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 parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

Reciprocal of $\displaystyle \frac{6}{3}$ is

  1. -$\displaystyle \frac{6}{3}$
  2. -$\displaystyle \frac{3}{6}$
  3. $\displaystyle \frac{3}{6}$
  4. $36$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The reciprocal of a number is $1$ divided by that number. For example, the reciprocal of $a$ is $\dfrac {1}{a}$


Now, we find the reciprocal of $\dfrac {6}{3}$ as follows:

$\dfrac { 1 }{ \dfrac { 6 }{ 3 }  } =\dfrac { 3 }{ 6 } \quad \quad \quad \quad \quad \quad \quad \left{ \because \quad \dfrac { 1 }{ \dfrac { 1 }{ x }  } =\dfrac { x }{ 1 }  \right}$ 

Hence, the reciprocal of $\dfrac {6}{3}$ is $\dfrac {3}{6}$

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

Reciprocal of $2 \displaystyle \frac{1}{3}$ is

  1. $\displaystyle \frac{7}{3}$
  2. $-\displaystyle \frac{7}{3}$
  3. $-\displaystyle \frac{3}{7}$
  4. $\displaystyle \frac{3}{7}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We first rewrite the given mixed fraction $2\dfrac { 1 }{ 3 }$ as $\dfrac {7}{3}$. 


We know that the reciprocal of a number is $1$ divided by that number. For example, the reciprocal of $a$ is $\dfrac {1}{a}$
 

Now, we find the reciprocal of $\dfrac {7}{3}$ as follows:

$\dfrac { 1 }{ \dfrac { 7 }{ 3 }  } =\dfrac { 3 }{ 7 } \quad \quad \quad \quad \quad \quad \quad \left\{ \because \quad \dfrac { 1 }{ \dfrac { 1 }{ x }  } =\dfrac { x }{ 1 }  \right\}$ 

Hence, the reciprocal of $2\dfrac { 1 }{ 3 }$ is $\dfrac {3}{7}$

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

Reciprocal of $3$ is________.

  1. $-3$
  2. $-\displaystyle \frac{1}{3}$
  3. $\displaystyle \frac{1}{3}$

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

The reciprocal of a number is $1$ divided by that number. For example, the reciprocal of $a$ is $\dfrac {1}{a}$


Hence, the reciprocal of $3$ is $\dfrac {1}{3}$

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

The reciprocal of $6-\sqrt{5}$ is equal to

  1. $\dfrac{3-\sqrt{5}}{8}$
  2. $\dfrac{6+\sqrt{5}}{31}$
  3. $\dfrac{6+2\sqrt{5}}{41}$
  4. $\dfrac{6-2\sqrt{5}}{56}$
  5. $\dfrac{6+2\sqrt{5}}{56}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The reciprocal of $6-\sqrt5$ is $\dfrac{1}{(6-\sqrt5)}$
Multiply and divide it by $6+\sqrt5$ , we get $\dfrac{6+\sqrt5}{(6+\sqrt5)(6-\sqrt5)} = \dfrac{6+\sqrt5}{31}$

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

Find the reciprocal of $\dfrac23 \div \dfrac{14}{15}$

  1. $\dfrac57$
  2. $\dfrac56$
  3. $\dfrac32$
  4. $\dfrac75$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\dfrac{2}{3} \div \dfrac{14}{15} = \dfrac{2\times15}{3\times14}$


                $= \dfrac{30}{42}$

                $= \dfrac{5\times6}{7\times6}$

                $= \dfrac{5}{7}$

Reciprocal of $\dfrac{5}{7}$ is $\dfrac{7}{5}$

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

The value of $(1024)^{-\dfrac {4}{5}}$ is ________.

  1. $\left (\dfrac {1}{4}\right )^{3}$
  2. $\left (\dfrac {1}{4}\right )^{2}$
  3. $\dfrac {1}{256}$
  4. $\dfrac {1}{512}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$1024=2\times2\times2\times2\times2\times2\times2\times2\times2\times2 = 2^{10}$


To find,
$(1024)^{-\dfrac{4}{5}} = 2^{-\dfrac{10\times4}{5}}$ 
                   $= 2^{-8}$

$2^{8}= 2\times2\times2\times2\times2\times2\times2\times2 = 256$

$\therefore (1024)^{-\dfrac{4}{5}} = \dfrac{1}{256}$

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

$\left( 1-\dfrac {1}{3} \right) \left( 1-\dfrac {1}{4} \right) \left( 1-\dfrac {1}{5} \right) ....\left( 1-\dfrac {1}{n} \right) $ equals

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

$\quad \left( 1-\cfrac { 1 }{ 3 }  \right) \left( 1-\cfrac { 1 }{ 4 }  \right) \left( 1-\cfrac { 1 }{ 5 }  \right) ...=\cfrac { 2 }{ 3 } .\cfrac { 3 }{ 4 } .\cfrac { 4 }{ 5 } ...\cfrac { n-1 }{ n } =\cfrac { 2 }{ n } $

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

The product of the reciprocals of $\dfrac {x + 3}{x + 2}$ and $\dfrac {x^{2} -4}{x^{2} - 9}$ is

  1. $\dfrac {1}{(x -3)(x - 2)}$
  2. $\dfrac {x - 2}{x - 3}$
  3. $\dfrac {x - 3}{x - 2}$
  4. $(x - 3)(x - 2)$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
The reciprocal of $\cfrac {x + 3}{x + 2}$ is $\cfrac {x + 2}{x + 3}$ 
And the reciprocal of $\cfrac {x^{2} -4}{x^{2} - 9}$ is $\cfrac {x^{2} -9}{x^{2} - 4}$
$\Rightarrow \cfrac {x^{2} -9}{x^{2} - 4} = \cfrac {(x-3)(x+3)}{(x-2)(x+2)}$
$\Rightarrow \cfrac {(x + 2)}{(x + 3)} \times \cfrac {(x - 3)}{(x - 2)}\times \cfrac {(x + 3)}{(x + 2)} = \cfrac {x - 3}{x - 2}$.
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

The value of $\large{\frac{1}{3}} \ of\ \large{4\frac{2}{3}}$ $\div$ $\large{2\frac{1}{3}} of\ \large{1\frac{1}{2}}$ is

  1. 1

  2. 2

  3. 3

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

$\large{\frac{1}{3}} \ of\ \large{4\frac{2}{3}}$ $\div$ $\large{2\frac{1}{3}} of\ \large{1\frac{1}{2}}$



$=\dfrac13\times4\dfrac23\div2\dfrac13\ of\ \dfrac12$


$=\dfrac{14}{9}\div\dfrac73\ of\ \dfrac32$


$=\dfrac{14}{9}\div\dfrac73\times\dfrac32$


$=\dfrac{14}{9}\div\dfrac72$


$=\dfrac{14}{9}\times\dfrac27$


$=\dfrac49$


$\text{option D (None of these) is correct}$

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

Product of $\displaystyle \frac{12}{24}$ and $\displaystyle \frac{36}{72}$ is:

  1. $\displaystyle \frac{16}{24}$
  2. $\displaystyle \frac{3}{5}$
  3. $4$
  4. $\displaystyle \frac{1}{4}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Product of the fraction is $\dfrac{12}{24}$ and $\dfrac{36}{72}$ is 

$\dfrac{12}{24} \times \dfrac{36}{72} = \dfrac{432}{1728} $ 
After simplifying, $\dfrac{432}{1728}$ can also be written as $\dfrac{1}{4}$.
Hence, the answer is $\dfrac{1}{4}$.