The number of 3-digit numbers that are divisible by either 2 or 3 but not divisible by 7 i…

Question

The number of 3-digit numbers that are divisible by either $2$ or $3$ but not divisible by $7$ is \_\_\_\_\_\_\_\_.

Answer: 514

Accepted Answer

Among 3-digit numbers: divisible by $2$: $450$; by $3$: $300$; by $7$: $128$; by $2\&7$: $64$; by $3\&7$: $43$; by $2\&3$: $150$; by $2,3\&7$: $21$.

$450+300-150 - 64-43+21 = 514.$

Solutions · 1