Quantitative Aptitude

Simplification and Approximation

647 Questions
All Approximate with option-sensitive rounding 386 Percentage calculation 112 Calculate squares and identify square roots 38 Simplify surds and indices 29 VBODMAS 27 Recognize algebraic identity patterns 23 Use cube patterns and perfect cube roots 15 Fraction and mixed number reduction 13 Mixed recurring decimals 3 Integer division and remainders 1

Simplification and Approximation Questions

Multiple choice

Find the value of the following expression.

{( 25/36 x 216/125) + (2401/343 x 1296/216) } / {(- 25/36 x 6/5) + (- 4/9 x 81/64)}.

  1. 216/5 x 48/67
    • 216/5 x 48/67

  3. 5/216 x 67/48

  4. 67/48 x 5/216
    • 5/216
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The given expression is {( 25/36 x 216/125) + (2401/343  x 1296/216) } / {(- 25/36 x 6/5) + (- 4/9 x 81/64)} Solve the expression part by part: ( 25/36 x 216/125) = 25/36 x 216/125 = 6/5

(2401/343 x 1296/216) = 7 x 6 = 42

  • 25/36 x 6/5 = - 5/6
  • 4/9 x 81/64 = - 9/16 Therefore, the required value of the expression is    6/5 + 42 / - 5/6 - 9/16  = {(216/5) / {(- 40 - 27)/48} = - 216/5 x 48/67
Multiple choice maths cube and cube root estimation of cube root estimation of cube roots cubes and cube roots

What is the approximate value of the cube root of the number $9?$

  1. $2.08$
  2. $2.19$
  3. $2.34$
  4. $2.51$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

First multiply and divide by $1,000,000,$ we get
$\sqrt[3]{\dfrac{9\times 1000,000}{1000,000}}$
$\sqrt[3]{9,000,000} \div 100$
Now find the closest cube root of $9,000,000.$
$208^3 = 8,998,912,$ therefore we can say that $\sqrt[3]{9}$ $\sim$ $\dfrac{208}{100} \sim 2.08$

Multiple choice maths perimeter and area converting between units of areas the metric system metric system

The area of a square field is $325\ m^2$. Find the approximate length of one side of the field. (upto 2 places of decimals) (in $m^2$)

  1. $19.03$
  2. $18.02$
  3. $18.03$
  4. $17.03$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

We know area of any square is its side x side 

Let us assume that side of square field is x 
Then area of square field $= x^2$
According to question

$x^2 = 325 m^2$

$\Rightarrow x^2 = 325$

$x = \sqrt{325}$

So $x = 18.03$

Hence side of square field is $18.03 m$

option (C)

Multiple choice maths indices exponentiation index notation and products of prime factors powers

The approximate value of ${ \left{ { { \left( 3.92 \right)  }^{ 2 }\quad +3\left( 2.1 \right)  }^{ 4 } \right}  }^{ { 1 }/{ 6 } }$

  1. $2.0466$
  2. $2.755$
  3. $2.345$
  4. $0.242718$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

${(3.92^2+3(2.1^4)}^\dfrac{1}{6}$

 
$=(15.3664+3\times19.4481)^\dfrac{1}{6}$


$=(15.3664+58.3443)^\dfrac{1}{6}$

$=(73.7107)^\dfrac{1}{6}$

$=2.0476$

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

What is the percentage approximate for the fraction $\dfrac{12}{35}$?

  1. $34.28\%$
  2. $23.78\%$
  3. $30.12\%$
  4. $29.10\%$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To get the percent you will divide the numerator by the denominator.

Then multiply $100$ to the answer and add the percent sign.
therefore, the percentage approximate value if $\dfrac{12}{35}\times 100 = 34.28$ $\%$.

