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

$11^{2}-1$ is a product of two consecutive even numbers. Find those two even numbers.

  1. 12 and 22

  2. 12 and 13

  3. 10 and 12

  4. 12 and 14
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$11^{2}-1 = 120$
we can express the above number into general form $a^{2}-1 = (a + 1)\times (a - 1)$
Where a = 11
So, $11^{2}-1 = (11 + 1)\times (11 - 1)$
= $12 \times 10 = 120$
Therefore, the two even consecutive numbers are 10 and 12.

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

Find the sum of two consecutive numbers for $15^2$.

  1. 112 and 113

  2. 113 and 114

  3. 115 and 112

  4. 113 and 115
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the two consecutive numbers be, $\dfrac{n^{2} - 1}{2}$ and $\dfrac{n^{2} + 1}{2}$
$15^2= 225$
n = 15
$\dfrac{n^{2} - 1}{2} = \dfrac{15^{2} - 1}{2} = 112$
$\dfrac{n^{2} + 1}{2} = \dfrac{15^{2} + 1}{2} = 113$
So, the sum of two consecutive numbers = 112 + 113 = 225.

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

$96^{2}-1$ is a product of two consecutive odd numbers. Find those two odd numbers.

  1. 96 and 98

  2. 93 and 95

  3. 95 and 97

  4. 99 and 101
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$96^{2}-1 = 9215$
we can express the above number into general form $a^{2}-1 = (a + 1)\times (a - 1)$
Where a = 96
So, $96^{2}-1 = (96 + 1)\times (96 - 1)$
= $97 \times 95 = 9215$
Therefore, the two odd consecutive numbers are 95 and 97.

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

Find the series and also find the total of first 10 consecutive odd numbers.

  1. $1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 100$
  2. $1 + 3 + 5 + 7 + 9 + 11 + 13 + 16 + 17 + 19 = 101$
  3. $1 + 3 + 5 + 7 + 10 + 11 + 13 + 15 + 17 + 19 = 101$
  4. $1 + 3 + 6 + 6 + 9 + 11 + 13 + 15 + 17 + 19 = 100$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Sum of first 10 consecutive odd numbers $= 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 100$
Since, we know the formula for sum of consecutive odd numbers = $n^2$
So, $n = 10$, Sum $= 10^2 = 100$

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

Observe the following pattern and find the missing number.
$12^2 = 144$
$102^2 = 10404$
$1002^2 = 1004004$
$10000002^2 = ? $

  1. $100400400004$
  2. $100000040000004$
  3. $100040040004$
  4. $100404000004004$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$12^2 = 144$
$102^2 = 10404$
$1002^2 = 1004004$
$10000002^2 = 100000040000004$
Start with 1 followed as many zeroes as there are between the first and the last 4, followed by two again followed by as many zeroes and end with 4.

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

Fill in the blanks:
$11^2 +8^2 + 3^2 = 19^2$
$12^2 + 2^2 + 10^2 = 14^2$
$14^2 + 7^2 $ + ____ = ____

  1. $7^2, 11^2$
  2. $14^2, 21^2$
  3. $7^2, 19^2$
  4. $7^2, 21^2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

From the pattern, the third number is the difference of the first two numbers.
The fourth number can be obtained by addition of the first two numbers.
Then, the missing numbers will be
$14^2 + 7^2 + 7^2 = 21^2$
So, $7^2, 21^2$ are the missing numbers.

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

Find the missing number of the pattern.
$3^2 + 6^2 + 18^2 = 19^2$
$4^2 + 3^2 + 12^2$ = ___

  1. $13^2$
  2. $19^2$
  3. $7^2$
  4. $18^2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

From the pattern, the third number is the product of the first two number.
The fourth number can be obtained by adding 1 to the third number.
Then, the missing number will be
$4^2 + 3^2 + 12^2 = 13^2$
So, $13^2$ is the missing number.

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

Find the missing number of the pattern.
$4^2 + 2^2 + 6^2 = 36^2$
$5^2 + 2^2 +$ ___ = $49^2$

  1. $13^2$
  2. $19^2$
  3. $7^2$
  4. $18^2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

From the pattern, the third number is the sum of the first two number.
The fourth number can be obtained by squaring the third number.
Then, the missing number will be
$5^2 + 2^2 +7^2 = 49^2$
So, $7^2$ is the missing number.