Source: Economist GMAT
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.
The OA is D
All of the students who took a certain test answered the two
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Let the number of students that got the first question correctly = w
let the number of students that got the second question correctly = x
let the number of students that got the first question wrong = y
And lastly, let the number of students that got the second question wrong = z
With w = 60% and x = 40%, we are to find the percentage of students that answered neither of the two questions correctly.
Statement 1: 20% of students answered both the first and second question correctly. So, wx = 20%.
w + x + wx + yz = 100%
(60-20)% + (40-20)% + 20% + yz = 100%
40% + 20% + 20% + yz = 100%
80% + yz = 100%
yz = 20%
So, 20% of students got wrong answer for the z questions. Statement is SUFFICIENT
Statement 2: Two-third of the students who did not answer the second question of the test correctly answered the first question of the test correctly.
z = 60%
$$zw=\frac{2}{3}\cdot60\%=40\%$$
Since, w=60% and wx=20%. Then,
(60-20)% + (40-20)% + 20% + yz = 100%
80% + yz = 100%
yz = 20%
Statement 2 is also SUFFICIENT.
The correct answer is OPTION D
let the number of students that got the second question correctly = x
let the number of students that got the first question wrong = y
And lastly, let the number of students that got the second question wrong = z
With w = 60% and x = 40%, we are to find the percentage of students that answered neither of the two questions correctly.
Statement 1: 20% of students answered both the first and second question correctly. So, wx = 20%.
w + x + wx + yz = 100%
(60-20)% + (40-20)% + 20% + yz = 100%
40% + 20% + 20% + yz = 100%
80% + yz = 100%
yz = 20%
So, 20% of students got wrong answer for the z questions. Statement is SUFFICIENT
Statement 2: Two-third of the students who did not answer the second question of the test correctly answered the first question of the test correctly.
z = 60%
$$zw=\frac{2}{3}\cdot60\%=40\%$$
Since, w=60% and wx=20%. Then,
(60-20)% + (40-20)% + 20% + yz = 100%
80% + yz = 100%
yz = 20%
Statement 2 is also SUFFICIENT.
The correct answer is OPTION D