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Manager  Joined: 02 Dec 2012
Posts: 174
If 75 percent of a class answered the first question on a ce  [#permalink]

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4
28 00:00

Difficulty:   5% (low)

Question Stats: 83% (01:27) correct 17% (01:52) wrong based on 1083 sessions

### HideShow timer Statistics 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%
Math Expert V
Joined: 02 Sep 2009
Posts: 56244
Re: If 75 percent of a class answered the first question on a ce  [#permalink]

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12
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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9
3
Attached Venn Diagram:

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

X=50%

Hence the OA
Attachments ssss.JPG [ 14.43 KiB | Viewed 46541 times ]

##### General Discussion
SVP  Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1787
Location: India
Concentration: General Management, Technology
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Re: If 75 percent of a class answered the first question on a ce  [#permalink]

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3
1
Refer diagram below:
Attachment: ssss.JPG [ 26.15 KiB | Viewed 42567 times ]

We require to find the value of x

100 = 75 + 55 -x + 20

x = 50

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Kindly press "+1 Kudos" to appreciate Intern  Joined: 22 Oct 2014
Posts: 27
Re: If 75 percent of a class answered the first question on a ce  [#permalink]

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1
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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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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If 75 percent of a class answered the first question on a ce  [#permalink]

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8
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.

Attachments exam.jpg [ 42.07 KiB | Viewed 41274 times ]

Intern  Joined: 22 Oct 2014
Posts: 27
Re: If 75 percent of a class answered the first question on a ce  [#permalink]

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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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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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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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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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Joined: 10 Apr 2018
Posts: 270
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Re: If 75 percent of a class answered the first question on a ce  [#permalink]

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Hi,

Questions like these help in improving our concepts of percentages and mental math ability.
Say there are 100 Students
75 Answered correct in first Exam and 20 Answered incorrect in both exam, then 5 answered Correctly in only Second exam.
If 55 Answered correctly in second exam then 25 answered correct in First exam only.
Then people who answered correctly in both the exams are 50.
Only First Exam 25, Only second exam 5, both first and second 50 & none 20 = 100

Probus.
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~You Just Can't beat the person who never gives up~ Babe Ruth Re: If 75 percent of a class answered the first question on a ce   [#permalink] 13 Aug 2018, 21:18
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