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 cube and cube root estimation of cube root estimation of cube roots cubes and cube roots

If $\displaystyle \sqrt[3]{3\left ( \sqrt[3]{x}-\frac{1}{\sqrt[3]{x}} \right )}=2$ then $\displaystyle \sqrt[3]{x}+\frac{1}{\sqrt[3]{x}}=$_________

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

  2. 0

  3. 1

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

$\displaystyle \sqrt[3]{3\left ( \sqrt[3]{x}-\frac{1}{\sqrt[3]{x}} \right )}=2$ 
Let us assume $\left( \sqrt [ 3 ]{ x } -\frac { 1 }{ \sqrt [ 3 ]{ x }  }  \right) $=a
So, $\sqrt [ 3 ]{ 3a } =2$
Taking  cube both sides,
$3a=8$
$a=\frac { 8 }{ 3 } $
So, $\left( \sqrt [ 3 ]{ x } -\frac { 1 }{ \sqrt [ 3 ]{ x }  }  \right) =\frac { 8 }{ 3 } $

Multiple choice conversion of time time conversion time measurement of time maths

$21$ months are equal to how many years?

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

$1$ year $=12$ months 

$1$ month $=\dfrac{1}{12}$ years
$21$ months $=\dfrac{1}{12}\times21=\dfrac{7}{4}=1\dfrac{3}{4}$
So option $C$ is correct.

Multiple choice converting decimals to fractions and vice-versa decimal to fraction addition, subtraction and multiplication of fractions decimal fractions maths

$\displaystyle \frac{0.25}{0.4}$ is equal to

  1. $\displaystyle \frac{5}{8}$
  2. $\displaystyle \frac{25}{40}$
  3. $\displaystyle \frac{16}{19}$

  4. None of the above
Reveal answer Fill a bubble to check yourself
A,B Correct answer
Explanation
$\dfrac {0.25}{0.4}$ = $\dfrac{\dfrac {25}{100}}{ \dfrac {4}{10}}$

$= \displaystyle \frac{25\times 10}{4 \times 100} = \frac{25}{40}$

So. options A and B are correct.
Multiple choice converting decimals to fractions and vice-versa decimal to fraction addition, subtraction and multiplication of fractions decimal fractions maths

$\dfrac {p}{q}$ form of $0.0875$ is _______

  1. $\dfrac {7}{2^{4}\times 5}$
  2. $\dfrac {7}{2\times 5^{4}}$
  3. $\dfrac {7}{2^{4}\times 5^{4}}$
  4. $\dfrac {5^{3}\times 7}{2^{3}\times 5^{4}}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Since, $0.0875=\displaystyle \frac {875}{10000}=\frac {175}{2000}=\frac{35}{400} =\frac {7}{80}=\frac 7{16\times 5}=\frac 7{2^4\times 5}$

Option $A$ is correct.

Multiple choice maths multiply and divide division trick division division of numbers

 $\displaystyle \frac{3x}{2}-\frac{x}{4}=2$. Find value of x

  1. $2$
  2. $\dfrac85$
  3. $4$
  4. $\dfrac45$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
$\cfrac { 3x }{ 2 } -\cfrac { x }{ 4 } =2$
$\cfrac { 6x-x }{ 4 } =2$
$\cfrac { 5x }{ 4 } =2$
$x=\cfrac { 4 }{ 5 } \times 2=\cfrac { 8 }{ 5 } $
Multiple choice maths multiply and divide division trick division division of numbers

$\frac {171\tfrac {3}{4}\times 171\tfrac {3}{4}-91\tfrac {3}{4}\times 91\tfrac {3}{4}}{171\tfrac {3}{4}+91\tfrac {3}{4}}$ is equal to

  1. $263\frac {1}{2}$
  2. $90\frac {1}{4}$
  3. $80$
  4. $80\frac {3}{4}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If $a=171\frac {3}{4}, b=91\frac {3}{4}$, then given expression is


$\dfrac {a^2-b^2}{a+b}=\dfrac {(a+b)(a-b)}{(a + b)}=a-b=171\frac {3}{4}-91\frac {3}{4}=80$

Multiple choice maths number system representation of irrational numbers on number line existence of irrational numbers irrational numbers

Which of the following numbers lie between $1$ and $3$?

  1. $\dfrac13$
  2. $\sqrt{2}$
  3. $\sqrt{10}$
  4. $\dfrac{8}3$
Reveal answer Fill a bubble to check yourself
B,D Correct answer
Explanation

Converting all option in decimal format (approximately)

A. $\frac{1}{3}=0.33$
B.$\sqrt {2  } =1.41$
C.$ \sqrt { 10 }=3.16 $
D. $\frac{8}{3}=2.67$
It is clear that option B and D lies between 1 and 3
So correct answer will be option B and D

Multiple choice maths number system representation of irrational numbers on number line existence of irrational numbers irrational numbers

The value of $0.\overline{2}$ in the form $\frac{p}{q}$ , where p and q are integers and $q\ne 0$ is :

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

$Let\quad x=.222....\ On\quad multiplying\quad by\quad 10\quad on\quad both\quad sides\quad \ 10x=2.222....\ On\quad subtracting\quad both\quad equations\quad \ 9x=2\ x=\dfrac { 2 }{ 9 } $

Hence,correct answer is option B.

Multiple choice mathematics and statistics angle and their measurement degree measure of angle measure of angle radians or degrees

The value of $ \displaystyle 36^{\circ} $ in radians is 

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

$\displaystyle 180^{\circ}      $    =  $\displaystyle \pi       $ radians 


$\displaystyle  \therefore  1^{\circ}=\frac{\pi }{180}    radians     $
$\displaystyle  \Rightarrow 36^{\circ}=\frac{\pi }{180}\times 36 \ radians = \frac{\pi }{5}radians      $

Multiple choice maths decimal fractions rounding decimals non-terminating recurring decimals in rational numbers rounding off decimals rounding of decimals

$0.\overline{5}$ in the form of $\frac{p}{q}$ is :

  1. $\dfrac{9}{5}$
  2. $\dfrac{5}{10}$
  3. $\dfrac{5}{9}$
  4. $\dfrac{10}{5}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$Let\quad x=.555....\ On\quad multiplying\quad by\quad 10\quad on\quad both\quad sides\quad \ 10x=5.555....\ On\quad subtracting\quad both\quad equations\quad \ 9x=5\ x=\dfrac { 5 }{ 9 } \ $

Hence, correct answer is option C.

Multiple choice trigonometric equations trigonometric functions trigonometry maths

$\cot^{2} \dfrac{\pi}{11}+\cot^{2} \dfrac{2\pi}{11}+\cot^{2} \dfrac{3\pi}{11}........+\cot^{2} \dfrac{5\pi}{11}=?$

  1. $15$
  2. $45$
  3. $9$
  4. $18$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The sum of cot^2(k*pi/11) for k=1 to 5 is a known trigonometric series result equal to 15.