abhirup1711 wrote:A Palindrome is a number that the same forward and backward eg 242. How many even 5 digit numbers are palindromes?
40
400
500
5000
100000
So, our 5-digit number will look like this
XYZYX (where X, Y and Z represent digits)
We'll take the task of building 5-digit numbers and break it into stages.
Stage 1: choose the value of X
Since we need to have a 5-digit number, the first digit cannot be zero (e.g, 07470 is not a 5-digit value). Also, since the 5-digit number must be even, the units digit must be even.
So, the possible value of X are 2, 4, 6 and 8 (4 options)
So, we can complete stage 1 in
4 different ways
Stage 2: choose the value of Y
Y can be any digit from 0 to 9
So, we can complete stage 2 in
10 different ways
Stage 3: choose the value of Z
Z can be any digit from 0 to 9
So, we can complete stage 3 in
10 different ways
By the Fundamental Counting Principle (FCP) we can complete all 3 stages (and thus build a 5-digit number) in
(4)(10)(10) ways ([spoiler]= 400 ways = B[/spoiler])
Cheers,
Brent
Aside: For more information about the FCP, we have a free video on the subject:
https://www.gmatprepnow.com/module/gmat-counting?id=775
