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 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 $\dfrac{1}{4}$.

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 $\displaystyle\frac{11}{12}\times \frac{16}{4}\times \frac{9}{16}$ is 

  1. $\displaystyle 2\frac{1}{16}$
  2. $\displaystyle \frac{3}{4}$
  3. $\displaystyle \frac{2}{8}$
  4. $\displaystyle \frac{9}{6}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The product of $\dfrac{11}{12} \times \dfrac{16}{4} \times \dfrac{9}{16} $ is

$=\dfrac{11\times 16\times 9}{12\times 4\times 16}=\dfrac{33}{16}$ 
This can also be written as $\dfrac{32+1}{16}=2\dfrac{1}{16}$.
Hence, the answer is $2\dfrac{1}{16}$.

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 $\displaystyle \frac{7}{5}$

  1. $\displaystyle 1\frac{2}{5}$
  2. $\displaystyle \frac{5}{7}$
  3. $\displaystyle 5\frac{2}{3}$
  4. $\displaystyle \frac{12}{5}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
In the reciprocal, numerator and denominator interchanges
So, the reciprocal of $\dfrac{7}{5}$ is $\dfrac{5}{7}$.
Hence, the answer is $\dfrac{5}{7}$.
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

Find the product:

$\displaystyle 1\frac{1}{3}\times 3\frac{1}{4}\times \frac{7}{8}$

  1. $\displaystyle 3\frac{18}{24}$
  2. $\displaystyle 2\frac{19}{24}$
  3. $\displaystyle 3\frac{19}{24}$
  4. $\displaystyle 2\frac{18}{24}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let's first convert the mixed fraction into simple fraction $\dfrac{4}{3},$ $\dfrac{13}{4},$ $\dfrac{7}{8}$ .

The product is 
$\dfrac{4}{3} \times \dfrac{13}{4}\times \dfrac{7}{8}=\dfrac{91}{24}$
This can also be written as $3\dfrac{19}{24}$.

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

If $\displaystyle 40-\frac{1}{5}\times $ ____ $= 0$, then the missing value is 

  1. $0$
  2. $\displaystyle \frac{1}{5} $
  3. $\displaystyle \frac{199}{5} $
  4. $200$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Let missing value is $x$

$40$ $-\dfrac{1}{5}\times x=0$

$40$ $=\dfrac{1}{5}\times x$

$x=200$

Hence, the answer is $200$.