Question

In a survey of 250 people about three activities (Reading, Sports, Travel), the following data are given:
130 like Reading,
110 like Sports,
120 like Travel,
55 like both Reading and Sports,
50 like both Sports and Travel,
45 like both Reading and Travel,
25 like all three.
How many like only Travel?

• A. 35
• B. 40
• C. 45
• D. 50

Hint:

For “only” in three-set Venn problems, always subtract the two-way intersections and add back the three-way intersection.

Answer 1

The Correct Option is D

Step 1: People who like Travel AND at least one other activity = (Reading&Travel) + (Sports&Travel) - (all three), since the all-three group would otherwise be counted twice: \(45+50-25=70\).
Step 2: Subtract this from the total who like Travel to isolate those who like Travel and nothing else.
\[ 120 - 70 = \boxed{50} \]
Final Answer: 50.