Question

a math tutor working with a small study group has classified students in the group by whether or not they scored 90% or above on each of three tests. the results are shown in the venn diagram to the right. use the venn diagram to represent the set of students who scored 90% or above on exam 1, not 90% or above on exam 3, and not 90% or above on exam 2 in roster form. choose the set of students who scored 90% or above on exam 1, not 90% or above on exam 3, and not 90% or above on exam 2. a. {al, ben, eva} b. {al, ben, eva, roz, gus, flo} c. {roz, gus, flo} d. {ny, jen, don, mel}

Explanation:

Step1: Analyze the conditions

We need students who scored ≥90% on exam 1 (so they are in the Exam 1 circle), not ≥90% on exam 3 (so they are not in the Exam 3 circle), and not ≥90% on exam 2 (so they are not in the Exam 2 circle).

Step2: Check each option

• Option A: {Al, Ben, Eva} are in Exam 1 circle, not in Exam 2 and Exam 3 circles.
• Option B: {Al, Ben, Eva, Roz, Gus, Flo} - Roz, Gus, Flo are in the intersection of Exam 1 and Exam 3 (for Roz) or in the intersection of all three (Gus, Flo), which violates the "not exam 3" condition.
• Option C: {Roz, Gus, Flo} - Roz is in Exam 3 (violates "not exam 3"), Gus and Flo are in all three exams (violate "not exam 2" and "not exam 3").
• Option D: {Ny, Jen, Don, Mel} - not in Exam 1 circle (violates "exam 1 ≥90%").

Answer:

A. {Al, Ben, Eva}