Mathematics · Quantitative Aptitude

Number Operations and Properties

896 Questions

Improve your quantitative aptitude with these number operations and properties questions. The topics range from basic subtraction and division to highest common factor and roman numerals. Regular practice of these fundamentals builds speed for exams.

Basic arithmetic operationsHCF and number propertiesRoman numeral calculationsNumber series evaluation

Number Operations and Properties Questions

Multiple choice maths geometric sequences sum of terms of g.p sum of n terms of an gp summing geometric series

$6^{1/2}\, .\, 6^{1/4}\, .\, 6^{1/8}\, ..... \infty\, =\, ?$ 

  1. 6
  2. $\infty$

  3. 216

  4. 36
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given $6^{\frac{1}{2}}.6^{\frac{1}{4}}.6^{\frac{1}{8}}....\infty$
Here power of 6 are in G.P
Sum of $\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8} ...\infty$

$S _{\infty} = \dfrac{a}{1-r}$
Here $a = \dfrac{1}{2}, r = \dfrac{\dfrac{1}{4}}{\dfrac{1}{2}} = \dfrac{1}{2}$
$S _{\infty} = \dfrac{\dfrac{1}{2}}{1-\dfrac{1}{2}}$
$S _{\infty} = \dfrac{\dfrac{1}{2}}{\dfrac{1}{2}} = 1$
$\therefore S _{\infty} = 6^1 = 6$

Multiple choice maths geometric sequences sum of terms of g.p sum of n terms of an gp summing geometric series

Find $3 + 12 + 48 +...$ up to $5$ terms.

  1. $1023$
  2. $2023$
  3. $3023$
  4. $4023$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given series is $3+12+48+....$ upto $5$ terms
To find the sum of the first $S _n$ terms of a geometric sequence by using the formula,
Here $a = 3, r = 4, n = 5$
$S _n = \dfrac{a _1(1-r^n)}{1-r}$
$S _5 = \dfrac{3(1-(4)^{5})}{1-4}$
$ = \dfrac{3(-1023)}{-3}$
$ = 1023$

Multiple choice maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

Find G.C.D of: $8(x^4-16)$ and $12(x^3-8)$

  1. $4(x-2)$
  2. $3(x^3-8)$
  3. $2(x^2-4)$

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

$p(x) =8(x^4-16)$
   $= 4\times 2 [(x^2)^2 - 4^2] $
   $ = 4\times 2 (x^2 - 4) (x^2 + 4) $
   $ = 4\times 2  (x+2)(x-2) (x^2 +4) $
and
 $q(x) = 12(x^3-8)$
       $=4\times 3 (x^3 - 2^3) $
         $=4\times 3 (x - 2)(x^2 + 2x + 4) $
$\therefore $ G.C.D of $p(x)$ and $q(x) = 4(x-2) $
Option A is correct.

Multiple choice maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

What is the greatest common factor of $45,135$ and $270$?

  1. $5$
  2. $9$
  3. $15$
  4. $25$
  5. $45$
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

The factors of the given numbers are :
$45  = 1,3,5,9,15$ and $45$
$135 = 1,3,5,9,15,45$ and $135$
$270 = 1,3,5,9,15,45,90,135$ and $270$
The common factors in each of the above numbers are $3,3$ and $5$.
Hence, the GCF is $3\times 3\times 5$ = 45
and as $45$ is also a factor of both $135$ and $270$.
The GCF of $45, 135$ and $270$ is $45$.
The correct answer is Option E, the number $45$.

Ans: E

Multiple choice maths hcf-lcm common factors and hcf hcf highest common factor (h.c.f.)

How many different positive integers are factors of both $28$ and $42$?

  1. $1$
  2. $2$
  3. $3$
  4. $4$
  5. More than $4$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$4$ positive integers are factors of $28$ and $42$ both.
For example,
$1,4, 7, 6$ and $28$ itself is a factor of $28$.
$1,4, 7, 6$ and $42$ itself is factor of $42$.