Question

How many integers in the set {n is in Z | 1 ≤ n ≤ 700} are divisible by 2 or 7?

Answer 1

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

$\left\lfloor\dfrac{700}2\right\rfloor=\lfloor350\rfloor=350$

100 of them are exact multiples of 7:

$\left\lfloor\dfrac{700}7\right\rfloor=\lfloor100\rfloor=100$

Half of these are multiples of 14:

$\left\lfloor\dfrac{700}{14}\right\rfloor=\lfloor50\rfloor=50$

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

$350+100-50=400$