Tag: fun with numbers

Questions Related to fun with numbers

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

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

  1. True

  2. False

  3. Ambiguous

  4. Insufficient information

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Correct Option: B
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.

If $\displaystyle n = 1 + x $, where $x$ is the product of four consecutive positive integers then which of the following is/are true:
A) n is odd

B) n is prime
C) n is a perfect square

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

  1. A and C only

  2. A and B only

  3. A only

  4. None of these

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Correct Option: A
Explanation:

Let us take $\displaystyle x=1\times2\times3\times4=24 $

Then $\displaystyle n=1+24=25$
i.e. an odd number and a perfect square
Again let $\displaystyle x=2\times3\times4\times5=120.$
Then, $\displaystyle n=1+120=121$
i.e. an odd number and a perfect square
$\displaystyle \therefore $ Option (A) is correct

The squares of which of the following would be odd numbers:
$431$
$2826$
$7779$
$82004$

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

  1. $431$ and $7779$

  2. $431$ and $2826$

  3. $2826$ and $7779$

  4. $2826$ and $82004$

Show answer
Correct Option: A
Explanation:

The squares of $431\;and\;7779$ would be odd numbers.
(Because we know that squares of odd numbers are always odd). 

The sum of  first eight odd numbers is 

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

  1. 64

  2. 74

  3. 80

  4. 95

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Correct Option: A
Explanation:

The sum of the first odd numbers is,


$1+3+5+7+9+11+13+15= 64$

So option A is the correct answer

$121$ can also be represented as ?

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

  1. $40+41$

  2. $11^2$

  3. $120+3$

  4. All of these

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Correct Option: B
Explanation:

$11 \times 11= 121$ 

$= 11^2$
Thus option $B$ is correct

$5^2=?$

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

  1. $25$

  2. $15$

  3. $14$

  4. $12+13$

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Correct Option: A,D
Explanation:

52 = 5  × 5 = 25 = 12 + 13

The value of $3^2$ is

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

  1. $9$

  2. $4+5$

  3. $8$

  4. None of these

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Correct Option: A,B
Explanation:

$3^2$ means taking square of $3$, i.e. $3\times 3=9$

$9$ can be written as addition of $9=4+5$.
Hence, options A and B are correct.

$24+25=?$

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

  1. $49$

  2. $34$

  3. $7^2$

  4. $36$

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Correct Option: A,C
Explanation:

24 + 25 = 49 = 72

Which of the following option matches with $361$?

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

  1. $360+1$

  2. $19^2$

  3. $180+181$

  4. None of these

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Correct Option: A,B,C
Explanation:

361 = 19 × 19 = 192
361 = 360 + 1 = 180 + 181

Evaluate: $220+221$

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

  1. $437$

  2. $441$

  3. $21^2$

  4. None of these

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Correct Option: B,C
Explanation:

220 + 221 = 441 = 21  × 21 = 212