Question

How many integers between 100 and 200 are divisible by 6? (are there any shortcut method to get this?)

Answer 1

first such number -- 102
last such number -- 198

(198-102)/6 = 16

but !! .....

let's look at the first 4 of our numbers:
102 108 114 120

if I follow my above method
I would get (120-102)/6 = 3
notice I would not be counting the very first number

so our answer of 16 should be increased by 1

number of integers between 100 and 200 which divide evenly by 6 are 17

Can you generalize my method?

Answer 2

17