Question

There are 20 numbers lying between the square of __ and __ numbers.
$
  {\text{A}}{\text{. 10 and 11}} \\
  {\text{B}}{\text{. 10 and 20}} \\
  {\text{C}}{\text{. 9 and 8}} \\
  {\text{D}}{\text{. 12 and 11}} \\
 $

Answer 1

Hint: Check every option. Square the numbers given in the option and find the difference between their squares.
Formula Used:
To know the count of numbers present between any two numbers say a and b-
a-b-1, where a is the larger of the two numbers.

Complete step-by-step answer:
Take the square of each number in every option and apply the formula.
Option A:
b=10 and a=11. Square of 10 is 100 and square of 11 is 121. Using the formula,
a-b-1 = 121-100-1 = 20
SO, 20 numbers lie between squares of 10 and 11.
Option B:
b=10 and a=20. Square of 10 is 100 and 20 is 400. Using the formula:
a-b-1 = 400-100-1 = 299
SO, 299 numbers lie between squares of 10 and 20.

Option C:
A=9 and b=8. Square of 9 is 81 and that of 8 is 64. Using the formula:
a-b-1 = 81-64-1 = 16
SO, 16 numbers lie between squares of 9 and 8.

Option D:
A=12 and b=11. Square of 12 is 144 and square of 11 is 121. Using formula:
a-b-1 = 144-121-1 = 22
SO, 22 numbers lie between squares of 11 and 12.
The correct option is A.

Note-
To do this question, a guess should be made to pick the correct option for evaluation by checking the numbers in between questions.