Question

Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11 , is equal to

Answer 1

Answer: 710

$1000-2799$
Divisible by 3
$1002+(n-1)3=2799$
$n=600$
Divisible by 11
$1-2799\to \left[\frac{2799}{11}\right]=[254]=254$
$1-999=\left[\frac{999}{11}\right]=90$
$1000-2799=254-90=164$
Divisible by 33
$1-2799\to \left[\frac{2799}{33}\right]=84$
$1-999\to \left[\frac{999}{33}\right]=30$
$1000-2799\to 54$
$\therefore n(3)+n(11)-n(33)$
$600+164-54=710$