Bunuel
All of the students who took a certain test answered the two first questions on the test. If 60% of the students answered the first question on the test correctly, and 40% of the students answered the second question on the test correctly, then what percent of the students answered neither of the two questions correctly?
(1) 20% of the students answered both the first and the second questions on the test correctly.
(2) Two thirds of the students who did not answer the second question on the test correctly answered the first question on the test correctly.
Given all the students answered the first two questions, hence the possible combinations can be
1) Q1 Incorrect; Q2 Correct
2) Q1 Correct ; Q2 Incorrect
3) Q1 Incorrect ; Q2 Incorrect
3) Q1 Correct ; Q2 Correct
Assume -
- Number of students (who answered the two first questions on the test) = 100
- The number of people who answered only Q1 correctly is represented by x
- The number of people who answered only Q2 correctly is represented by z
- The number of people who answered both Q1 & Q2 correctly is represented by y
- The number of people who answered neither Q1 correctly nor Q2 correctly is represented by z
Attachment:
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x + y = 60
y + z = 40
x + z + 2y = 100
Statement 1y = 20
Given the information of y, we can find the value of x, y, and z.
x = 60 - 20 = 40
z = 40 - 20 = 20
x + y + z = 80
m = 100 - 80 = 20
The statement is sufficient.
Statement 2\(y = \frac{2}{3} x\)
As the relationship between x and y is given, we can find values of x, y and z and use the same process used in statement 1 to find m.
The statement is also sufficient.
Option D