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 numbers and place value forming numbers formation of greatest and smallest numbers identifying the largest and smallest numbers with given digits

Which of the following fractions is the largest?

  1. $\dfrac { 7 }{ 8 } $
  2. $\dfrac { 13 }{ 16 } $
  3. $\dfrac { 31 }{ 40 } $
  4. $\dfrac { 63 }{ 80 } $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

L.C.M. of $8$, $16$, $40$ and $80 = 80$.
$\dfrac { 7 }{ 8 } =\dfrac { 70 }{ 80 }$; $\dfrac { 13 }{ 16 } =\dfrac { 65 }{ 80 }$; $\dfrac { 31 }{ 40 } =\dfrac { 62 }{ 80 } $


Since, $\dfrac { 70 }{ 80 } > \dfrac { 65 }{ 80 } > \dfrac { 63 }{ 80 } > \dfrac { 62 }{ 80 } $

       So $\dfrac { 7 }{ 8 } > \dfrac { 13 }{ 16 } > \dfrac { 63 }{ 80 } > \dfrac { 31 }{ 40 } $
      $\therefore$ $\dfrac { 7 }{ 8 } $ is the largest.

Multiple choice maths numbers and place value forming numbers formation of greatest and smallest numbers identifying the largest and smallest numbers with given digits

Which of the following fractions is greater than $\dfrac { 3 }{ 4 } $ and less than $\dfrac { 5 }{ 6 } $?

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

$\dfrac { 3 }{ 4 } =0.75,\quad \dfrac { 5 }{ 6 } =0.833,\quad \dfrac { 1 }{ 2 } =0.5,\quad \dfrac { 2 }{ 3 } =0.66,\quad \dfrac { 4 }{ 5 } =0.8,\quad \dfrac { 9 }{ 10 } =0.9$.


Clearly, $0.8$ lies between $0.75$ and $0.833$.

$\therefore \dfrac { 4 }{ 5 } $ lies between $\dfrac { 3 }{ 4 } $ and $\dfrac { 5 }{ 6 } $.

Multiple choice vedic methods of multiplication history of mathematics maths

Identify the larger fraction between $\dfrac{4}{5}, \dfrac{5}{9}$ using Vedic mathematics.

  1. $\dfrac{4}{5}$
  2. $\dfrac{5}{9}$

  3. Both are equal

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

5/4 , 5/9
Difference of cross product = 45 - 20 = 25
If the difference of the cross product is positive then the first fraction is larger.
hence 5/4 is larger.

Multiple choice vedic methods of multiplication history of mathematics maths

Identify the larger fraction between $\dfrac{2}{3}, \dfrac{5}{8}$ using Vedic mathematics.

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

  3. Both are equal

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

2/3, 5/8
Difference of cross product = 16 - 15 = 1

If the difference of the cross product is positive then the first fraction is larger.
So, 2/3 is larger fraction.

Multiple choice vedic methods of multiplication history of mathematics maths

Identify the larger fraction between $\dfrac{7}{12}, \dfrac{9}{20}$ using Vedic mathematics.

  1. $\dfrac{7}{12}$
  2. $\dfrac{9}{20}$

  3. Both are equal

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

7/12, 9/20

Difference of cross product = 140 - 108 = 32

If the difference of the cross product is positive then the first fraction is larger.
So, 7/12 is larger fraction.

Multiple choice vedic methods of multiplication history of mathematics maths

Identify the larger fraction between $\dfrac{11}{21}, \dfrac{12}{25}$ using Vedic mathematics.

  1. $\dfrac{11}{21}$
  2. $\dfrac{12}{25}$

  3. Both are equal

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

11/21, 12/25
Difference of cross product = 275 - 252 = 23

If the difference of the cross product is positive then the first fraction is larger.
So, 11/21 is larger fraction.

Multiple choice vedic methods of multiplication history of mathematics maths

$\displaystyle\frac{1}{5}$ of $\displaystyle\frac{2}{7}$ of $\displaystyle \frac{8}{3}$ of $4095=?$

  1. $642$
  2. $598$
  3. $648$
  4. $475$

  5. None of these
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

$\displaystyle \frac{1}{5}$ of $\displaystyle\frac{2}{7}$ of $\displaystyle\frac{8}{3}$ of $4095$
$=\displaystyle\frac{1}{5}\times \frac{2}{7}\times \frac{8}{3}\times 4095=624$.

