A palindrome is a number, such as 32123, that reads the same forward

The question is basically asking for the number of 3 digit palindromic numbers.

__ __ __ For the 1st blank there are 9 possibilities. (Since, 1st digit cannot be zero)
For the 2nd blank there are 10 possibilities. (the middle digit does not matter - will remain the same forwards and backwards)
For the 3rd blank there is only 1 possibility. (Since the 3rd digit must be the same as the 1st digit)

Next, multiply the number of possibilities for each digit: 9*10*1 = 90. OA: D

Hi Archit3110
Can you please explain the process in detail?

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Observation 1:

Between 100 and 1000, all the palindrome numbers will be 3 digit numbers

Observation 2:

Unit digit of the number will be same as the hundreds digit i.e _ _ _

Calculation:

Hundred's digit can be filled by any digit from 1 to 9 i.e. in 9 ways and Unit digit must be same as hundreds digit i.e. it has only one choice
i.e 9 _ 1

Tens digit can be filled by any digit from 0 to 9 i.e. 10 ways

i.e. Total Numbers = 9*10*1 = 90

ANswer: Option D

Mck2023

Mck2023

total digits are 10 (0-10)
for a 3 digit palindrome that reads the same forward and backward
hundredth's we have 9 places
tens 10 (0 to 9)
and units as place ; 9*10*1 ; 90

Palindromes between 100 and 1000 are essentially three-digit palindromes. Examples of three-digit palindromes could be numbers like 111, 121, 242, 353 and so on.
From this stage onwards, this question can be solved very easily by following the space filling approach.

Let us use 3 blanks to represent the three digits of the number,
__ __ __

the left most blank representing the hundreds’ digit, the middle blank representing the tens’ digit and the right most blank representing the units’ digit of the number.

The hundreds’ digit can be filled in 9 different ways, since this digit cannot be filled with Zero.
The tens’ digit can be filled in 10 different ways, since this digit CAN be filled with Zero.
The units’ digit can be filled in 1 way since this digit MUST be the same digit as the one in the hundreds’ place.

Therefore, number of palindromes between 100 and 1000 = 9 * 10 * 1 = 90.
The correct answer option is D.