Mathematics - Sequence & Series Question with Solution | TestHub

Four-digit numbers that are less than or equal to $2800$ are $\left\{1000,1001,1002,....,2800\right\}$

Numbers divisible by $3$ are $\left\{1002, 1005, ....,2796,2799\right\}$

Let total numbers be $n$, then

$1002+\left(n-1\right) 3=2799$ 

$\Rightarrow n=600$

Numbers divisible by $11$ are $\left\{1001, 1012, ..., 2794\right\}$

Let total numbers be $m$, then

$2794=1001+\left(m-1\right)11$

$\Rightarrow m=164$

Numbers divisible by $33$ are

$\left\{1023,1056,...,2772\right\}$

Let total numbers be $r$, then

$2772=1023+\left(r-1\right)33$

$\Rightarrow r=54$

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

$=600+164-54=710$