Question
How many four-digit numbers divisible by 11 are not palindromes? (A palindrome is a number that reads the same in either direction, e.g. 121)
Answer: Option D
:
D
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D
The number of four digit numbers divisible by 11=(9999−1001)11+1=818+1=819.
A four-digit palindrome can be written as xyyx then, as (x+y) - (y+x) = 0, it is always divisible by 11. For xyyx, x can be chosen from 1 to 9 and y from 0 to 9.
Hence, the number of four-digit palindrome numbers =9×10=90.
∴ The required number = 819 - 90 = 729.
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