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 range and mean deviation statistics and probability maths coefficient of variance variance and standard deviation

Coefficient of range $5, 2, 3, 4, 6, 8, 10$ is?

  1. $\dfrac{2}{3}$
  2. $\dfrac{1}{3}$
  3. $\dfrac{3}{5}$
  4. $\dfrac{1}{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
${ x _{ m } }=10{ x _{ 0 } }=2$
coefficient of range 
$\begin{array}{l} =\frac { { { x _{ m } }-{ x _{ 0 } } } }{ { { x _{ m } }t{ x _{ 0 } } } }  \\ =\frac { { 10-2 } }{ { 10+2 } } =\frac { 8 }{ { 12 } } =\frac { 2 }{ 3 }  \end{array}$
Multiple choice maths fraction one fraction, many forms use of decimals in measure of length decimal fractions in the units of currency, length, weight, capacity

To convert $\displaystyle ^{\circ}C$ to $\displaystyle ^{\circ}F$ the formula used is

  1. $\displaystyle \left(C\times\frac{9}{5}\right)-32$
  2. $\displaystyle \left(C\times\frac{9}{5}\right)+32$
  3. $\displaystyle \left(C\times\frac{5}{9}\right)+32$

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

The conversion formula for celcius to farenheit is 

= $\left( C\times \dfrac { 9 }{ 5 }  \right) +32$
So, correct answer is option B.

Multiple choice telescopic summation for infinte series binomial theorem, sequence and series maths

If y= -1  then the value of 
$\displaystyle 1+\frac{1}{y}+\frac{1}{y^{2}}+\frac{1}{y^{3}}+\frac{1}{y^{4}}+\frac{1}{y^{5}}$ is

  1. -1

  2. 0

  3. 1

  4. 2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$1+\frac{1}{y}+\frac{1}{y^{2}}+\frac{1}{y^{3}}+\frac{1}{y^{4}}+\frac{1}{y^{5}}$

Put the value y=-1
Then $1+\frac{1}{-1}+\frac{1}{(-1)^{2}}+\frac{1}{(-1)^{3}}+\frac{1}{(-1)^{4}}+\frac{1}{(-1)^{5}}= 1-1+1-1+1-1= 3-3=0$

Multiple choice telescopic summation for infinte series binomial theorem, sequence and series maths

Let $a-i=i+\dfrac{1}{i}$ for $i=1, 2,..., 20$. Put $p=\dfrac{1}{20}(a _1+n _2+...+n _{20})$ and $q=\dfrac{1}{20}\left(\dfrac{1}{a _1}+\dfrac{1}{a _2}+...+\dfrac{1}{a _{20}}\right)$. Then?

  1. $q\in \left(0, \dfrac{22-p}{21}\right)$
  2. $q\in \left(\dfrac{22-p}{21}, \dfrac{2(22-p)}{21}\right)$
  3. $q\in \left(\dfrac{2(22-p)}{21}, \dfrac{22-p}{7}\right)$
  4. $q\in \left(\dfrac{22-p}{7}, \dfrac{4(22-p)}{21}\right)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

This is a mathematical problem involving averages of a sequence. Given the complexity and potential typos in the variable names (n vs a), this is likely a standard inequality problem related to the AM-HM inequality.

Multiple choice telescopic summation for infinte series binomial theorem, sequence and series maths

What is the value of $\frac {1}{1+\sqrt 2}+\frac {1}{\sqrt 2+\sqrt 3}+\frac {1}{\sqrt 3+\sqrt 4}.....$ upto 15 terms?

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

By rationalising each term,
$\frac {1}{1+\sqrt 2}=\frac {1}{\sqrt 2+1}\times \frac {\sqrt 2-1}{\sqrt 2-1}=\frac {\sqrt 2-1}{2-1}=\sqrt 2-1$
$\frac

{1}{\sqrt 2+\sqrt 3}=\frac {1}{\sqrt 3+\sqrt 2}\times \frac {\sqrt

3-\sqrt 2}{\sqrt 3-\sqrt 2}=\frac {\sqrt 3-\sqrt 2}{3-2}$
$=\sqrt 3-\sqrt 2$
............................
$\frac {1}{\sqrt {15}+4}=\frac {1}{4+\sqrt {15}}\times \frac {4-\sqrt {15}}{4-\sqrt {15}}=\frac {4-\sqrt {15}}{16-15}$
$=4-\sqrt {15}$
$\therefore$ Given expression
$=(\sqrt 2-1)+(\sqrt 3-\sqrt 2)+.....+4-\sqrt {15}$
$=4-1=3$.

