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.
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