In a group of 73 friends, 14 friends go to Gym and Karate classes both, whereas 7 friends neither go to Gym class nor to Karate class. If a total of 36 friends go to Gym class, then how many friends go to only Karate class?

30

THE LOGIC;

Let's denote the number of friends who go to both Gym and Karate classes as ($x)$. The total number of friends who go to Gym class is given as 36. The number of friends who neither go to Gym class nor Karate class is 7.

We can use the principle of inclusion-exclusion to find the number of friends who go to only Karate class.

Total friends = Gym only + Karate only + (Gym and Karate) + Neither

Given that the total number of friends is 73, we can write the equation:

$73=(36-x)+(\text{Karate only})+x+7$

Simplifying this equation, we get:

73 = 43 + Karate only 

Karate only=73−43

Karate only=30

Thus, 30 is correct.