How many even number in the range between 6 to 100 inclusive are not divisible by 3
How many even number in the range between 6 to 100 inclusive are not divisible by 3
Answer/Solution
32
Steps/Work
We have to find the number of terms that are divisible by 2 but not by 6( as the question asks for the even numbers only which are not divisible by 3)
For 2,
6,8,10,12,14...100
using AP formula, we can say 100 = 10 + (n-1) *2
or n=48.
For 6,
6,12,18,...96
using AP formula, we can say 96 = 12 + (n-1) *6
or n=16.
Hence, only divisible by 2 but not 3 = 48-16 = 32. hence, Answer C
For 2,
6,8,10,12,14...100
using AP formula, we can say 100 = 10 + (n-1) *2
or n=48.
For 6,
6,12,18,...96
using AP formula, we can say 96 = 12 + (n-1) *6
or n=16.
Hence, only divisible by 2 but not 3 = 48-16 = 32. hence, Answer C