Question

Which one is wrong in the given series?
49 36 25 18 9 4

A) 9 B) 18 C) 25 D) 49

Answer 1

Answer:

(B) 18

Step-by-step explanation:

Given a series such that,

49, 36, 25, 18, 9, 4

To find the wrong number.

On observation, we can write ,

• 49 = 7^2
• 36 = 6^2
• 25 = 5^2
• 18 = 2×3^2
• 9 = 3^2
• 4 = 2^2

Therefore, we came to know that,

All of the numbers are sauares of some natural numbers except one number.

That number is 18, which is not a square.

Thus, it violates the rule of the series.

Hence, the wrong number is (B) 18.

Answer 2

✎Given,

The given series is -

49 , 36 , 25 , 18 , 9 , 4

According to the analysis,

The numbers are perfect squares , except one number

where,

$49 = {(7)}^{2}$

$36 = {(6)}^{2}$

$25 = {(5)}^{2}$

$9 = {(3)}^{2}$

$4 = {(2)}^{2}$

The first six square numbers are -

1 , 4 , 9 , 16 , 25 , 36

which are squares of 1,2,3,4,5 and 6 respectively.

✎In the Given Question,

Every number is a square number except the number 18.

We also know that 18 is not a perfect square number.

18 can be written as -

$18 = { (3\sqrt{2} )}^{2} \\ = (3 \times 3 \times \sqrt{2} \times \sqrt{2} \\ = 3 \times 3 \times 2 \\ = 9 \times 2 \\ = 18$

Since 18 is not a perfect square number,

18 is the number which is given wrong in the series.

Option B is correct(18 is the wrong number in the given series).

We can define square number as-

A number , which , when multiplied by itself, gives a number , which is called a perfect square number.

For example,

$\implies8 \times 8 = 64$

Here, 8 ,when multiplied by itself(8) results in 64(perfect square number).