Palindrome MGMAT

[rommysingh]

A palindrome is a number that reads the same forward and backward, such as 121. How many odd, 4-digit numbers are palindromes?
40
45
50
90
2500

[theCEO]

A palindrome is a number that reads the same forward and backward, such as 121. How many odd, 4-digit numbers are palindromes?
40
45
50
90
2500

XYYX - Number format

number of choices for X = 5 [1,3,5,7,or 9]
number of choices for Y = 10 [0,1,2,3...,9]
Total possibities = 5 x 10 = 50

[GMATGuruNY]

A palindrome is a number that reads the same forward and backward, such as 121. How many odd, 4-digit numbers are palindromes?

A)40
B)45
C)50
D)90
E)2500

For the 4-digit integer to be a palindrome:
The THOUSANDS digit must be the SAME as the UNITS digit.
The TENS digit must be the SAME as the HUNDREDS digit.

Since the integer must be ODD, the number of options for the units digit = 5. (1, 3, 5, 7, or 9.)
Number of options for the thousands digit = 1. (Must be the SAME as the units digit.)
Number of options for the hundreds digit = 10. (Any digit 0-9.)
Number of options for the tens digit = 1. (Must be the SAME as the hundreds digit.)
To combine the options above, we multiply:
5*1*10*1 = 50.

The correct answer is C.

[Brent@GMATPrepNow]

A palindrome is a number that reads the same forward and backward, such as 121. How many odd, 4-digit numbers are palindromes?

A)40
B)45
C)50
D)90
E)2500

OAC

Take the task of building palindromes and break it into stages.
Begin with the most restrictive stage.

Stage 1: Select the units digit
We can choose 1, 3, 5, 7 or 9
So, we can complete stage 1 in 5 ways

Stage 2: Select the tens digit
We can choose 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9
So, we can complete stage 2 in 10 ways

IMPORTANT: At this point, the remaining digits are already locked in.

Stage 4: Select the hundred digit
This digit must be the SAME as the tens digit (which we already chose in stage 2)
So, we can complete this stage in 1 way.

Stage 5: Select the thousands digit
This digit must be the SAME as the units digit (which we already chose in stage 1)
So, we can complete this stage in 1 way.

By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus build a 4-digit palindrome) in (5)(10)(1)(1) ways ([spoiler]= 50 ways[/spoiler])

Answer: C
--------------------------

Note: the FCP can be used to solve the majority of counting questions on the GMAT. For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmat-counting?id=775

Then you can try solving the following questions:

EASY
- https://www.beatthegmat.com/what-should- ... 67256.html
- https://www.beatthegmat.com/counting-pro ... 44302.html
- https://www.beatthegmat.com/picking-a-5- ... 73110.html
- https://www.beatthegmat.com/permutation- ... 57412.html
- https://www.beatthegmat.com/simple-one-t270061.html
- https://www.beatthegmat.com/mouse-pellets-t274303.html


MEDIUM
- https://www.beatthegmat.com/combinatoric ... 73194.html
- https://www.beatthegmat.com/arabian-hors ... 50703.html
- https://www.beatthegmat.com/sub-sets-pro ... 73337.html
- https://www.beatthegmat.com/combinatoric ... 73180.html
- https://www.beatthegmat.com/digits-numbers-t270127.html
- https://www.beatthegmat.com/doubt-on-sep ... 71047.html
- https://www.beatthegmat.com/combinatoric ... 67079.html


DIFFICULT
- https://www.beatthegmat.com/wonderful-p- ... 71001.html
- https://www.beatthegmat.com/ps-counting-t273659.html
- https://www.beatthegmat.com/permutation- ... 73915.html
- https://www.beatthegmat.com/please-solve ... 71499.html
- https://www.beatthegmat.com/no-two-ladie ... 75661.html
- https://www.beatthegmat.com/laniera-s-co ... 15764.html

Cheers,
Brent

[Brent@GMATPrepNow]

Here's a palindrome question I created for BTG a longggg time ago (for their Math Challenge Question contest):

A palindrome is a word that is read the same backwards as forwards. For example, the words "BADAB," "IAGAI," and "HHHHH" are all palindromes.

How many 5-letter palindromes can be created using the letters A, B, C, D, E, F, G, H, I and J?

For a full solution, watch the following YouTube video: https://youtu.be/qfiPnXIBx7g

Cheers,
Brent

[nikhilgmat31]

Don't make a mistake to multiply 5 * 10 * 10 * 5

since thousand & unit digit should be same - we only have 5 choices - 1,3,5,7,9

since hundred & tenth digit should be same - we only have 10 choices 0 - 9

5* 10 = 50

Answer C