Question

Linda invited 200 people to her birthday party. 100 ate pizzas, 120 drank chocolate shakes, 80 ate sandwiches, and 10 had none of these three. 100 people had exactly one of the three items. How many people had two of the three items?

• A. 80
• B. 50
• C. 20
• D. 70

Answer 1

The correct option is D 70

Let's draw a Venn diagram and represent the data on it.
100 people had exactly one of the three items.

People having only one item (only pizza + only sandwich + only chocolate shake) represented in red color = 100 (given)
People having only two items represented in green color = B
People having all the three items = C
People having no item = 10 (given)

Total number of people = 200
100 + B + C + 10 = 200
110 + B + C = 200
B + C = 90

People who had exactly one item was counted once.
People who had exactly two items was counted twice.
People who had exactly three items was counted thrice.

100 + 2B + 3C = 100 + 120 + 80
100 + 2B + 3C = 300
2B + 3C = 300 – 100 = 200

Using the two equations, we can find the values of B and C.
B = 90 – C

2(90 – C) + 3C = 200
180 – 2C + 3C = 200
C = 200 – 180
C = 20

B = 90 – C
B = 90 – 20 = 70

So, 70 people had exactly two items.