SOLUTION: 75 percent of a class answered the first question on a certain test correctly, 55 percent answered the second question on the test correctly, 20 percent answered neither of the que

Question 979182: 75 percent of a class answered the first question on a certain test correctly, 55 percent answered the second question on the test correctly, 20 percent answered neither of the questions correctly. What percent answered exactly one question correctly?
Found 2 solutions by anand429, MathTherapy:
Answer by anand429(138) (Show Source): You can put this solution on YOUR website!
Let the strength of class be 100
So, students who answered both ques. wrong =20
So students who answered at least one correct = 80
Let no. of students who answered only 1st ques correct = x
Let no. of students who answered only 2nd ques correct = y
Let no. of students who answered both ques correct = z
Now, as per ques,
x+z = 75% of 100 = 75 ----(i)
y+z = 55% of 100 = 55 ----(ii)
Also, as derived earlier,
x+y+z = 80 ------(iii)
Subtracting (i) from (iii)
y = 5
Subtracting (ii) from (iii)
x = 25
So students, answering exactly one question = x+y = 30% (Since total taken 100,hence %)
Note: You can also use Venn diagram for this question.
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
75 percent of a class answered the first question on a certain test correctly, 55 percent answered the second question on the test correctly, 20 percent answered neither of the questions correctly. What percent answered exactly one question correctly?

% (see below)
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