AAPL wrote:e-GMAT
50% of students' study science and 30% of students score more than 80% marks in the exam. If 40% of all students (science + non-science) get more than 80% marks in the exam, what percentage of non-science students score less than 80% marks?
A. 30%
B. 40%
C. 50%
D. 60%
E. 70%
Let the total number of students = 100.
Since 50% of the students study science, the number of science students = (50/100)(100) = 50, implying that the number of non-science students = 100-50 = 50.
Since 30% of the 50 science students score more than 80%, the number of science students who score more than 80% = (30/100)(50) = 15.
Since 40% of all 100 students score more than 80%, the total number of students who score more than 80% = (40/100)(100) = 40.
Thus, the number of non-science students who score more than 80% = 40-15 = 25.
Since 25 of the 50 non-science students score more than 80%, the remaining 25 non-science students score 80% or less.
Thus:
Percentage of non-science students who score 80% or less = 25/50 = 1/.2 = 50%.
The correct answer is
C.
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