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

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: 710

Accepted Answer

Range: $1000$ to $2799$.

Divisible by 3: first term $1002$, last term $2799$, common difference 3: $n=600$.

Divisible by 11: count up to $2799$ is $\lfloor2799/11\rfloor=254$; up to $999$ is $\lfloor999/11\rfloor=90$; so in range: $254-90=164$.

Divisible by 33 (both 3 and 11): up to $2799$: $\lfloor2799/33\rfloor=84$; up to $999$: $\lfloor999/33\rfloor=30$; in range: $84-30=54$.

$$\text{Total} = 600+164-54 = 710$$

Solutions · 1