Students Who Got Both Questions Correct

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A particular class was given a quiz consisting of two questions, which were marked either correct or incorrect. Of the 150 students, 100 got the first question correct and 120 got the second question correct. If at least 10 students got neither question correct, then the number of students who got both questions correct could be any number from

Review: Students Who Got Both Questions Correct


Explanation

This is an overlapping sets question of two sets, so we can draw a Venn diagram or cut straight to the formula . Filling in what we know, we get



We care about B, so we can isolate it:





The question tells us that N must be at least 10, so B must be at least 80. That narrows the answer choices to (D) and (E). From an arithmetic standpoint, B could range freely; the upper constraint is logically derived. It boils down to the fact that if 100 got the first question correct, then the number that got both questions correct cannot be greater than 100.

The correct answer is (D).


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