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 operations on rational numbers rational numbers on number line rational numbers and their decimal expansions rational numbers between two rational numbers

Which of the following numbers lies between $\dfrac {-5}{2}$ and $\dfrac {3}{4}$?

  1. $1$
  2. $0$
  3. $-3$
  4. $3$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

From the options, only $0$ can lie between $\dfrac {-5}{2}$ and $\dfrac {3}{4}.$

$-3=\dfrac{-6}{2}$
$-3$ is less than $\dfrac {-5}{2}.$ 
$1=\dfrac{4}{4}$

$3=\dfrac{12}{4}$
$1$ and $3$ are greater than $\dfrac {3}{4}$.

Multiple choice maths operations on rational numbers rational numbers on number line rational numbers and their decimal expansions rational numbers between two rational numbers

What is the sum of the addictive inverse of $\frac{2}{3}$ and the reciprocal of $\frac{9}{8}$?

  1. $\frac{3}{8}$
  2. -$\frac{3}{8}$
  3. $\frac{2}{9}$
  4. -$\frac{2}{9}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Additive inverse of 2/3 is -2/3. Reciprocal of 9/8 is 8/9. Sum = -2/3 + 8/9 = -6/9 + 8/9 = 2/9.

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

Find the sum of $\displaystyle\frac{0.3}{0.5}+\frac{0.33}{0.55}+\frac{0.333}{0.555}+\cdots\cdots$ to 15 terms.

  1. 10

  2. 9

  3. 3

  4. 5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Each dfraction can be simplified to $ \dfrac {3}{5} $ by dividing by their highest common factor. 

So, expression is simplified to $ \dfrac {3}{5} + \dfrac {3}{5} + \dfrac {3}{5} + --- 15 $ terms. 
$ = \dfrac {3}{5} \times 15 = 9 $
Multiple choice maths arithmetic sequences forming an arithmetic progression between two quantities a and b sums arithmetic progression

Sum to infinity of the series $ \frac {2}{3}- \frac {5}{6} +\frac {2}{3} - \frac {11}{24}+ ....$

  1. $\frac {4}{9}$
  2. \frac {1}{3}$
  3. \frac {2}{9}$

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

This is an infinite series that can be grouped or solved using standard summation techniques for alternating series. The sum converges to 4/9.

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

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