GMAT Focus EditionQuantitative ReasoningMedium
In a survey of 300 students, 180 students indicated they like pizza, and 120 students indicated they like burgers. If 70 students like both pizza and burgers, how many students like neither pizza nor burgers?
- A70
- B90
- C80
- D100
Show answer & explanationAnswer & explanation
Correct answer: A. 70
Use the Inclusion-Exclusion Principle: Total = A + B - (A and B) + Neither. Here, Total = 300, A = 180 (pizza), B = 120 (burgers), (A and B) = 70. So, 300 = 180 + 120 - 70 + Neither. This simplifies to 300 = 300 - 70 + Neither, so 300 = 230 + Neither. Therefore, Neither = 300 - 230 = 70.
Why the other options are wrong
- B. This could be an error in subtracting the 'both' group or the final subtraction from the total.
- C. This might result from a miscalculation or incorrect application of the formula.
- D. This would be the case if the 'both' group was not subtracted from the sum of individuals.
Inclusion-Exclusion Principle (Two Sets)
A counting technique used to find 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.
- |A U B| = |A| + |B| - |A ∩ B|
- For problems involving 'neither': Total = |A| + |B| - |A ∩ B| + |Neither|
- It prevents double-counting elements that belong to both sets.
Memory trick: Add, subtract overlap, then subtract from total to get outside!