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All of the students who took a certain test answered the two

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All of the students who took a certain test answered the two

by BTGmoderatorLU » Thu Mar 21, 2019 7:10 pm

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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
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Source: — Data Sufficiency |
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by deloitte247 » Fri Mar 29, 2019 7:33 pm

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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
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