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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]

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26 Dec 2012, 07:46
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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]

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26 Dec 2012, 07:48
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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%

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

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

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Re: If 75 percent of a class answered the first question on a ce [#permalink]

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18 Aug 2013, 05:25
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Attached Venn Diagram:

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

X=50%

Hence the OA
Attachments

ssss.JPG [ 14.43 KiB | Viewed 18560 times ]

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If 75 percent of a class answered the first question on a ce [#permalink]

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02 Nov 2014, 22:35
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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%

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.

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exam.jpg [ 42.07 KiB | Viewed 13285 times ]

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Re: If 75 percent of a class answered the first question on a ce [#permalink]

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02 Nov 2014, 19:37
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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

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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Re: If 75 percent of a class answered the first question on a ce [#permalink]

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06 Sep 2014, 22:39
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Re: If 75 percent of a class answered the first question on a ce [#permalink]

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08 Sep 2014, 01:33
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Refer diagram below:
Attachment:

ssss.JPG [ 26.15 KiB | Viewed 14553 times ]

We require to find the value of x

100 = 75 + 55 -x + 20

x = 50

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Re: If 75 percent of a class answered the first question on a ce [#permalink]

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02 Nov 2014, 13:56
PareshGmat wrote:
Refer diagram below:
Attachment:
ssss.JPG

We require to find the value of x

100 = 75 + 55 -x + 20

x = 50

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]

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03 Nov 2014, 10:31
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

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

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If 75 percent of a class answered the first question on a ce [#permalink]

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04 Nov 2014, 01:24
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

Yes; this is absolutely correct
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Re: If 75 percent of a class answered the first question on a ce [#permalink]

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22 Nov 2015, 04:05
I don't know why this question took me quite some time to understand. It appears so simple, yet I couldn't grasp it at first.

My solution:
Looking for x = #students who got Q1 AND Q2 correct
100 students
20 got both Q1 and Q2 incorrect
100 - 20 = 80

80 = (#students who got Q1 correct) + (#students who got Q2 correct) + (#students who got Q1 AND Q2 correct)

#students who got Q1 correct = 75 - x
#students who got Q2 correct = 55 - x
#students who got Q1 and Q2 correct = x

That gives us 80 = (75 - x) + (55 - x) + x
Solve for x, gives us x = 50.
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Re: If 75 percent of a class answered the first question on a ce [#permalink]

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13 Jul 2016, 07:33
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%

For this overlapping sets problem we can use the following equation:

Total percent = % in category A + % in category B – % in both categories + % in neither categories

Since the answer choices are in percentage form we can use 100 as the total. We are given that 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. Using these values, we have:

100 = 75 + 55 – B + 20

100 = 150 – B

B = 50

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Re: If 75 percent of a class answered the first question on a ce [#permalink]

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14 Oct 2016, 22:45
I suggest the fastest way to do 2 variable is by using the table, will save a lot of time
Re: If 75 percent of a class answered the first question on a ce   [#permalink] 14 Oct 2016, 22:45
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