Question : Directions: In a group of 73 friends, 14 friends go to Gym and Karate classes, whereas 7 friends neither go to gym or Karate classes. If a total of 36 friends go to Gym class, then how many friends go to only Karate class?
Option 1: 30
Option 2: 32
Option 3: 44
Option 4: 23
Correct Answer: 30
Solution :
Given:
(I) In, a group of 73 friends, 14 friends go to Gym and Karate classes both.
(II) 7 friends neither go to Gym class nor Karate class.
(III) A total of 36 friends go to Gym class.
Solve the above–given statements by using a venn diagram.
In the figure below, the left circle shows friends going to the gym only, the right circle shows friends going to karate only. The intersection part shows friends going to both gym and karate. The outer part shows friends going neither gym nor karate.
According to statement 1→14 will be placed in the intersection part
According to statement 3→7 will be in the outer area
Total friends = 73
Total friends go to the gym = 36
Friends going to gym only = 36 – 14 = 22
Friends going to karate only = [73 – (22 + 14 + 7) = 73 – 43 = 30
So, friends going to karate only is equal to 30. Hence, the first option is correct.
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