Question

Which of the following alternative will fit in place of R?

649, 256, 498, 8110, R
(1) 147 (2) 189 (3) 165 (4) 179

Answer 1

Working out:

The above question is a series following a certain rule, and we have to find the next number by using the same rule.

GiveN Series:

• 649, 256, 498, 8110, R

To find the number in place of R....?

Let's see the LOGIC !

All the numbers are having digits and the logic is hidden in it. So, let's checkout these numbers.

$\large{ \underline{ \red{64}}} \: \underline{9}$

• 64 is the square of 8
• And 9 is the successor of 8.

$\large{ \underline{ \red{25}}} \: \underline{6}$

• 25 is the square of 5
• 6 is the successor of 5.

$\large{ \underline{ \red{49}}} \: \underline{8}$

• 49 is the square of 7
• 8 is the successor of 7.

$\large{ \underline{ \red{81}}} \: \underline{10}$

• 81 is the square of 9
• 10 is the successor of 9.

So, let's see the options which satisfy the above rule.

• 147 - 14 is not a perfect square.
• 189 - 18 is not a perfect square.
• 179 - 17 is not a perfect square.

But 165, Here 16 is the square of 4 and 5 is the successor of 4. So, it is satisfying the above rule. R = 165

The correct option is:

$\LARGE{ \boxed{ \bf{ \purple{Option \: C}}}}$

And we are done !!

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Answer 2

Working with the Question:-

• Here in the question we have to find out the nest number given in the series.

SeRies:-

• 649, 256, 498, 8110, R
• So here we have to find out the number to be placed at 'R'.

$\large\mathtt \purple{ \underline{S᭄olution}} :-$

• A trick is used here.
• Let's see what's the trick.

✿64 9

• Square of 8 is 64.
• 9 is the successor of 8.

✿25 6

• Same here, Square of 5 is 25.
• 6 is successor of 5.

✿49 8

• 49 is the square of 7.
• 8 is the successor of 7.

✿81 10

• 81 is the square of 9.
• 10 is the successor of 9.

So here, We will use Trial and Error Method:-

• 147:- Not a perfect square.
• 189:- Not a perfect square.
• 179:- Not a perfect square.

Here, 16 5

• 16 is the square of 4.
• 5 is the successor of 4.

Hence,

The answer we got is

$\large\mathtt\pink{Option \: C}$