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 surface area and volume of cube and cuboid finding out the diagonal of cube and cuboid length of the diagonal of cube diagonal of cube and cuboid

Write the Pythagorean triplet whose one member is 30.

  1. $226$ and $224$
  2. $220$ and $222$
  3. $227$ and $229$

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

Solution:

General form of pythagorean triplets are $m^2-1,2m,m^2+1$

$\Rightarrow$First member of triplet $a=2m=30\Rightarrow m=15$


Since, it is even 
$\Rightarrow$So, second member of triplet $b=\left(m\right)^2-1=15^2-1=225-1=224$

$\Rightarrow$And third member of triplet $c=m^2+1=225+1=226$

Hence, $A$ is the correct option.

Multiple choice maths surface area and volume of cube and cuboid finding out the diagonal of cube and cuboid length of the diagonal of cube diagonal of cube and cuboid

Find the pythagorean triplet.

  1. $12,35,37$
  2. $12,36,37$
  3. $12,43,47$

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

Every right triangle has side length satisfying:

a$^{2}$ $+$ b$^{2}$ $=$ c$^{2}$
c is the longest side,
Here 
$12^{2}$ $+$ $35^{2}$ $=$ $37^{2}$
Hence it is a pythagorean triplet.
Option A is correct.

Multiple choice maths surface area and volume of cube and cuboid finding out the diagonal of cube and cuboid length of the diagonal of cube diagonal of cube and cuboid

Write the Pythagorean triplet whose one member is $24$.

  1. $143$ and $145$
  2. $133$ and $144$
  3. $112$ and $115$
  4. $324$ and $325$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using  $ 2m, m^2+1, m^2-1$ forms

 Let us take $2m = 24$

$m=\dfrac{24}{2}=12$

if $m = 12, m^2-1=12^2= 144-1 =143$

if $ m = 12, m^2 +1=12^2= 144+1 =145$

Therefore, option A is the correct answer.

Multiple choice maths surface area and volume of cube and cuboid finding out the diagonal of cube and cuboid length of the diagonal of cube diagonal of cube and cuboid

Find the Pythagorean triplet whose one member is $18$.

  1. $28$ and $20$
  2. $80$ and $82$
  3. $72$ and $92$
  4. $34$ and $54$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using  $ 2m, m^2+1, m^2-1$ forms 
Let us take $2m = 18$
           

$m=\dfrac{18}{2}=9$
if $m = 9, m^2-1=9^2= 81-1 =80$
if $ m = 9, m^2 +1=9^2= 81+1 =82$
Therefore, B is the correct answer.

Multiple choice maths surface area and volume of cube and cuboid finding out the diagonal of cube and cuboid length of the diagonal of cube diagonal of cube and cuboid

Find the Pythagorean triplets, whose one member is $22.$

  1. $22, 183, 185$
  2. $22, 483, 485$
  3. $22, 23, 25$
  4. $22, 120, 122$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For any natural numbers m > 1, $2m, m^{2} - 1$, $m^{2} + 1$ form a Pythagorean triplet.
If we take $m^2 + 1 = 22$, then $m^2 = 21$
The value of m will not be an integer.
If we take $m^2 - 1 = 22$, then $m^2 = 23$
Again the value of m will not be an integer.
Let $2m = 22$
$m = \cfrac{22}{2}$
$m = 11$
$2m = 2 \times 11 = 22$
$m^{2} - 1$ = $11^{2} - 1$
$= 121 - 1 = 120$
$m^{2} + 1$ = $11^{2} + 1$
$= 121 + 1 = 122$
Therefore, the Pythagorean triplets are $ 22, 120, 122.$

Multiple choice maths surface area and volume of cube and cuboid finding out the diagonal of cube and cuboid length of the diagonal of cube diagonal of cube and cuboid

What is the Pythagorean triplet, whose one member is $34$?

  1. $34, 278, 290$
  2. $34, 288, 291$
  3. $34, 288, 290$
  4. $35, 288, 290$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For any natural numbers m > 1, $2m, m^{2} - 1$, $m^{2} + 1$ forms a Pythagorean triplet.
If we take $m^2 + 1 = 34$, then $m^2 = 33$
The value of m will not be an integer.
If we take $m^2 - 1 = 34$, then $m^2 = 35$
Again the value of m will not be an integer.
Let $2m = 34$
$m = \dfrac{34}{2}$
$m = 17$
$2m = 2 \times 17 = 34$
$m^{2} - 1$ = $17^{2} - 1$
$= 289 - 1 = 288$
$m^{2} + 1$ = $17^{2} + 1$
$=289 + 1 = 290$
Therefore, the Pythagorean triplets are $34, 288, 290.$

Multiple choice maths numbers and place value face value of digit large numbers general form of number

The difference between the place value and face value of 5 in 31520332 is

  1. 49998

  2. 499995

  3. 49995

  4. none
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\Rightarrow$  The given number is $31520332$.

$\Rightarrow$   Face value of 5 in the given number is $5$.
$\Rightarrow$   Place value of 5 in the given number is $500000.$
$\therefore$   Place value - Face value  = $500000-5=499995$
$\therefore$    Required difference is $499995$.