Mathematics · Quantitative Aptitude

Number Operations and Properties

974 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 numbers in indian and international systems international place value system international system of numeration use of commas and comparison and number systems

Numeral for five hundred three million eight thousand seven hundred two is

  1. $50,03,80,702$
  2. $50,38,00,702$
  3. $503,008,702$
  4. $50,30,80,702$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Numeral for five hundred three million eight thousand seven hundred two is 503,008,702
$\therefore$ Option C is correct.

Multiple choice maths numbers in indian and international systems international place value system international system of numeration use of commas and comparison and number systems

$648340021$ is written with commas as (International System)

  1. $648,340,021$
  2. $6,4,8,3,4,0,0,2,1$
  3. $64,83,40,02,1$

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

In international system of numeration,
The 1st period consists of - ones, tens and hundred.
The 2nd period consists of - thousand, 10 thousand and 100 thousands.
The 3rd period consists of - million, 10 million and 100 million.
The 4th period consists of - billion, 10 billion and 100 billion.
$\therefore $648340021 is written with commas as (International System)= 648,340,021
Option A is correct.

Multiple choice maths numbers in indian and international systems international place value system international system of numeration use of commas and comparison and number systems

$9849475825$ is written with commas as (International System)

  1. $9, 84, 94, 75, 825$
  2. $9, 849,475,825$
  3. $9849, 475, 82, 5$
  4. $9,8,4,9,4,7,5,8,2,5$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In international numbering system
The 1st period consists of - ones, tens and hundred.
The 2nd period consists of - thousand, $10 $ thousand and $100 $ thousand.
The 3rd period consists of - million, $10$ million and $100$ million.
The 4th period consists of - billion, $10$ billion and $100$ billion.
$\therefore $ 9849475825 is written with commas as (International System)$ = 9,849,475,825$
Option B is correct.

Multiple choice maths numbers in indian and international systems international place value system international system of numeration use of commas and comparison and number systems

9849475825 is witten with commas as (International System)

  1. $9, 84, 94, 75, 825$
  2. $9, 849, 475, 825$
  3. $9849, 475, 82, 5$
  4. $9, 8, 4, 9, 4, 7, 5, 8, 2, 5$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In International System commas are introduced after every 3 digits starting from right to left side


In Indian System commas are introduced after  3 digits for one time and then after 2 digits starting from right to left side.

given the number  $9849475825$

International System:
$9849475825 = 9 , 894,475,825$

Indian System :
$9849475825 = 9,84,94,75,825$

So option $B$ is correct

Multiple choice maths numbers in indian and international systems international place value system international system of numeration use of commas and comparison and number systems

The product of the numbers $5623$ and $6$ in the scale of eight is:

  1. $41672$
  2. $33738$
  3. $42562$
  4. $45262$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To multiply 5623 (base 8) by 6 (base 8): 3*6=18 (decimal) = 22 (base 8), write 2 carry 2. 2*6=12 + 2 = 14 (decimal) = 16 (base 8), write 6 carry 1. 6*6=36 + 1 = 37 (decimal) = 45 (base 8), write 5 carry 4. 5*6=30 + 4 = 34 (decimal) = 42 (base 8). Result is 42562.

Multiple choice maths numbers in indian and international systems international place value system international system of numeration use of commas and comparison and number systems

Number name for $123,080,603$ is:

  1. one two three eighty thousand six hundred three

  2. one hundred twenty three million eight thousand six hundred three

  3. one hundred twenty three million eighty thousand six hundred three

  4. one twenty three million eighty thousand six hundred
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

By using International number system the naming of the number $123,080,603$ is:

one hundred twenty three million eighty thousand six hundred three.

Multiple choice maths numbers in indian and international systems international place value system international system of numeration use of commas and comparison and number systems

Express in international number system.
$81,894,650$

  1. Eighty one million,eight hundred ninety four thousand six hundred fifty.

  2. Eighty million,eight hundred ninety four thousand six hundred fifty.

  3. Eight hundred one million,eight hundred ninety four thousand six hundred fifty.

  4. Eighty one million,eight ninety four thousand six hundred .
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Let us convert the given numerals into words as follows:

$81,000,000=$Eighty one million
$894,000=$Eight hundred ninety four thousand
$600=$Six hundred
$50=$Fifty

Now, combine the numbers in words as shown below:

Eighty one million,eight hundred ninety four thousand six hundred fifty.

Hence, the International number system is eighty one million,eight hundred ninety four thousand six hundred fifty.
Multiple choice maths numbers in indian and international systems international place value system international system of numeration use of commas and comparison and number systems

Express as International number system.
$3,45,90,430$

  1. Thirty four million,five hundred ninety thousand hundred thirty.

  2. Thirty four million,five hundred nine thousand four hundred thirty.

  3. Thirty million,five hundred ninety thousand four hundred thirty.

  4. Thirty four million,five hundred ninety thousand four hundred thirty.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Let us convert the given numerals into words as follows:

$34,000,000=$Thirty four million
$590,000=$Five hundred ninety thousand
$400=$Four hundred
$30=$Thirty

Now, combine the numbers in words as shown below:

Thirty four million,five hundred ninety thousand four hundred thirty.

Hence, the International number system is thirty four million,five hundred ninety thousand four hundred thirty.
Multiple choice maths ways to multiply and divide division trick division multiply and divide

238 $\div$ 238 is ________

  1. $0$
  2. $238$
  3. $28$
  4. $1$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The number divided by itself and we get $1$ as quotient except $0$


This is not valid for $0$

Now as per the question 
the number $238$ is divided by itself

$238 \div 238 = \dfrac{238}{238} =1$

So , option $D$ 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 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.