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 direct proportion and inverse proportion rule of three types of proportions direct proportion

If $20: 28= x:7=10:y$.
The values of $x$ and $y$ in the box respectively are __________.

  1. $5, 14$
  2. $14, 5$
  3. $8, 10$
  4. $10, 8$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
We have, $20:28=x:7=10:y$
Taking first two ratios, we have
$20:28=x:7$
$\Rightarrow 20\times 7=x\times 28$
$\Rightarrow x=\displaystyle\frac{20\times 7}{28}=5$
Again taking last and first ratio, we get
$20:28=10:y\Rightarrow 20\times y=28\times 10$
$\Rightarrow y=\displaystyle\frac{10\times 28}{20}=14$.
Multiple choice maths brackets order operations and algebra using brackets in algebraic expressions order of operations

The value of $100 - { ( 7 $of $8 + 4 ) \div 5 } $ is

  1. $92$
  2. $78$
  3. $96$
  4. $88$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We apply BODMAS rule to find the value of the given expression. According to BODMAS rule, if an expression contains brackets we have to first solve or simplify the bracket followed by of (powers and roots etc.), then division, multiplication, addition and subtraction from left to right.


Since 'of' stands for multiplication, therefore the given expression becomes 
$100-[(7\times 8+4)\div 5]$ and apply BODMAS rule as shown below:
$ \Rightarrow 100-[(56+4)\div 5]\ \Rightarrow 100-(60\div 5)\ \Rightarrow 100-12\ \Rightarrow 88$
Hence, the value of $100-[(7\times 8+4)\div 5]$ is $88$.

Multiple choice properties of proportion ratio and proportions ratio and proportion maths

After applying invertendo to $31:15::18:19$  we get $15:a::b:18$ 
What is the value of $a+b$

  1. $40$
  2. $50$
  3. $30$
  4. $60$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If $a : b :: c : d$ then $b : a :: d : c$ is invertendo property of ratios

We have $31:15::18:19$
After applying invertendo we get
$15:31::19:18\equiv  15:a::b:18\ a+b=31+19=50$
Option B is correct

Multiple choice properties of proportion ratio and proportions ratio and proportion maths

After applying invertendo to $30:50::80:20$  we get $50:a::b:80$ 
Find the value of $a-b$

  1. $10$
  2. $20$
  3. $30$
  4. $40$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If $a : b :: c : d$ then $b : a :: d : c$ is invertendo property of ratios

We have $30:50::80:20$
After applying invertendo we get
$50:30::20:80\equiv 50:a::b:20\ a-b=30-20=10$
Option A is correct

Multiple choice properties of proportion ratio and proportions ratio and proportion maths

After applying invertendo to $9:12::13:40$ we get

  1. $9:13::12:40$
  2. $40:12::13:9$
  3. $9:12::13:40$
  4. $12:9::40:13$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If $a : b :: c : d$ then $b : a :: d : c$ is invertendo property of ratios

We have $9:12::13:40$
After applying invertendo we get
$12:9::40:13$
Option D is correct

Multiple choice maths numbers and place value many forms of ten thousand standard form of numbers number names, numerals and place values

Which of the following expressions is true?

  1. $2940000=$$\displaystyle 2\cdot 94\times 10^{5}$
  2. $502000=$$\displaystyle 5\cdot 02\times 10^{5}$
  3. $3683000=$$\displaystyle 3\cdot 683\times 10^{5}$
  4. $40404000=$$\displaystyle 4\cdot 0404\times 10^{5}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\displaystyle 502000= 5\cdot 02\times 10^{5}$

Therefore, option B is correct.

Multiple choice maths numbers and place value many forms of ten thousand standard form of numbers number names, numerals and place values

When $70, 000$ is written as $7.0\times10^n$, what is the value of $n$?

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

Given that $70,000$ is written as $7.0$ $\times $ ${10}^{n}$

From this, we can write
$70,000$ $=$ $7.0$ $\times$ ${10}^{n}$
$\Rightarrow {10}^{n}$ $=$ $\dfrac {70,000}{7}$
$\Rightarrow {10}^{n}$ $=$ $10,000$
$\Rightarrow {10}^{n}$ $=$ ${10}^{4}$
$\Rightarrow n$ $=$ $\log _{10}$ ${10}^{4}$
$\Rightarrow n$ $=$ $4$ $\log _{10}$ $10$
$\Rightarrow $ $=$ $4$
Therefore, the value of $n$ is $'4'$.