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

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Intern
Joined: 05 Aug 2015
Posts: 5
In an engineering class that contains 50 students, the final exam  [#permalink]

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14 May 2016, 05:08
1
4
00:00

Difficulty:

25% (medium)

Question Stats:

75% (01:42) correct 25% (02:26) wrong based on 107 sessions

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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?

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?
Math Expert
Joined: 02 Aug 2009
Posts: 7201
In an engineering class that contains 50 students, the final exam  [#permalink]

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14 May 2016, 06:33
1
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?

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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14 May 2016, 06:48
1
Answer will definitely be (A) as chetan2u has shown here is the grid approach ( in case you find it useful )
Attachment:

GRID.PNG [ 3.92 KiB | Viewed 1394 times ]

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Intern
Joined: 05 Aug 2015
Posts: 5
Re: In an engineering class that contains 50 students, the final exam  [#permalink]

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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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25 Apr 2017, 01:11
1
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?

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.

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

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01 Dec 2018, 19:33
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Re: In an engineering class that contains 50 students, the final exam &nbs [#permalink] 01 Dec 2018, 19:33
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