VJesus12 wrote: ↑Wed Nov 17, 2021 7:59 am
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
Answer:
C
Source: Manhattan GMAT
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 (= 50 ways)
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 this video:
https://www.gmatprepnow.com/module/gmat- ... /video/775
You can also watch a demonstration of the FCP in action:
https://www.gmatprepnow.com/module/gmat ... /video/776
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
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https://www.beatthegmat.com/picking-a-5- ... 73110.html
-
https://www.beatthegmat.com/permutation- ... 57412.html
-
https://www.beatthegmat.com/simple-one-t270061.html
MEDIUM
-
https://www.beatthegmat.com/combinatoric ... 73194.html
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https://www.beatthegmat.com/arabian-hors ... 50703.html
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https://www.beatthegmat.com/sub-sets-pro ... 73337.html
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https://www.beatthegmat.com/combinatoric ... 73180.html
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https://www.beatthegmat.com/digits-numbers-t270127.html
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https://www.beatthegmat.com/doubt-on-sep ... 71047.html
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https://www.beatthegmat.com/combinatoric ... 67079.html
DIFFICULT
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https://www.beatthegmat.com/wonderful-p- ... 71001.html
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https://www.beatthegmat.com/permutation- ... 73915.html
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https://www.beatthegmat.com/permutation-t122873.html
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https://www.beatthegmat.com/no-two-ladie ... 75661.html
-
https://www.beatthegmat.com/combinations-t123249.html
Cheers,
Brent
