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

Question

A palindrome is a number, such as 32123, that reads the same forward and backward. How many palindromes are there between 100 and 1000?

A. 81
B. 88
C. 89 
D. 90
E. 91

Archit3110 · Answer

0 to 9 = 10 digits

palindromes = 9*10*1*1 = 90 IMO D

mskx · Answer

The number has 3 figures: XYX - the first X can be from 1-9, Y can be from 0-9, the 2nd X must have the same value as the first X, so only 1 possibility. 9*10*1 = 90 = D

sakshamjinsi · Answer

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

Mck2023 · Answer

Hi  Archit3110 
Can you please explain the process in detail?

Posted from my mobile device

GMATinsight · Answer

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

Archit3110 · Answer

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

GMATWhizTeam · Answer

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.

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

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

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