If 75 percent of a class answered the first question
on a certain test correctly, 55 percent answered the
second question on the test correctly, and 20 percent
answered neither of the questions correctly, what
percent answered both correctly?
(A) 10%
(B) 20%
(C) 30%
(D) 50%
(E) 65%
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20% answered neither correctly. So 80% would have answered one or both correctly.
80=75+55-Both
Both = D D
80=75+55-Both
Both = D D
- GmatMathPro
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Assume 100 people. 20 answered neither question correctly, so 80 answered at least one question correctly. 75+55=130, but the people who answered both correctly are counted in each group, and we only want to count them once. Let x=the number of people who answered both correctly. 130-x=80. x=50. So, 25 answered only the first correctly, 5 answered only the second correctly, 50 answered both correctly, and 20 answered neither correctly. 25+5+20+50=100, so it checks out.
So, [spoiler]D. 50%[/spoiler] is the answer
So, [spoiler]D. 50%[/spoiler] is the answer
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For this overlapping sets problem, we can use the following equation:gmatblood wrote:If 75 percent of a class answered the first question
on a certain test correctly, 55 percent answered the
second question on the test correctly, and 20 percent
answered neither of the questions correctly, what
percent answered both correctly?
(A) 10%
(B) 20%
(C) 30%
(D) 50%
(E) 65%
Total percent = % in category A + % in category B - % in both categories + % in neither category
Since the answer choices are in percentage form we can use 100 as the total. We are given that 75 percent of a class answered the first question on a certain test correctly, 55 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly. Using these values, we have:
100 = 75 + 55 - B + 20
100 = 150 - B
B = 50
Answer: D
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