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PCAT Quantitative Reasoning – Probability of Green Eyes or Red Hair

If one in 40 people has green eyes and one in 50 people has red hair, how many people in a city of 230,000 have red hair or green eyes if 320 people in the city have both red hair and green eyes?

A. 9,710
B. 10,030
C. 10,350
D. 10,670

Click for Explanation

A is correct. First, let’s determine how many people in this city have green eyes and how many have red hair:

Keep in mind that 320 of those with green eyes also have red hair, and 320 of those with red hair also have green eyes. You can think of a Venn diagram where 320 people fall in the area where these two groups overlap. Let’s subtract those to identify those who have only green eyes or red hair:

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