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 calculations and mental strategies 4 mental additions and subtractions of decimals multiplication and division of decimals mental multiplication and division

Which number is equal to
$\left ( \displaystyle \frac {0.1}{0.01}\, +\, \displaystyle \frac {0.01}{0.1} \right )\, ?$

  1. $10.1$
  2. $1.10$
  3. $1.01$
  4. $10.01$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let us first write the decimals as fractions as follows:


$0.1=\dfrac { 1 }{ 10 } \ 0.01=\dfrac { 1 }{ 100 }$ 

Now, the given expression $\dfrac { 0.1 }{ 0.01 } +\dfrac { 0.01 }{ 0.1 }$ can be solved as follows:
 
$\dfrac { 0.1 }{ 0.01 } +\dfrac { 0.01 }{ 0.1 } =\dfrac { \dfrac { 1 }{ 10 }  }{ \dfrac { 1 }{ 100 }  } +\dfrac { \dfrac { 1 }{ 100 }  }{ \dfrac { 1 }{ 10 }  } =\dfrac { \dfrac { 1 }{ 1 }  }{ \dfrac { 1 }{ 10 }  } +\dfrac { \dfrac { 1 }{ 10 }  }{ \dfrac { 1 }{ 1 }  } =10+\dfrac { 1 }{ 10 } =\dfrac { (10\times 10)+1 }{ 10 } =\dfrac { 100+1 }{ 10 } =\dfrac { 101 }{ 10 } =10.1$

Hence, $\dfrac { 0.1 }{ 0.01 } +\dfrac { 0.01 }{ 0.1 }=10.1$

Multiple choice maths calculations and mental strategies 4 mental additions and subtractions of decimals multiplication and division of decimals mental multiplication and division

Simplify : $\displaystyle \frac{0.2\times0.2+0.2\times0.02}{0.044}$

  1. $0.4$
  2. $0.2$
  3. $0.1$
  4. $1$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We will first convert the decimals into fraction in the given fraction and then solve it as follows:


$\dfrac { 0.2\times 0.2+0.2\times 0.02 }{ 0.044 } =\dfrac { \left( \dfrac { 2 }{ 10 } \times \dfrac { 2 }{ 10 }  \right) +\left( \dfrac { 2 }{ 10 } \times \dfrac { 2 }{ 100 }  \right)  }{ \dfrac { 44 }{ 1000 }  } =\dfrac { \dfrac { 4 }{ 100 } +\dfrac { 4 }{ 1000 }  }{ \dfrac { 44 }{ 1000 }  } =\dfrac { \dfrac { 40+4 }{ 1000 }  }{ \dfrac { 44 }{ 1000 }  } =\dfrac { \dfrac { 44 }{ 1000 }  }{ \dfrac { 44 }{ 1000 }  } =1$

Hence, $\dfrac { 0.2\times 0.2+0.2\times 0.02 }{ 0.044 } =1$

Multiple choice maths calculations and mental strategies 4 mental additions and subtractions of decimals multiplication and division of decimals mental multiplication and division

Evaluate the square root of $\displaystyle \frac{0.342\times 0.684}{0.000342\times 0.000171}$.

  1. $1000$
  2. $1500$
  3. $2000$
  4. $2500$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Consider the given fraction $\dfrac { 0.342\times 0.684 }{ 0.000342\times 0.000171 }$ and find the square root as follows:

 
$\sqrt { \dfrac { 0.342\times 0.684 }{ 0.000342\times 0.000171 }  } \ =\sqrt { \dfrac { 342\times 684 }{ 342\times 171 } \times \dfrac { 1000000\times 1000000 }{ 1000\times 1000 }  } \quad \quad \quad \quad \quad \quad \quad \left{ \because \quad 0.1=\dfrac { 1 }{ 10 }  \right} \ =\sqrt { 4\times 1000000 } \ =\sqrt { 4000000 } \ =\sqrt { { \left( 2000 \right)  }^{ 2 } } \ =2000$

Hence, the square root of $\dfrac { 0.342\times 0.684 }{ 0.000342\times 0.000171 }$ is $2000$.

Multiple choice maths calculations and mental strategies 4 mental additions and subtractions of decimals multiplication and division of decimals mental multiplication and division

The value of the following is $\displaystyle \frac{(0.44)^{2}+(0.06)^{2}+(0.024)^{2}}{(0.044)^{2}+(0.006)^{2}+(0.0024)^{2}}$

  1. $0.100$
  2. $0.01$
  3. $100$
  4. $1$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The expression is (0.44^2 + 0.06^2 + 0.024^2) / (0.044^2 + 0.006^2 + 0.0024^2). Since 0.44 = 10 * 0.044, 0.06 = 10 * 0.006, and 0.024 = 10 * 0.0024, the numerator is 10^2 times the denominator, which equals 100.

