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

Question

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%

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

Bunuel · Accepted Answer

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

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

Answer: D.

TGC · Answer

Attached Venn Diagram:

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

X=50%

Hence the OA

PareshGmat · Answer

Refer diagram below: ssss.JPG We require to find the value of x 100 = 75 + 55 -x + 20 x = 50 Answer = D

appleid · Answer

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?

PareshGmat · Answer

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

Ashishmathew01081987 · Answer

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

appleid · Answer

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 -   = 20 .......... values are in percent
x = 20 - 100 + 130
x = 50

Ans: D

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

PareshGmat · Answer

Yes; this is absolutely correct

alseca1927 · Answer

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.

ScottTargetTestPrep · Answer

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

The answer is D.

Probus · Answer

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.

Ramnik1003 · Answer

is the following way correct?

let class size be 100

100 - 75 = 25 incorrect (20 neither + 5 incorrect) 
100 - 55 = 45 incorrect ( 20 neither + 25 incorrect)

so

total no. of correct ans - incorrect ans

75+55 - 30 
130 - 30
100

now we divide 100 by 2 = 50 ( because no. of questions were 2)

please let me know if this is the right approach or not

ArnauG · Answer

To find the percentage of students who answered both questions correctly, we need to consider the percentages who answered each question correctly and the percentage who answered neither question correctly.

Given:
Percentage of students who answered the first question correctly = 75%
Percentage of students who answered the second question correctly = 55%
Percentage of students who answered neither question correctly = 20%

Let's denote:
A = Percentage of students who answered the first question correctly
B = Percentage of students who answered the second question correctly
N = Percentage of students who answered neither question correctly
AB = Percentage of students who answered both questions correctly (overlap)

We can represent the situation using the formula:

Total students (T) = A + B - AB + N

Substituting the given values:
T = 75% + 55% - AB + 20% = 150% - AB

Since T represents the total percentage of students, it is equal to 100%.

100% = 150% - AB

Simplifying the equation, we find:
AB = 150% - 100% = 50%

Therefore, (D) 50% of the students answered both questions correctly.

totaltestprepNick · Answer

B https://www.youtube.com/watch?v=nYaFITjfgGU Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

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