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 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

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

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

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

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

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

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

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

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

$\Rightarrow$  $25\times 13(17-8)$

$\Rightarrow$  $25\times 13\times 9$

$\Rightarrow$  $2925$

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

Having $5$ at units place, find the square of the number $185$.

  1. $34225$
  2. $48034$
  3. $15620$
  4. $83450$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$185$ $=$ $(200-15)$

$185^{2}$ $=$ $(200-15)^{2}$
$(200-15)^{2}$ $=$ $200^{2}$ $+$ $15^{2}$ $-$ $2\times200\times15$
$185^{2}$ $=$ $40000$ $+$ $225$ $-$$6000$
$185^{2}$ $=$ $34225$
Hence, Option A is correct.