The number of 4-digit numbers which are neither a multiple of 7 nor a multiple of 3 is ___…

Question

The number of 4-digit numbers which are neither a multiple of $7$ nor a multiple of $3$ is \_\_\_\_\_\_\_\_.

Answer: 5143

Accepted Answer

Total 4-digit numbers: $9000$. Multiples of $7$: $1286$; multiples of $3$: $3000$; multiples of $21$: $429$.

By inclusion--exclusion: multiples of $3$ or $7$: $1286+3000-429 = 3857$.

$9000-3857 = 5143.$

Solutions · 1