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In an engineering class that contains 50 students, the final exam

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In an engineering class that contains 50 students, the final exam [#permalink]

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New post 14 May 2016, 05:08
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Question Stats:

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In an engineering class that contained 50 students, the final exam consisted of 2 questions. Three fifths of the students answered the first question correctly. If four fifths of the remainder answered the second question correctly, how many students answered both questions incorrectly?

Answer Options

A) 4
B) 6
C) 10
D) 12
E) 24

I thought the answer was E but it's not. Can anybody give me a detailed explanation of the solution please?
[Reveal] Spoiler: OA
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In an engineering class that contains 50 students, the final exam [#permalink]

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New post 14 May 2016, 06:33
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mmch wrote:
In an engineering class that contained 50 students, the final exam consisted of 2 questions. Three fifths of the students answered the first question correctly. If four fifths of the remainder answered the second question correctly, how many students answered both questions incorrectly?

Answer Options

A) 4
B) 6
C) 10
D) 12
E) 24

I thought the answer was E but it's not. Can anybody give me a detailed explanation of the solution please?



Hi,
we are looking for students who answered BOTH Qs incorrectly..
1st Question : Three fifths of the students answered the first question correctly - so \(\frac{3}{5} *50 = 30\)
2nd Question : four fifths of the remainder answered the second question correctly so \(\frac{4}{5}* (50-30) = \frac{4}{5} * 20 = 16\)..
total students who answered atleast one Q correct =\(30+16 = 46\)..
so students who answered BOTH incorrectly = \(50-46 = 4\)
A
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Re: In an engineering class that contains 50 students, the final exam [#permalink]

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New post 14 May 2016, 06:48
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Answer will definitely be (A) as chetan2u has shown here is the grid approach ( in case you find it useful )
Attachment:
GRID.PNG
GRID.PNG [ 3.92 KiB | Viewed 879 times ]

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Re: In an engineering class that contains 50 students, the final exam [#permalink]

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New post 14 May 2016, 07:00
Thank you guys! The explanation helped a lot!
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Re: In an engineering class that contains 50 students, the final exam [#permalink]

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New post 25 Apr 2017, 01:11
mmch wrote:
In an engineering class that contained 50 students, the final exam consisted of 2 questions. Three fifths of the students answered the first question correctly. If four fifths of the remainder answered the second question correctly, how many students answered both questions incorrectly?

Answer Options

A) 4
B) 6
C) 10
D) 12
E) 24

I thought the answer was E but it's not. Can anybody give me a detailed explanation of the solution please?


Total number of students: 50

No. of students who answered the 1st question correctly: 3/5 of 50 =30
No. of students who answered the 2nd question correctly: 4/5 of remaining i.e. 20 = 16.

Since, the students have to answer the questions and 46 of them answered at least one of them correctly, therefore students who have answered both incorrectly would be 50-46 = 4.

Answer: A
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Re: In an engineering class that contains 50 students, the final exam   [#permalink] 25 Apr 2017, 01:11
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