Multiple choice telescopic summation for infinte series binomial theorem, sequence and series maths

The value of $ \displaystyle  \left ( 1-\dfrac{1}{3} \right )\left ( 1-\dfrac{1}{4} \right )\left ( 1-\dfrac{1}{5} \right )...\left ( 1-\dfrac{1}{n} \right )  $  is equal to

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

On simplification of first two term , we observed that
$\left(\frac{2}{3}\right)$ $\times \left(\frac{3}{4}\right)...$
So numerator is the multiplication from 2 to n-1 and denominator is the multiplication from 3 to n
So making it as factorial of first n and n-1 term we have to multiply 1 to numerator and 1 and 2 to denominator
$2\left(\frac{(n-1)!}{n!}\right)= \frac{2}{n}$

Multiple choice maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

Arrange the following fractions is ascending order :
$\dfrac{7}{10},\dfrac{3}{8},\dfrac{4}{5}$

  1. $\dfrac{3}{8},\dfrac{7}{10},\dfrac{4}{5}$
  2. $\dfrac{3}{8},\dfrac{4}{5},\dfrac{7}{10}$
  3. $\dfrac{4}{5},\dfrac{3}{8},\dfrac{7}{10}$
  4. $\dfrac{7}{10},\dfrac{3}{8},\dfrac{4}{5}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$7/10= 0.7$
$3/8 = 0.375$
$4/5=0.8$

So ascending order, = $\dfrac 3 8, \dfrac 7 {10}, \dfrac 4 5$
Multiple choice maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

Arrange the given fractions in ascending order:

$\displaystyle\frac{2}{7}$, $\displaystyle\frac{4}{5}$, $\displaystyle\frac{3}{4}$

  1. $\displaystyle\frac{4}{5}$, $\displaystyle\frac{3}{4}$, $\displaystyle\frac{2}{7}$
  2. $\displaystyle\frac{4}{5}$, $\displaystyle\frac{2}{7}$, $\displaystyle\frac{3}{4}$
  3. $\displaystyle\frac{2}{7}$, $\displaystyle\frac{3}{4}$, $\displaystyle\frac{4}{5}$
  4. $\displaystyle\frac{3}{4}$, $\displaystyle\frac{2}{7}$, $\displaystyle\frac{4}{5}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

First, we make all divisors common.
So l.c.m of $7,5,4 = 140$


Now $\dfrac{2}{7}\times \dfrac{20}{20} = \dfrac{40}{140}$

$\dfrac{4}{5}\times \dfrac{28}{28} = \dfrac{112}{140}$

$\dfrac{3}{4}\times \dfrac{35}{35} = \dfrac{102}{140}$

So the order will be $\displaystyle\frac{2}{7}$, $\displaystyle\frac{3}{4}$, $\displaystyle\frac{4}{5}$

Multiple choice maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

Which one of the following is correct?

  1. $\dfrac {-7}{10} < \dfrac {-2}{3} < \dfrac {-5}{8}$
  2. $\dfrac {-5}{8} < \dfrac {-2}{3} < \dfrac {-7}{10}$
  3. $\dfrac {-5}{8} < \dfrac {-7}{10} < \dfrac {-2}{3}$
  4. $\dfrac {-7}{10} < \dfrac {-5}{8} < \dfrac {-2}{3}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Convert fractions to decimals: -7/10 = -0.7, -2/3 = -0.666, -5/8 = -0.625. Since -0.7 < -0.666 < -0.625, the correct order is -7/10 < -2/3 < -5/8.

Multiple choice maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

Which of the following fractions are in order from the least to the greatest?

