Maths Olympiad Prep

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Problem 208

Algebra Difficulty 1.8 Find the answer CEMC Pascal

There are 20 students in a class. In total, 10 of them have black hair, 5 of them wear glasses, and 3 of them both have black hair and wear glasses. How many of the students have black hair but do not wear glasses?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

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Official solution

Since 10 students have black hair and 3 students have black hair and wear glasses, then a total of 103=710-3=7 students have black hair but do not wear glasses.

Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.