enigma123
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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