Hence the correct answer is option E

Multiple choice vedic methods of multiplication history of mathematics maths

The value of $3\dfrac{1}{12}$ - $\big[ 1\dfrac{3}{4} $+$\big[$ 2$\dfrac{1}{2}$ - $\big(1\dfrac{1}{2}$ - $\dfrac{1}{3}$ $\big)\big]\big]$

  1. $\dfrac{1}{2}$
  2. $2$
  3. $1$
  4. $0$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We have, 3$\dfrac{1}{12}$ - $\bigg[$ 1$\dfrac{3}{4}$ +$\big[2\dfrac{1}{2}$ - $\big(1\dfrac{1}{2}$ - $\dfrac{1}{3}\big)\big]\bigg]$
= $\dfrac{37}{12}$ - $\bigg[$ $ \dfrac{7}{4}$ +$\big[\dfrac{5}{2}$ - $\big(\dfrac{3}{2}$ - $\dfrac{1}{3}$ $\big)\big]\bigg]$
= $\dfrac{37}{12}$ - $\bigg[\dfrac{7}{4}$ + $\big[\dfrac{5}{2}$ - $\big(\dfrac{9-2}{6}\big)\big]\bigg]$   $\bigg[ \because$ LCM of 2,3 =6$\bigg]$
= $\dfrac{37}{12}$ - $\big[\dfrac{7}{4}$ + $\big(\dfrac{5}{2}$ - $\dfrac{7}{6}\big)\big]$
=$\dfrac{37}{12}$ - $\big(\dfrac{7}{4}$ + $\big(\dfrac{15-7}{6}\big)\big]$        $\bigg[\because$ LCM of 2, 6 = 6$\bigg]$
=$\dfrac{37}{12}$ - $\big[\dfrac{7}{4}$ + $\dfrac{8}{6}$ $\big]$
= $\dfrac{37}{12}$ - $\big[\dfrac{21+16}{12}$ $\big]$            $\big[\because$ LCM of 4, 6 = 12 $\big]$
= $\dfrac{37}{12}$ - $\dfrac{37}{12}$ = 0

Multiple choice vedic methods of multiplication history of mathematics maths

Which of the following fraction equals $\displaystyle101\frac{3}{5}\%$

  1. $\displaystyle\frac{508}{5}$
  2. $\displaystyle\frac{254}{5}$
  3. $\displaystyle\frac{51}{25}$
  4. $\displaystyle\frac{127}{125}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$ 101 \dfrac {3}{5} = \dfrac {101 \times 5 + 3}{5} = \dfrac {505+3}{5} = \dfrac {508}{5}$

Multiple choice vedic methods of multiplication history of mathematics maths

Fraction  $\displaystyle \frac { 2 }{ 5 }, \frac {3} {10} , \frac {9} {10}, \frac {16} {35} $ in ascending order are:

  1. $\displaystyle \frac { 2 }{ 5 }, \frac {3} {10} , \frac {9} {10}, \frac {16} {35} $
  2. $\displaystyle \frac { 3 }{ 10 }, \frac {2} {5}, \frac {16} {35}, \frac {9} {14} $
  3. $\displaystyle \frac { 3 }{ 10 } , \frac {9} {14} , \frac {16} {35}, \frac {2} {5} $
  4. $\displaystyle \frac { 16 }{ 35 } , \frac {2} {5} , \frac {3} {10}, \frac {9} {14} $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The given Fraction are $\displaystyle \frac { 2 }{ 5 }, \frac {3} {10} , \frac {9} {10}, \frac {16} {35} $
LCM of 5, 10, 14, 35 = $\displaystyle (5\times 2\times 7\times)= 70 $
Now change each of the following into an equivalent fraction having 70 as its denominator.
Now, $\displaystyle \frac { 2 }{ 5 } =\frac { 2\times 14 }{ 5\times 14 } =\frac { 28 }{ 70 } \ \frac { 3 }{ 10 } =\frac { 3\times 7 }{ 10\times 7 } =\frac { 21 }{ 70 } \ \frac { 9 }{ 14 } =\frac { 9\times 5 }{ 14\times 5 } =\frac { 45 }{ 70 } \ and\quad \frac { 16 }{ 35 } =\frac { 16\times 2 }{ 35\times 2 } =\frac { 32 }{ 70 } \ Clearly,\quad \frac { 28 }{ 70 } >\frac { 21 }{ 70 } <\frac { 45 }{ 70 } >\frac { 32 }{ 70 } \ Hence,\quad \frac { 3 }{ 10 } <\frac { 2 }{ 5 } <\frac { 16 }{ 35 } <\frac { 9 }{ 14 } $

