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 decimal fraction multiplying decimals multiplication of decimals multiplication of division of decimal fraction by whole number and decimal fraction

If we write November 8, 1988, as 8.11.88, we see $8\times11=88$. How many such days are in 1972?

  1. 6

  2. 4

  3. 3

  4. 2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Multiples of 72 = 2,4,6,8,9,12,18,24,36,72
But in a year we have only 12 months and in a month we have only 30 days
So We have
$24.3.72 = 24\times 3 = 72$
$18.4.72 = 18\times 4 = 72$
$12.6.72= 12\times6 = 72$
$9.8.72 = 9\times8 = 72$
$8.9.72 = 8\times 9 = 72$
$6.12.72 = 6\times 12 = 72$

Multiple choice maths decimal fraction multiplying decimals multiplication of decimals multiplication of division of decimal fraction by whole number and decimal fraction

What is $27\times 1.\overline {2} \times 5.526\overline {2} \times 0.\overline {6}$ equal to?

  1. $121.5\overline {7}$
  2. $121.\overline {75}$
  3. $121.7\overline {5}$

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

It can be solved as $27\times 1.\overline {2} \times 5.526\overline {2} \times 0.\overline {6}$
$= 27\times \left (1 + \dfrac {2}{9}\right )\times \dfrac {6}{9} \times (5.526\overline {2})$
$= 27\times \dfrac {11}{9}\times \dfrac {2}{3}\times (5.526\overline {2})$
$= 22\times (5.526\overline {2})$
$= 22\times (5.5 + 0.026\overline {2})$
$= 121 + (22\times 0.026\overline {2})$
$= 121 + 0.\overline {57}$
$= 121.\overline {57}$

Multiple choice maths decimal fraction multiplying decimals multiplication of decimals multiplication of division of decimal fraction by whole number and decimal fraction

Number of zero's in the product of
$5 \times 10 \times 25 \times 40 \times 50 \times 55 \times 65 \times 125 \times 80 $

  1. $8$
  2. $9$
  3. $12$
  4. $13$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$5 \times 10 \times 25 \times 40 \times 50 \times 55 \times 65 \times 125 \times 80 $
$= 5 \times 2 \times 5 \times 5^2 \times 2^3 \times 5 \times 2 \times 5^2 \times 11 \times 5 \times 13 \times 5 \times 5^3 \times 2^4 \times 5$
$= 2^9 \times 5^{13}\times 11 \times 13 = (2 \times 5)^9 \times 5^4 \times 11 \times 13$


As we know that zeroes are formed by the product of a $2$ and a $5$ i.e. $2$ x $5$. 

Therefore, number of zeroes depends on the number of pairs of $2$'s and $5$'s that can be formed in the given product. 

Since $9$ pairs of $2$'s and $5$'s are formed in the given product, hence there will be $9$ zeroes in the given product.

Multiple choice maths decimal fraction multiplying decimals multiplication of decimals multiplication of division of decimal fraction by whole number and decimal fraction

Calculate $456.78\times 8$.

  1. $36542.4$
  2. $365.424$
  3. $3,654.24$
  4. $36.5424$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Let us first multiply the two given numbers $456.78$ and $8$ without decimal point:

$45678\times 8=365424$

Since, $456.78$ has two decimal places, therefore the answer $365424$ should also have two decimal places that is $3654.24$.

Hence, $456.78\times 8=3,654.24$.
Multiple choice maths decimal fraction multiplying decimals multiplication of decimals multiplication of division of decimal fraction by whole number and decimal fraction

$45.678\times \text{ ? }=1187.628$. Find $?$.

  1. $26$
  2. $27$
  3. $28$
  4. $29$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let $x$ be the missing number.


$45.678\times x=1187.628\ \Rightarrow 45.678x=1187.628\ \Rightarrow \dfrac { 45678x }{ 1000 } =\dfrac { 1187628 }{ 1000 } \quad \quad \quad \quad \quad \left{ \because \quad \dfrac { 1 }{ 10 } =0.1,\dfrac { 1 }{ 100 } =0.01,.... \right} \ \Rightarrow x=\dfrac { 1187628 }{ 1000 } \times \dfrac { 1000 }{ 45678 } \ \Rightarrow x=26$

Hence, the missing number is $26$.

Multiple choice maths decimal fraction multiplying decimals multiplication of decimals multiplication of division of decimal fraction by whole number and decimal fraction

Multiply $43.09$ with $23$.

  1. $99.107$
  2. $991.07$
  3. $9910.7$
  4. $9.9107$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Let us first multiply the two given numbers $43.09$ and $23$ without decimal point:
$4309\times 23=99107$
Since, $43.09$ has two decimal places, therefore the answer $99107$ should also have two decimal places that is $991.07$.
Hence, $43.09\times 23=991.07$.
Multiple choice maths decimal fraction multiplying decimals multiplication of decimals multiplication of division of decimal fraction by whole number and decimal fraction

Without actual multiplication, the value $79.01 \times 79.01 + 2 \times 79.01 \times 20.99 + 20.99 \times 20.99$

  1. $10,009$
  2. $1000.06$
  3. $10,000$
  4. $1007$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
$79.01\times 79.01+2\times 79.01\times 20.99+20.99\times 20.99....(1)$
$\dfrac {7901}{100}\times \dfrac {7901}{100}+2\times \dfrac {7901}{100}\times  \dfrac {2099}{100}+\dfrac {2099}{100}\times \dfrac {2099}{100}....(2)$

$7901\times 7901=(7901)^2 =(7900 +1)^2$    $\quad [\because \ 79^2=(80-1)^2\\ =80^2+1-2.80\\ =6400+1-160\\ =6241]$
$=(7900)^2 +1^2+2(7900)(1)$
$=62410000+1+15800$
$=62425801$ 

$2099\times 2099 =(2099)^2=(2100-1)^2$ $\quad [\because \ 21^2=(20+1)^2\\ =20^2+1+2.20\\ =400+40+1\\ =441]$
$=(2100)^2+1^2-2(2100)(1)$
$=4410000+1-4200$
$=4405801$

$7901\times 2099=(7900+1) (2100-1)$
$=(7900)(2100)-7900+2100-1$
$=16590000-7900+2100-1$
$=16584299\ =16584199$
from $(2)$
$\dfrac {62425801}{10000}+\dfrac {2\times 16584199}{10000}+\dfrac {4405801}{10000}$
$6242.5801+\dfrac {33168398}{10000}+440.5801$
$6242.5801+3316.8398+440.5801$
$=10,000$
Multiple choice maths introduction to euclid's geometry conditional statements and converse euclid's postulates axioms, postulates and theorems euclid's fifth postulate

By applying Euclid's division lemma $72$ and $28$ can be expressed as

  1. $28 = (72 - 16) \times 2$
  2. $72 = (28 \times 2) + 16$
  3. $72 = (28 \times 2) - 16$
  4. $16 = 72 - (28 + 2)$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Solution:

According to Euclid's division lemma if $a$ and $b$ are two numbers then they can be expressed as $b=ap+r.$
Therfore,
$72$ and $28$ can be expressed as
$72=(28\times2)+16$
So, $B$ is the correct option.