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If 75 percent of a class answered the first question on a ce

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If 75 percent of a class answered the first question on a ce [#permalink] New post 26 Dec 2012, 06:46
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If 75 percent of a class answered the first question on a certain test correctly, 55 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?

(A) 10%
(8) 20%
(C) 30%
(D) 50%
(E) 65%
[Reveal] Spoiler: OA
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Re: If 75 percent of a class answered the first question on a ce [#permalink] New post 18 Aug 2013, 04:25
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Attached Venn Diagram:

75-X+X+55-X+20=Total=100

X=50%

Hence the OA
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ssss.JPG [ 14.43 KiB | Viewed 5738 times ]


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Re: If 75 percent of a class answered the first question on a ce [#permalink] New post 26 Dec 2012, 06:48
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Walkabout wrote:
If 75 percent of a class answered the first question on a certain test correctly, 55 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?

(A) 10%
(8) 20%
(C) 30%
(D) 50%
(E) 65%


{Total} = {First} + {Second} - {Both} + {Neither}

100% = 75% + 55% - {Both} + 20% --> {Both} = 50%.

Answer: D.
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Re: If 75 percent of a class answered the first question on a ce [#permalink] New post 02 Nov 2014, 18:37
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appleid wrote:
PareshGmat wrote:
Refer diagram below:
Attachment:
ssss.JPG

We require to find the value of x

100 = 75 + 55 -x + 20

x = 50

Answer = D


I didn't understand how to connect 20 percent with the whole equation.
Why 20 is out of the percentile diagram (circles) but inside of 100?


20% appeared in the exam; however did not answer Question A & Question B correctly

So they are out of the two circles, however as they have appeared in the exam, they have to be taken into consideration for calculation purpose
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If 75 percent of a class answered the first question on a ce [#permalink] New post 02 Nov 2014, 21:35
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Walkabout wrote:
If 75 percent of a class answered the first question on a certain test correctly, 55 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?

(A) 10%
(8) 20%
(C) 30%
(D) 50%
(E) 65%



Let total no of students = 100

75% answered 1st Question Correct = 75 (Given)
Therefore, 25% answered 1st Question Incorrect = 25 (Derived)

55% answered 2nd Question Correct = 55 (Given)
Therefore, 45% answered 2nd Question Incorrect = 45 (Derived)

20% answered neither correct = 20 (Given)

Entering above data in tabular form, We get;

50% of students answered both Question 1 and Question 2 correctly.

Answer is D

Attachments

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exam.jpg [ 42.07 KiB | Viewed 432 times ]

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Re: If 75 percent of a class answered the first question on a ce [#permalink] New post 06 Sep 2014, 21:39
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Re: If 75 percent of a class answered the first question on a ce [#permalink] New post 08 Sep 2014, 00:33
Refer diagram below:
Attachment:
ssss.JPG
ssss.JPG [ 26.15 KiB | Viewed 1724 times ]

We require to find the value of x

100 = 75 + 55 -x + 20

x = 50

Answer = D
_________________

Kindly press "+1 Kudos" to appreciate :)

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Re: If 75 percent of a class answered the first question on a ce [#permalink] New post 02 Nov 2014, 12:56
PareshGmat wrote:
Refer diagram below:
Attachment:
ssss.JPG

We require to find the value of x

100 = 75 + 55 -x + 20

x = 50

Answer = D


I didn't understand how to connect 20 percent with the whole equation.
Why 20 is out of the percentile diagram (circles) but inside of 100?
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Re: If 75 percent of a class answered the first question on a ce [#permalink] New post 03 Nov 2014, 09:31
PareshGmat wrote:
appleid wrote:
PareshGmat wrote:
Refer diagram below:
Attachment:
ssss.JPG

We require to find the value of x

100 = 75 + 55 -x + 20

x = 50

Answer = D


I didn't understand how to connect 20 percent with the whole equation.
Why 20 is out of the percentile diagram (circles) but inside of 100?


20% appeared in the exam; however did not answer Question A & Question B correctly

So they are out of the two circles, however as they have appeared in the exam, they have to be taken into consideration for calculation purpose


I am doing it this way:
Suppose the total class size is 100, then 20 percent of the class answered incorrectly and rest 80 percent answered correctly in question 1 or 2 or both.

Now,
100 - [(75 - x) + x + (55 - x)] = 20 .......... values are in percent
x = 20 - 100 + 130
x = 50

Ans: D

Is it the right way?? Thanks for your reply (+1ed)
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If 75 percent of a class answered the first question on a ce [#permalink] New post 04 Nov 2014, 00:24
appleid wrote:
I am doing it this way:
Suppose the total class size is 100, then 20 percent of the class answered incorrectly and rest 80 percent answered correctly in question 1 or 2 or both.

Now,
100 - [(75 - x) + x + (55 - x)] = 20 .......... values are in percent
x = 20 - 100 + 130
x = 50

Ans: D

Is it the right way?? Thanks for your reply (+1ed)



Yes; this is absolutely correct :)
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If 75 percent of a class answered the first question on a ce   [#permalink] 04 Nov 2014, 00:24
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