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 numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

In a number system the product of 44 and 11 is 3414 The number 3111 of this system when converted to the decimal number system becomes

  1. 406

  2. 1086

  3. 213

  4. 691
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The product of 44 and 11 is 484
If base is x then 3411
$3x^3+4x^2+1x^1+4x^0=484$
$3x^3+4x^2+x=480$
This equation is satisfy when x=5
then base is 5
In decimal system number 3111 will be  written
$3\times 5^3+1\times 5^2+1\times 5^1+1\times 5^0=406$

Multiple choice maths decimal numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

$3.\overline { 87 } -2.\overline { 59 } =$?

  1. $1.20$
  2. $1.\overline { 2 } $
  3. $1.\overline { 27 } $
  4. $1.\overline { 28 } $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$3.\overline { 87 } -2.\overline { 59 } =\left( 3+0.\overline { 87 }  \right) -\left( 2+0.\overline { 59 }  \right) $

$=\left( 3+\dfrac { 87 }{ 99 }  \right) -\left( 2+\dfrac { 59 }{ 99 }  \right) $

$=1+\left( \dfrac { 87 }{ 99 } -\dfrac { 59 }{ 99 }  \right) $

$=1+\dfrac { 28 }{ 99 } $

$=1.\overline { 28 } $.

Multiple choice maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

If $\displaystyle { a }^{ 2 }$ ends in 5, then $\displaystyle { a }^{ 3 }$ ends in 25.

  1. True

  2. False

  3. Ambiguous

  4. Insufficient information
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

False. 15 x 15=225 and 15 x 15 x 15=3375. so the statement $\displaystyle { a }^{ 2 }$ ends in 5, then $\displaystyle { a }^{ 3 }$ ends in 25 is not true in all cases.

Multiple choice maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

The value of $1^{2}+3^{2}+5^{2}+.....25^{2}$ is:

  1. $1728$
  2. $1456$
  3. $2925$
  4. $1469$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$1^2+3^2+5^2+....+25^2$

$\Rightarrow$  $(1^2+2^2+3^2+4^2+....+25^2)-(2^2+4^2+6^2+8^2....24^2)$

$\Rightarrow$  $(1^2+2^2+3^2+4^2+...25^2)-[(2\times 1)^2+(2\times 2)^2+(2\times 3)^2+....(2\times 12)^2]$

$\Rightarrow$  $(1^2+2^2+3^2+....+25^2)-2^2(1^2+2^2+3^2+.....12^2)$

$1^2+2^2+3^2+...+n^2=\dfrac{n(n+1)(2n+1)}{6}$

$\Rightarrow$  $\dfrac{25(25+1)(2\times 25+1)}{6}-2^2\dfrac{12(12+1)(2\times 12+1)}{6}$

$\Rightarrow$  $\dfrac{25\times 26\times 51}{6}-4\times\dfrac{12\times 13\times 25}{6}$

$\Rightarrow$  $25\times 13\times 17-4\times 2\times 13\times 25$

$\Rightarrow$  $25\times 13(17-8)$

$\Rightarrow$  $25\times 13\times 9$

$\Rightarrow$  $2925$