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If 60 percent of a class answered the first question on a certain test

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Sajjad1994
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If 60 percent of a class answered the first question on a certain test [#permalink] New post   14 Aug 2019, 10:07
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If 60 percent of a class answered the first question on a certain test correctly, 60 percent answered the second question on the test correctly, and 60 percent answered both questions correctly, what percent answered neither question correctly?

A. 0%

B. 20%

C. 30%

D. 40%

E. 60%
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D
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Mohammadmo
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Re: If 60 percent of a class answered the first question on a certain test [#permalink] New post   14 Aug 2019, 10:11
100=60+60-60+X
X=100-60=40%
Option D

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Re: If 60 percent of a class answered the first question on a certain test [#permalink] New post   14 Aug 2019, 11:39
SajjadAhmad wrote:
If 60 percent of a class answered the first question on a certain test correctly, 60 percent answered the second question on the test correctly, and 60 percent answered both questions correctly, what percent answered neither question correctly?

A. 0%

B. 20%

C. 30%

D. 40%

E. 60%


Let total number of students be 100

1st Question Correct = 60

2nd Question Correct = 60

1st & 2nd Question Correct = 60

Let, Incorrect Answer be X

Now, We have 100 = 60 + 60 - 60 + x

Thus, Answer must be (D) 40
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If 60 percent of a class answered the first question on a certain test [#permalink] New post   Updated on: 15 Aug 2019, 07:59
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Whenever we encounter a question with two independent categories we can use a 2x2 table to solve it. The table looks like the following:


The 60% in the top right represents 60% of the students answered the 2nd question correctly, similarly for the 60% on the bottom it is for the 1st question. The 60% on the top left represents 60% of all students answered both questions correctly. Finally each row or column is an equation, for example in the last column out of 100% total there must be 40% who didn't answer the first question correctly. Then we can work out way towards the neither incorrect square and see it is 40%. This table method can be used to represent Venn diagrams and tree diagrams as well, so it is a great tool for bookkeeping values.

Originally posted by TestPrepUnlimited on 15 Aug 2019, 07:34.
Last edited by TestPrepUnlimited on 15 Aug 2019, 07:59, edited 1 time in total.
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If 60 percent of a class answered the first question on a certain test [#permalink] New post   15 Aug 2019, 14:00
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60 percent answered 1st ques correctly.
60 percent answered 2nd ques correctly.
and 60 percent answered both the ques correctly. Henceforth, all of them have to be the same candidates.
So, people who did not ans any of them correctly should be 40 percent
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Re: If 60 percent of a class answered the first question on a certain test [#permalink] New post   21 Aug 2019, 23:21
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Bunuel wrote:
If 60 percent of a class answered the first question on a certain test correctly, 60 percent answered the second question on the test correctly, and 60 percent answered both questions correctly, what percent answered neither question correctly?

A. 0%
B. 20%
C. 30%
D. 40%
E. 60%


Similar question to practice: https://gmatclub.com/forum/if-75-percen ... 44736.html
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Re: If 60 percent of a class answered the first question on a certain test [#permalink]
21 Aug 2019, 23:21
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