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)

• A. 819
• B. 900
• C. 625
• D. 729

Answer 1

The correct option is D 729

The number of four digit numbers divisible by $11=\frac{(9999-1001)}{11}+1=818+1=819$.

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 $=9\times 10=90$.

$\therefore$ The required number = 819 - 90 = 729.