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A palindrome is a number that reads the same forward and

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Re: A palindrome is a number that reads the same forward and  [#permalink]

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New post 21 Apr 2018, 07:18
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enigma123 wrote:
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


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. So, be sure to learn it.

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Re: A palindrome is a number that reads the same forward and  [#permalink]

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New post 16 May 2018, 19:51
In the form of ABBA, where A must be an odd number, as it is required in the question.

So like some other users have mentioned above, A could only be 1 3 5 7 or 9 (5 numbers)

B could be any number from 0 to 9 (10 numbers)

5*10 = 50
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Re: A palindrome is a number that reads the same forward and  [#permalink]

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New post 13 Apr 2019, 18:51
enigma123 wrote:
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


So we have the 4-digit numbers in the form of ABBA where A is an odd number and B can be any digit including B = A.

Therefore, we have 5 choices for the first A and 10 choices for the first B. However, since the second A and B must be the same as the first A and B, respectively, there is only 1 choice for each of the second A and B. So we have 5 x 10 x 1 x 1 = 50 such numbers.

Answer: C
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Re: A palindrome is a number that reads the same forward and   [#permalink] 13 Apr 2019, 18:51

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