Tag: fun with numbers

Quizzes (2) Questions (69)

Questions Related to fun with numbers

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.

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

What is the series and also find the total of first $100$ consecutive odd numbers?

  1. $1 + 2 + 4 + 6 + 8 + 10 +... 100 = 12000$
  2. $2 + 3 + 4 + 7 + 9 + 11 +...100 = 10000$
  3. $1 + 3 + 5 + 7 + 10 + 11 +....100 = 1000$
  4. $1 + 3 + 5 + 7 + 9 + 11 +...100 = 10000$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Sum of first $100$ consecutive odd numbers $= 1 + 3 + 5 + 7 + 9 + 11 + ....+100 = 10000$
Since, we know the formula for sum of consecutive odd numbers $= n^2$
So, $n = 100$, Sum $= 100^2 = 10000$

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

Find the sum of two consecutive number for $13^2$.

  1. $84$ and $85$
  2. $83$ and $84$
  3. $86$ and $82$
  4. $81$ and $80$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the two consecutive numbers be, $\dfrac{n^{2} - 1}{2}$ and $\dfrac{n^{2} + 1}{2}$
$13^2= 169$
n = 13
$\dfrac{n^{2} - 1}{2} = \dfrac{13^{2} - 1}{2} = 84$
$\dfrac{n^{2} + 1}{2} = \dfrac{13^{2} + 1}{2} = 85$
So, the sum of two consecutive numbers = 84 + 85 = 169.

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

$21^{2}-1$ is a product of two consecutive even numbers. Find those numbers.

  1. 21 and 22

  2. 22 and 24

  3. 20 and 22

  4. 22 and 23
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$21^{2}-1 = 400$
we can express the above number into general form $a^{2}-1 = (a + 1)\times (a - 1)$
Where a = 21
So, $21^{2}-1 = (21 + 1)\times (21 - 1)$
= $22 \times 20 = 400$
Therefore, the two even consecutive numbers are 20 and 22.