Multiple choice maths calculations and mental strategies 4 mental additions and subtractions of decimals multiplication and division of decimals mental multiplication and division

$\displaystyle \frac{(0.22)^{3}+(0.11)^{3}+(0.32)^{3}}{(0.66)^{3}+(0.96)^{3}+(0.33)^{3}}-\frac{(0.32)^{3}+(0.45)^{3}-(0.77)^{3}}{81(0.32)(0.45)(0.77)}$ equals

  1. 1
  2. $\displaystyle \frac{1}{11}$

  3. 0

  4. -1
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\frac{(0.22)^{3}+(0.11)^{3}+(0.32)^{3}}{(0.66)^{3}+(0.96)^{3}-(0.33)^{3}}+\frac{(0.32)^{3}+(0.45)^{3}-(0.77)^{3}}{81(0.32)(0.45)(0.77)}$
$=\frac { 8(0.11)^{ 3 }+(0.11)^{ 3 }+(0.32)^{ 3 } }{ 216(0.11)^{ 3 }+27(0.32)^{ 3 }+27(0.11)^{ 3 } } -\frac { (0.32)^{ 3 }+(0.45)^{ 3 }-(0.32+0.45)^{ 3 } }{ 81(0.32)(0.45)(0.77) } $
$=\frac { 9(0.11)^{ 3 }+(0.32)^{ 3 } }{ 243(0.11)^{ 3 }+27(0.32)^{ 3 } } -\frac { (0.32)^{ 3 }+(0.45)^{ 3 }-(0.32+0.45)^{ 3 } }{ 81(0.32)(0.45)(0.77) } $
$=\frac { 9(0.11)^{ 3 }+(0.32)^{ 3 } }{ 27{ 9(0.11)^{ 3 }+(0.32)^{ 3 }}  } -\frac { (0.32)^{ 3 }+(0.45)^{ 3 }-[(0.32)^{ 3 }+(0.45)^{ 3 }+3(0.32)(0.45)(0.32)+(0.45) }{ { 81(0.32)(0.45)(0.77) } } $
$=\frac{1}{27}-\frac{1}{27}$
$=0$

Multiple choice maths mixture types of ratios ratios in proportion mathematical logic

The difference between the numerator and the denominator of a fraction is $5$ If $5$ is added to the denominator the fraction is decreased by $\displaystyle 1\frac{1}{4}$ then the value of the fraction will be equal to:

  1. $\displaystyle \frac{1}{6}$
  2. $\displaystyle 2\frac{1}{4}$
  3. $\displaystyle 3\frac{1}{4}$
  4. $6$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the numerator be $x+5$ and denominator be $x$


Given condition is :$\dfrac {x+5}{x}-\dfrac {x+5}{x+5}=\dfrac {5}{4}$

$\Rightarrow \dfrac {x+5}{x}=\dfrac {9}{4}=2\dfrac {1}{4}=$fraction value 

$\therefore $fraction value$ =2\dfrac {1}{4}$

Multiple choice maths mixture types of ratios ratios in proportion mathematical logic

If a, b, c, d are positive real number such that $\frac {a}{3}=\frac {a+b}{4}=\frac {a+b+c}{5}=\frac {a+b+c+d}{6}$, then $\frac {a}{b+2c+3d}$ is

  1. $\frac {1}{2}$

  2. 1

  3. 2

  4. not determinable
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$a =3k$
$b=k$
$c= 5k-4k =k$
$d =6k-5k =k$
$\frac {a}{b+2c+3d}=\frac {3k}{k+2k+3k}=\frac {1}{2}$

Multiple choice maths calculating and mental strategies 3 finding percentage of a number how many in all? problems on percentage

By evaluating $\dfrac{2.8^3\times 1.2^2}{0.56+3.78}$, closest estimate answer is:

  1. $7$
  2. $70$
  3. $0.7$

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

We need to evaluate $\dfrac{2.8^3 \times 1.2^2}{0.56+3.78}$

$\Rightarrow$  $\dfrac{3^3 \times 1.44}{4.34}$    $[\because\,\, 2.8\approx 3]$
$\Rightarrow$  $\dfrac{27\times 1}{4}$     $[\because\,\, 1.44\approx 1\,\text{and}\,\,4.34\approx 4]$
$\Rightarrow$  $6.75\approx 7.$
Therefore, $\dfrac{2.8^3\times 1.2^2}{0.56+3.78}=7$

Multiple choice maths percent and percentage use of percentages converting between fractions or decimals and percentages percentage of a quantity

If $x\%$ of $24=64$, then the value of x is __________.

