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
Palindrome MGMAT
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XYYX - Number formatrommysingh wrote: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
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
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For the 4-digit integer to be a palindrome: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
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.
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As a tutor, I don't simply teach you how I would approach problems.
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Take the task of building palindromes and break it into stages.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
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
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- 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
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Cheers,
Brent
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Here's a palindrome question I created for BTG a longggg time ago (for their Math Challenge Question contest):
Cheers,
Brent
For a full solution, watch the following YouTube video: https://youtu.be/qfiPnXIBx7gA 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?
Cheers,
Brent
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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
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