Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 178

If 75 percent of a class answered the first question on a ce
[#permalink]
Show Tags
26 Dec 2012, 07:46
Question Stats:
83% (01:39) correct 17% (01:27) wrong based on 903 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%
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 49251

Re: If 75 percent of a class answered the first question on a ce
[#permalink]
Show Tags
26 Dec 2012, 07:48




Director
Joined: 03 Aug 2012
Posts: 811
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29 GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)

Re: If 75 percent of a class answered the first question on a ce
[#permalink]
Show Tags
18 Aug 2013, 05:25
Attached Venn Diagram: 75X+X+55X+20=Total=100 X=50% Hence the OA
Attachments
ssss.JPG [ 14.43 KiB  Viewed 37845 times ]
_________________
Rgds, TGC! _____________________________________________________________________ I Assisted You => KUDOS Please _____________________________________________________________________________




SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1835
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: If 75 percent of a class answered the first question on a ce
[#permalink]
Show Tags
08 Sep 2014, 01:33
Refer diagram below: Attachment:
ssss.JPG [ 26.15 KiB  Viewed 33806 times ]
We require to find the value of x 100 = 75 + 55 x + 20 x = 50 Answer = D
_________________
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]
Show Tags
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 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?



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1835
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: If 75 percent of a class answered the first question on a ce
[#permalink]
Show Tags
02 Nov 2014, 19:37
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
_________________
Kindly press "+1 Kudos" to appreciate



Manager
Status: I am not a product of my circumstances. I am a product of my decisions
Joined: 20 Jan 2013
Posts: 124
Location: India
Concentration: Operations, General Management
GPA: 3.92
WE: Operations (Energy and Utilities)

If 75 percent of a class answered the first question on a ce
[#permalink]
Show Tags
02 Nov 2014, 22:35
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
exam.jpg [ 42.07 KiB  Viewed 32518 times ]



Intern
Joined: 22 Oct 2014
Posts: 27

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



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1835
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

If 75 percent of a class answered the first question on a ce
[#permalink]
Show Tags
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
Is it the right way?? Thanks for your reply (+1ed) Yes; this is absolutely correct
_________________
Kindly press "+1 Kudos" to appreciate



Intern
Joined: 28 Feb 2015
Posts: 17
GPA: 3.33

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



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3518
Location: United States (CA)

Re: If 75 percent of a class answered the first question on a ce
[#permalink]
Show Tags
13 Jul 2016, 07:33
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% 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.
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Manager
Joined: 10 Apr 2018
Posts: 97

Re: If 75 percent of a class answered the first question on a ce
[#permalink]
Show Tags
13 Aug 2018, 21:18
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.




Re: If 75 percent of a class answered the first question on a ce &nbs
[#permalink]
13 Aug 2018, 21:18






