GMAT Focus EditionQuantitative ReasoningHard
A survey of 200 students found that 120 students like coffee, 90 students like tea, and 50 students like neither coffee nor tea. How many students like both coffee and tea?
- A40
- B60
- C80
- D50
Show answer & explanationAnswer & explanation
Correct answer: B. 60
Let C be the set of students who like coffee and T be the set of students who like tea. Total students = 200. Students who like neither = 50. So, students who like at least one beverage = Total - Neither = 200 - 50 = 150. Using the Inclusion-Exclusion Principle: |C U T| = |C| + |T| - |C ∩ T|. We have 150 = 120 + 90 - |C ∩ T|. So, 150 = 210 - |C ∩ T|. Therefore, |C ∩ T| = 210 - 150 = 60.
Why the other options are wrong
- A. This is incorrect; it might be a result of miscalculation or misapplication of the formula.
- C. This is incorrect; it might be a result of miscalculation or misapplication of the formula.
- D. This is incorrect; this is the number of students who like neither, not both.
Inclusion-Exclusion Principle (Two Sets)
A counting technique that finds the number of elements in the union of two sets by summing the sizes of the individual sets and subtracting the size of their intersection.
- Formula: |A U B| = |A| + |B| - |A ∩ B|.
- Used to avoid double-counting elements that are common to both sets.
- Often applied in probability and set theory problems.
Memory trick: Total = A + B - Both + Neither.