Both coffee and tea – given at least one of the two: In a group of 70 people, 37 like coffee and 52 like tea. Each person likes at least one of coffee or tea. How many like both?

Introduction / Context:
When everyone likes at least one of two options, the size of the union equals the total. We can recover the intersection from inclusion-exclusion.

Given Data / Assumptions:

• Total = 70
• |Coffee| = 37
• |Tea| = 52
• Everyone likes at least one → |Coffee ∪ Tea| = 70

Concept / Approach:
|C ∩ T| = |C| + |T| − |C ∪ T|.

Step-by-Step Solution:
|C ∩ T| = 37 + 52 − 70 = 19

Verification / Alternative check:
Only-coffee = 37 − 19 = 18; Only-tea = 52 − 19 = 33; 18 + 19 + 33 = 70.

Why Other Options Are Wrong:
17, 21, 23 contradict the computed overlap.

Common Pitfalls:
Using 37 + 52 as if no overlap existed.

Final Answer:
19