Multiple choice vedic methods of multiplication history of mathematics maths

The value of the expression $\dfrac { 1 }{ \sqrt { 11-2\sqrt { 30 }  }  } -\dfrac { 3 }{ \sqrt { 7-2\sqrt { 10 }  }  } -\dfrac { 4 }{ \sqrt { 8+4\sqrt { 3 }  }  } $ after simplification is

  1. $\sqrt { 30 } $
  2. $2\sqrt { 10 } $
  3. $1$
  4. $0$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\dfrac { 1 }{ \sqrt { 11-2\sqrt { 30 }  }  } -\dfrac { 3 }{ \sqrt { 7-2\sqrt { 10 }  }  } -\dfrac { 4 }{ \sqrt { 8+4\sqrt { 3 }  }  } $


$=\left (\dfrac { 1 }{ { 11-2\sqrt { 30 }  }  }\right)^{\frac{1}{2}} -\left( \dfrac { 3 }{ { 7-2\sqrt { 10 }  }  }\right)^{\frac{1}{2}} -\left( \dfrac { 4 }{ { 8+4\sqrt { 3 }  }  }\right)^{\frac{1}{2}} $


$=\left (\dfrac { 1 }{ { 5+6-2\sqrt {5}\sqrt{6}}}\right)^{\frac{1}{2}} -\left( \dfrac { 3 }{ { 5+2-2\sqrt {5}\sqrt{2}}}\right)^{\frac{1}{2}} -\left( \dfrac { 4 }{ {6+2+2\sqrt {6}\sqrt{2}  }  }\right)^{\frac{1}{2}} $

$={ \left( \dfrac { 1 }{ (\sqrt { 6 } -\sqrt { 5 } )^2 }  \right)  }^{ \frac { 1 }{ 2 }  }-3{ \left( \dfrac { 1 }{( \sqrt { 5 } -\sqrt { 2 } )^2 }  \right)  }^{ \frac { 1 }{ 2 }  }-4{ \left( \dfrac { 1 }{ (\sqrt { 6 } +\sqrt { 2 } )^2 }  \right)  }^{ \frac { 1 }{ 2 }  }$

$={ \left( \dfrac { 1 }{ \sqrt { 6 } -\sqrt { 5 }  }  \right)  }^{ \frac { 2 }{ 2 }  }-3{ \left( \dfrac { 1 }{ \sqrt { 5 } -\sqrt { 2 }  }  \right)  }^{ \frac { 2 }{ 2 }  }-4{ \left( \dfrac { 1 }{ \sqrt { 6 } +\sqrt { 2 }  }  \right)  }^{ \frac { 2 }{ 2 }  }$

$={ \left( \dfrac { 1 }{ \sqrt { 6 } -\sqrt { 5 }  } \times {\dfrac{\sqrt{6}+\sqrt{5}}{\sqrt{6}+\sqrt{5}}} \right)  }^{ \frac { 2 }{ 2 }  }-3{ \left( \dfrac { 1 }{ \sqrt { 5 } -\sqrt { 2 }  } \times{\dfrac{\sqrt{5}+\sqrt{2}}{\sqrt{5}+\sqrt{2}}} \right)  }^{ \frac { 2 }{ 2 }  }-4{ \left( \dfrac { 1 }{ \sqrt { 6 } +\sqrt { 2 }  } \times{\dfrac{\sqrt{6}-\sqrt{2}}{\sqrt{6}-\sqrt{2}}} \right)  }^{ \frac { 2 }{ 2 }  }$

$=\left( \sqrt { 6 } +\sqrt { 5 }  \right) -\left( \sqrt { 5 } +\sqrt { 2 }  \right) -\left( \sqrt { 6 } -\sqrt { 2 }  \right) =0$
Hence, option D is correct.