Question

How many integers in the set
n is in Z
are divisible by 2 or 7?

Answer 1

Of the integers between 1 and 700 (inclusive), 350 of them are even:


`\left\lfloor\frac{700}2\right\rfloor=\lfloor350\rfloor=350`

100 of them are exact multiples of 7:


`\left\lfloor\frac{700}7\right\rfloor=\lfloor100\rfloor=100`

Half of these are multiples of 14:


`\left\lfloor(700)/(14)\right\rfloor=\lfloor50\rfloor=50`

This means the number of distinct integers in the given set that are multiples of 2 or 7 is


`350+100-50=400`