In a class of 20 students, 12 pass math, 15 pass science, and 9 pass both. How many pass at least one?

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Multiple Choice

In a class of 20 students, 12 pass math, 15 pass science, and 9 pass both. How many pass at least one?

When counting who passes at least one subject, add the people in each group, then subtract the overlap because those who pass both are included in both counts. Here, 12 pass math, 15 pass science, and 9 pass both. So the total is 12 + 15 − 9 = 18. This also means 2 students fail both, since there are 20 students in total. The other numbers don’t work because they ignore some of the groups (math-only, science-only, or those who pass both), which leads to undercounting.

When counting who passes at least one subject, add the people in each group, then subtract the overlap because those who pass both are included in both counts. Here, 12 pass math, 15 pass science, and 9 pass both. So the total is 12 + 15 − 9 = 18. This also means 2 students fail both, since there are 20 students in total. The other numbers don’t work because they ignore some of the groups (math-only, science-only, or those who pass both), which leads to undercounting.

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