Quantitative Aptitude

Number System and Simplification

548 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 arithmetic sequences forming an arithmetic progression between two quantities a and b sums arithmetic progression

Find the sum of 1 + $\dfrac{1}{4} + \dfrac{1.3}{4.8} + \dfrac{1.3.5}{4.8.12} +.......\infty $

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

This is a binomial expansion (1-x)^(-n). The series 1 + 1/4 + (1*3)/(4*8) + (1*3*5)/(4*8*12) + ... is of the form (1-x)^(-1/2) where x=1/2. Thus, (1 - 1/2)^(-1/2) = (1/2)^(-1/2) = sqrt(2).

Multiple choice maths arithmetic sequences forming an arithmetic progression between two quantities a and b sums arithmetic progression

The sum of infinity terms of the series $\dfrac{1}{1+1^2+1^4} + \dfrac{1}{1+2^2+2^4} + \dfrac{3}{1+3^2+3^4}+....\infty$ is 

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

The n-th term is 1 / (1 + n^2 + n^4) = 1 / ((n^2+1)^2 - n^2) = 1 / ((n^2-n+1)(n^2+n+1)). Using partial fractions, this is (1/2) * [ 1/(n^2-n+1) - 1/(n^2+n+1) ]. This is a telescoping series. The sum is 1/2.

Multiple choice maths arithmetic sequences forming an arithmetic progression between two quantities a and b sums arithmetic progression

$\frac { 3 }{ 6 } +\frac { 3.5 }{ 6.9 } +\frac { 3.5.7 }{ 6.9.12 } +...\infty =$

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

The given series can be recognized or derived from a binomial expansion form, specifically related to the expansion of (1 - x)^(-n). Evaluating the specific series yields 3*sqrt(3) - 4.

Multiple choice maths ratio, proportion and unitary method more on proportion terms related to proportion proportion

If $78$ is divided into three parts which are proportional to $1, \dfrac {1}{3}, \dfrac {1}{6}$, the middle part is

  1. $9\dfrac {1}{3}$
  2. $13$
  3. $17\dfrac {1}{3}$
  4. $18\dfrac {1}{3}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given, $x + \cfrac {1}{3} x + \cfrac {1}{6}x = 78$

$\Rightarrow 9x = 468$
$\Rightarrow \cfrac {1}{3}x = \cfrac {468 }{9} \times \cfrac 13=17\cfrac {1}{3}$.

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

$\displaystyle 0.04\times 0.08\times 4 $ is equal to

  1. $0.012$
  2. $0.128$
  3. $0.00128$
  4. $0.0128$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The rule of thumb in multiplying decimal numbers is we'll count the decimals from the right-hand side and the total places in the decimal in the question will be in the answer.


Example $0.04$ has $2$ places decimal and $0.08$ also has $2$ places. So the total places are $4$. 

The product will have a decimal $4$ places from the right.
$0.04×0.08×4=0.0128$

So option D is the correct answer.

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

Find the product
$\displaystyle 7.854\times 10$

  1. $785.4$
  2. $78.54$
  3. $7854$
  4. $78540$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
To find $7.854\times 10$
Since, $10$ has $1$ zero and $7.854$ has decimal point after $3$ digits
So, the product will have decimal point after $2$ digits from left

Therefore, value of $7.854\times 10$ is $78.54$.

Multiple choice maths calculating and mental strategies 3 written methods dividing decimals division of decimals

If $\displaystyle\frac { 1 }{ 6.198 } = 0.16134$, then the value of $\displaystyle\frac { 1 }{ 0.0006198 } $ is.

  1. $16134$
  2. $1613.4$
  3. $0.16134$
  4. $0.016134$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\displaystyle\frac { 1 }{ 0.0006198 } = \displaystyle\frac { 1 }{ \displaystyle\frac { 6.198 }{ 10000 }  } = \displaystyle\frac { 10000 }{ 6.198 } $

$= 10000 \times 0.16134 = 1613.4$

Multiple choice maths calculating and mental strategies 3 written methods dividing decimals division of decimals

If $\displaystyle \frac{547.527}{0.0082}=x $, then the value of $\displaystyle \frac{547527}{82}$ is 

  1. $\displaystyle \frac{x}{10}$

  2. 10x

  3. 100x
  4. $\displaystyle \frac{x}{100}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given, $\displaystyle \frac{547.527}{0.0082}=x $


$\displaystyle \Rightarrow \frac{5475270}{82}=x $

$\displaystyle \Rightarrow \frac{5475270}{82}=\frac{x}{10} $

Multiple choice maths calculating and mental strategies 3 written methods dividing decimals division of decimals

The value of $\dfrac { { \left( 0.96 \right)  }^{ 3 }-{ \left( 0.1 \right)  }^{ 3 } }{ { \left( 0.96 \right)  }^{ 2 }+0.096+{ \left( 0.1 \right)  }^{ 2 } } $ is:

  1. $0.86$
  2. $0.95$
  3. $0.97$
  4. $1.06$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given expression $=\dfrac { { \left( 0.96 \right)  }^{ 3 }-{ \left( 0.1 \right)  }^{ 3 } }{ { \left( 0.96 \right)  }^{ 2 }+\left( 0.96\times 0.1 \right) +{ \left( 0.1 \right)  }^{ 2 } } $
                             $=\left( \dfrac { { a }^{ 3 }-{ b }^{ 3 } }{ { a }^{ 2 }+ab+{ b }^{ 2 } }  \right) $
                             $=\left( a-b \right) $
                             $=\left( 0.96-0.1 \right) $
                             $= 0.86$