystyle \frac{8}{27}$
  2. $\displaystyle 2\frac{2}{3}$
  3. $\displaystyle 1\frac{1}{2}$

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

$Let\quad fraction\quad x\quad then\ x\times x\div \dfrac { 1 }{ x } =18\dfrac { 26 }{ 27 } =\dfrac { 512 }{ 27 }$


 $x\times x\times \dfrac { x }{ 1 } =\dfrac { 512 }{ 27 } \ we\quad get\quad x=\dfrac { 8 }{ 3 } =2\dfrac { 2 }{ 3 } $
So correct answer will be option B

Multiple choice maths part number dividing fractions division of a fractions division of a fraction

Find the value of $\displaystyle \frac{2}{1+\frac{1}{1-\frac{1}{2}}}\times\frac{3}{\frac{5}{6}of\frac{3}{2}\div 1\frac{1}{4}}$

  1. $2$
  2. $5$
  3. $6$
  4. $1$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\displaystyle \frac{2}{\displaystyle1+\frac{1}{\displaystyle1-\frac{1}{\displaystyle2}}}\times\frac{3}{\displaystyle\frac{5}{\displaystyle6}of\frac{3}{\displaystyle2}\div 1\frac{1}{\displaystyle4}}$
$=\displaystyle \frac{2}{\displaystyle1+\frac{1}{\displaystyle\frac{1}{\displaystyle2}}}\times\frac{3}{\displaystyle\frac{15}{\displaystyle12}\div \frac{5}{\displaystyle4}}$

$=\displaystyle\frac{2}{\displaystyle1+2}\times\frac{3}{\displaystyle\frac{15}{\displaystyle12}\times\frac{4}{\displaystyle5}}=\frac{2}{\displaystyle3}\times\frac{3}{\displaystyle1}=2$

Multiple choice maths part number dividing fractions division of a fractions division of a fraction

The value of $\displaystyle\frac{1}{\sqrt{3}+\sqrt{2}-1}$ on simplifying upto 3 decimal places, given that $\sqrt{2}=1.4142$ and $\sqrt{6}=2.4495$ is

  1. 0.166

  2. 0.366

  3. 0.466

  4. 0.566
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\frac { 1 }{ \sqrt { 3 } +\sqrt { 2 } -1 } $
$=\frac { \sqrt { 3 } -\left( \sqrt { 2 } -1 \right)  }{ \left( \sqrt { 3 } +\left( \sqrt { 2 } -1 \right)  \right) \left( \sqrt { 3 } -\left( \sqrt { 2 } -1 \right)  \right)  } Multiplying\sqrt { 3 } -\left( \sqrt { 2 } -1 \right) \quad with\quad numerator\quad and\quad denominator\quad $
$=\frac { \sqrt { 3 } -\left( \sqrt { 2 } -1 \right)  }{ 3-{ \left( \sqrt { 2 } -1 \right)  }^{ 2 } } $
 $=\frac { \sqrt { 3 } -\left( \sqrt { 2 } -1 \right)  }{ 3-{ \left( 2+1-2\sqrt { 2 }  \right)  } } $
 $=\frac { \sqrt { 3\quad  } -\sqrt { 2 } +1 }{ 2\sqrt { 2 }  } $
$=\frac { 1.732-1.4142+1 }{ 2.8284 } =0.466$
                                               $(\sqrt { 3 } =\frac { \sqrt { 6 }  }{ \sqrt { 2 }  } =\frac { 2.4495 }{ 1.4142 } =1.732)$

Multiple choice maths part number dividing fractions division of a fractions division of a fraction

If $\displaystyle 2805\div 2.55=1100$ then $\displaystyle 280.5\div 25.5=$ _______

  1. 1.1

  2. 1.01

  3. 0.11

  4. 11
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\displaystyle \frac{280.5}{25.5}=\frac{280.5}{25.5}\times \frac{10}{10}\times \frac{10}{10}$

$\displaystyle =\frac{2805}{2.55}\times \frac{1}{100}$

$\displaystyle =\frac{1100}{100}=11$

Multiple choice maths fractions dividing fractions division of a fractions division of a fraction

The fraction $\displaystyle \frac{9}{4}$ can be written as

  1. $\displaystyle \dfrac{\dfrac{9}{2}}{\dfrac{4}{2}}$
  2. $\displaystyle \dfrac{\dfrac{9}{4}}{1}$
  3. $\displaystyle \dfrac{\dfrac{9}{5}}{\dfrac{4}{5}}$
  4. $\displaystyle \dfrac{\dfrac{7}{6}}{\dfrac{9}{4}}$
Reveal answer Fill a bubble to check yourself
A,B,C Correct answer
Explanation
$ \dfrac{\dfrac{9}{2}}{\dfrac{4}{2}} = \dfrac{9}{2} \div \dfrac 42 =\dfrac 92 \times \dfrac 24  = \dfrac 94$

$ \dfrac{\dfrac{9}{4}}{1} = \dfrac{9}{4} \div 1 = \dfrac 92 \times 1 = \dfrac 94$

$ \dfrac{\dfrac{9}{5}}{\dfrac{4}{5}} = \dfrac{9}{5} \div \dfrac 45 =\dfrac 95 \times \dfrac 45  = \dfrac 94$

So, options $A, B$ and $C$ are correct.
Multiple choice maths part number dividing fractions division of a fractions division of a fraction

If we divide $1$ by a fraction $x$, we get ______ $x$.

  1. same fraction as

  2. reciprocal of

  3. double of

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

Every number has a reciprocal except 0 $(\dfrac{1}{0}$ is undefined$)$. The reciprocal is shown as $\dfrac{1}{x}$. 


When we multiply a number by its reciprocal we get $1$

$\Rightarrow$ If we divide $1$ by $x$, we get reciprocal of $x$.

Multiple choice maths part number dividing fractions division of a fractions division of a fraction

Divide the sum of $\displaystyle\frac{65}{12}$ and $\displaystyle\frac{12}{7}$ by their difference.

  1. $\displaystyle\frac{599}{311}$
  2. $\displaystyle\frac{680}{216}$
  3. $\displaystyle\frac{642}{133}$
  4. $\displaystyle\frac{501}{301}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

sum of $\dfrac{65}{12}$  and $\dfrac{12}{7} $


$ \dfrac{65}{12} +\dfrac {12}{7}= \dfrac{65\times 7 +12\times 12}{12\times 7} $

                  $=\dfrac{599}{84}$ ......................(1)

difference of  $\dfrac{65}{12}$  and $\dfrac{12}{7} $

$\dfrac{65}{12}-\dfrac{12}{7} = \dfrac{65\times 7 - 12\times 12}{84}= \dfrac{311}{84} $

                  $ =\dfrac{311}{84} $.........................(2)

divide the sum with difference i.e.

dividing equation (1) with equation (2)

$=\dfrac{\dfrac{599}{84}}{\dfrac{311}{84}}$

$=\dfrac{599}{311}$