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

What is the percentage error in using $\dfrac{22}{7}$ as an approximation for $\pi$?
(Give your answer to the nearest $0.01%$)

  1. $0.02\%$
  2. $0.03\%$
  3. $0.04\%$

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

$\Rightarrow$  Here, Approximate value of $\pi$ = $\dfrac{22}{7}=3.142857$

$\Rightarrow$  Exact value of $\pi$ is $3.141592$
$\Rightarrow$  $\%\,Error=\dfrac{|Approximate\,value-Exact\,value|}{|Exact\,value|}\times 100$

$\Rightarrow$  $\%\,Error=\dfrac{|3.142857-3.141592|}{|3.141592|}\times 100$
$\Rightarrow$  $\%\,Error=0.04\%$

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

The value of $\displaystyle\frac{1}{\sqrt{3}+\sqrt{2}-1}$ on simplifying upto 3 decimal places, given that $\sqrt{2}=1.4142$ and $\sqrt{6}=2.4495$ is

  1. 0.166

  2. 0.366

  3. 0.466

  4. 0.566
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\frac { 1 }{ \sqrt { 3 } +\sqrt { 2 } -1 } $
$=\frac { \sqrt { 3 } -\left( \sqrt { 2 } -1 \right)  }{ \left( \sqrt { 3 } +\left( \sqrt { 2 } -1 \right)  \right) \left( \sqrt { 3 } -\left( \sqrt { 2 } -1 \right)  \right)  } Multiplying\sqrt { 3 } -\left( \sqrt { 2 } -1 \right) \quad with\quad numerator\quad and\quad denominator\quad $
$=\frac { \sqrt { 3 } -\left( \sqrt { 2 } -1 \right)  }{ 3-{ \left( \sqrt { 2 } -1 \right)  }^{ 2 } } $
 $=\frac { \sqrt { 3 } -\left( \sqrt { 2 } -1 \right)  }{ 3-{ \left( 2+1-2\sqrt { 2 }  \right)  } } $
 $=\frac { \sqrt { 3\quad  } -\sqrt { 2 } +1 }{ 2\sqrt { 2 }  } $
$=\frac { 1.732-1.4142+1 }{ 2.8284 } =0.466$
                                               $(\sqrt { 3 } =\frac { \sqrt { 6 }  }{ \sqrt { 2 }  } =\frac { 2.4495 }{ 1.4142 } =1.732)$

Multiple choice maths decimal fraction multiplying decimals multiplication of decimals multiplication of division of decimal fraction by whole number and decimal fraction

Find the value of following expression:
$\dfrac{(0.1667)(0.8333)(0.3333)}{(0.2222)(0.6667)(0.1250)}$

  1. $2$
  2. $2.40$
  3. $2.43$
  4. $2.50$
  5. $None\ of\ these$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Converting the decimals to fractions: 0.1667 = 1/6, 0.8333 = 5/6, 0.3333 = 1/3, 0.2222 = 2/9, 0.6667 = 2/3, and 0.1250 = 1/8. Substituting these into the expression gives ((1/6)(5/6)(1/3)) / ((2/9)(2/3)(1/8)) = (5 / 108) / (2 / 54) = (5 / 108) * (54 / 2) = 5 / 4 = 1.25, wait let us re-evaluate carefully: numerator = (1/6)(5/6)(1/3) = 5/108. Denominator = (2/9)(2/3)(1/8) = 4/216 = 2/108. So (5/108) / (2/108) = 5/2 = 2.50.

Multiple choice maths squares and square roots approximation of square roots estimating square roots square root of non perfect squares

The approximate value of$\sqrt { { \left( 1.97 \right)  }^{ 2 }{ \left( 4.02 \right)  }^{ 2 }{ \left( 3.98 \right)  }^{ 2 } }$

  1. $31.59 $
  2. $5.099$
  3. $5.009$
  4. $5.734$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

We have,

$ \sqrt{{{\left( 1.97 \right)}^{2}}{{\left( 4.02 \right)}^{2}}{{\left( 3.98 \right)}^{2}}} $

$ =1.97\times 4.02\times 3.98 $

$ =31.59 $

Hence, this is the answer.