  1. $\displaystyle 37\frac{1}{2}$
  2. $\displaystyle 133\frac{1}{3}$
  3. $\displaystyle 266\frac{2}{3}$
  4. $\displaystyle 66\frac{2}{3}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$24\times\dfrac{x}{100}=64$

$x=\dfrac{64\times 100}{24}$$=266.667$$=266\dfrac{1}{3}$
Hence the correct answer is option C.

Multiple choice maths percent and percentage use of percentages converting between fractions or decimals and percentages percentage of a quantity

If $33\displaystyle\frac{1}{3}\%$ of $A=1.5$ of $B=\displaystyle\frac{1}{8}$ of $C$, then $A\colon\,B\colon\,C$ is

  1. $\;24\colon2\colon9$
  2. $\;2\colon9\colon24$
  3. $\;9\colon2\colon24$
  4. $\;9\colon24\colon2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\;\displaystyle\frac{100}{3\times100}\times\,A=\displaystyle\frac{3}{2}\times\,B=\displaystyle\frac{1}{8}\times\,C=x\,(say)$
$\;\;\;\;\;\Rightarrow\;A=3x,\,B=\displaystyle\frac{2}{3}x,\,C=8x$
$\;\;\;\;\;\;\Rightarrow\;A\colon\,B\colon\,C=3\colon\displaystyle\frac{2}{3}\colon8=9\colon2\colon24$.

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

Evaluate: $\dfrac{(3\dfrac{2}{3})^{2} -(2\dfrac{1}{2})^{2}}{(4\dfrac{3}{2})^{2} -(3\dfrac{1}{3})^{2}}$ $\div$ $\dfrac{3\dfrac{2}{3} -2\dfrac{1}{2}}{4\dfrac{3}{2} -3\dfrac{1}{3}}$

  1. $\dfrac{35}{53}$
  2. $\dfrac{37}{53}$
  3. $\dfrac{42}{59}$
  4. $\dfrac{47}{60}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\dfrac{(3\frac{2}{3})^2-(2\frac{1}{2})^2}{(4\frac{3}{2})^2-(3\frac{1}{3})^2} \div \dfrac{3\frac{2}{3}-2\frac{1}{2}}{4\frac{3}{2}-3\frac{1}{3}}$


$=\dfrac{(3\frac{2}{3}+2\frac{1}{2})(3\frac{2}{3}-2\frac{1}{2})}{(4\frac{3}{2}+3\frac{1}{3})(4\frac{3}{2}-3\frac{1}{3})} \div \dfrac{3\frac{2}{3}-2\frac{1}{2}}{4\frac{3}{2}-3\frac{1}{3}}$

$=\dfrac{3\frac{2}{3}+2\frac{1}{2}}{4\frac{3}{2}+3\frac{1}{3}}$

$=\dfrac{\dfrac{11}{3}+\dfrac{5}{2}}{\dfrac{11}{2}+\dfrac{10}{3}}$

$=\dfrac{\dfrac{22+15}{6}}{\dfrac{33+20}{6}}$

$=\dfrac{37}{53}$

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

Divide the difference of $\dfrac{1}{5}$ and $\dfrac{2}{7}$ by $\dfrac{2}{7}$.

  1. $\dfrac{1}{10}$
  2. $\dfrac{21}{10}$
  3. $\dfrac{3}{10}$
  4. $\dfrac{4}{10}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Difference of  $\dfrac{1}{5}$  and $\dfrac{2}{7}$ is  


$\dfrac{2}{7} - \dfrac{1}{5} = \dfrac{2\times5 - 1\times7}{35} =\dfrac{10 - 7}{35} =\dfrac{3}{35}$

Now divide $\dfrac{3}{35}$  by $\dfrac{2}{7}$  

we have, $\dfrac{3}{35}÷\dfrac{2}{7} =\dfrac{3}{35}\times \dfrac{7}{2} =\dfrac{3}{10}$

Ans: $\dfrac{3}{10}$

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

Find the value of $ \cfrac{2}{3}\times \cfrac{3}{\tfrac{5}{6}\div \tfrac{2}{3} \, \text {of} \, \,1\tfrac{1}{4}}$

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

Given expression

$ \cfrac{2}{3}\times \cfrac{3}{\tfrac{5}{6}\div \tfrac{2}{3} \, \text {of} \, \,1\tfrac{1}{4}}$

$=\displaystyle \frac{2}{3}\times\dfrac{3}{\tfrac{5}{6}\div \left ( \tfrac{2}{3}\times\tfrac{5}{4} \right )}$


$\displaystyle=\frac{2}{3}\times\dfrac{3}{\tfrac{5}{6}\div \tfrac{5}{6}}=\frac{2}{3}\times\frac{3}{1}=2$