Question

Find the no. of terms between 100 and 500 that are divisible by 7 but not 21

Answer 1

Explanation:

First method:

Two ways to do it, the long way is to start listing them:

105

112

119

126

133

etc

and then finding the first one divisible by 21 (hint, it's 105) and then crossing out every third one.

Second Method:

The second way is subtract 500 - 100 = 400, so there are 400 numbers to consider, of which 1/7 is divisible by 7, so

400/7 = 57.1 which means there are 57.  Again, 1/3 of those will be divisible by 21 so 57/3 = 19 that are and 38 that are not.