  1. $\dfrac {1}{2}, \dfrac {2}{3}, \dfrac {2}{6}$
  2. $\dfrac {1}{2}, \dfrac {2}{6}, \dfrac {2}{3}$
  3. $\dfrac {2}{6}, \dfrac {2}{3}, \dfrac {1}{2}$
  4. $\dfrac {2}{6}, \dfrac {1}{2}, \dfrac {2}{3}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

First convert the given fractions into like fractions.
L.C.M. of $2, 3, 6 = 6$
So,
$\dfrac {1}{2} = \dfrac {1\times 3}{2\times 3} = \dfrac {3}{6}; \dfrac {2}{3} = \dfrac {2\times 2}{3\times 2} = \dfrac {4}{6}; \dfrac {2}{6} = \dfrac {2\times 1}{6\times 1} = \dfrac {2}{6}$
So, ascending order is,
$\dfrac {2}{6}, \dfrac {3}{6}, \dfrac {4}{6}$ i.e. $\dfrac {2}{6}, \dfrac {1}{2}, \dfrac {2}{3}$.

Multiple choice maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

Among $\dfrac{5}{6},\dfrac{5}{7}$ and $\dfrac{5}{8}$, the greatest fraction is 

  1. $\dfrac{5}{6}$
  2. $\dfrac{5}{7}$
  3. $\dfrac{5}{8}$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Since all the fractions having same numarator so the greatest fraction will one with lowest denominator
 So the greatest fraction is $\dfrac{5}{6}$
Multiple choice maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

The value of $1+\dfrac{1}{4\times 3}+\dfrac{1}{4\times 3^2}+\dfrac{1}{4\times 3^3}+\dfrac{1}{4\times 3^4}$ is?

  1. $\dfrac{121}{108}$
  2. $\dfrac{3}{2}$
  3. $\dfrac{31}{2}$
  4. $\dfrac{91}{81}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$1+\dfrac{1}{4\times 3}+\dfrac{1}{4\times 3^2}+\dfrac{1}{4\times 3^3}+\dfrac{1}{4\times 3^4}$


$=1+\dfrac{1}{12}+\dfrac{1}{36}+\dfrac{1}{108}+\dfrac{1}{324}$


$=\dfrac{324+27+9+3+1}{324}$

$=\dfrac{364}{324}$

$=\dfrac{91}{81}$

Hence, the answer is $\dfrac{91}{81}.$

Multiple choice maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

Arrange the following in descending order.
$\dfrac{5}{2}$, $\dfrac{3}{2}$, $\dfrac{7}{2}$, $\dfrac{9}{5}$, $\dfrac{9}{8}$ 

  1. $\dfrac{7}{2}$, $\dfrac{9}{8}$, $\dfrac{3}{2}$, $\dfrac{9}{5}$, $\dfrac{5}{2}$
  2. $\dfrac{7}{2}$, $\dfrac{5}{2}$, $\dfrac{9}{5}$, $\dfrac{3}{2}$, $\dfrac{9}{8}$
  3. $\dfrac{5}{2}$, $\dfrac{9}{5}$, $\dfrac{3}{2}$, $\dfrac{9}{8}$, $\dfrac{7}{2}$
  4. $\dfrac{9}{8}$, $\dfrac{5}{2}$, $\dfrac{3}{2}$, $\dfrac{7}{2}$, $\dfrac{9}{5}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\cfrac{5}{2},\cfrac{3}{2},\cfrac{7}{2},\cfrac{9}{5},\cfrac{9}{8}$

We know that the number with largest denominator is the smallest one.
And among $\cfrac{5}{2},\cfrac{3}{2},\cfrac{7}{2}$ the one with largest numerator is the largest one.
Among $\cfrac{9}{5}$ and $\cfrac{3}{2},$ $\cfrac{9}{5}$ is larger.
Hence descending order is $\cfrac { 7 }{ 2 } ,\cfrac { 5 }{ 2 } ,\cfrac { 9 }{ 5 } ,\cfrac { 3 }{ 2 } ,\cfrac { 9 }{ 8 }.$

Multiple choice maths equivalence of fraction, decimal fraction, percentage and ratio converting a fraction or decimal to percentage conversion of fraction, decimal to percent fraction and percent

Find the fraction of $25$ paise to $Rs  2$.

  1. $\dfrac{9}{8}$
  2. $\dfrac{3}{8}$
  3. $\dfrac{5}{8}$
  4. $\dfrac{1}{8}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Rs.1 is equal to 100 paise 

Rs 2 is equal to 200 paise
fraction of 25 paise to Rs 2 $=\dfrac{25paise}{200paise}$
                                              $=\dfrac{1}{8}$