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Updated on: 30 Sep 2014, 03:45
Originally posted by saxenarahul021 on 27 Nov 2012, 01:20.
Last edited by Bunuel on 30 Sep 2014, 03:45, edited 2 times in total.
Last edited by Bunuel on 30 Sep 2014, 03:45, edited 2 times in total.
Renamed the topic and edited the tags.
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
71% (02:07) correct
29%
(02:47)
wrong
based on 987
sessions
History
Date
Time
Result
Not Attempted Yet
When Professor Wang looked at the rosters for this term's classes, she saw that the roster for her economics class (E) had 26 names, the roster for her marketing class (M) had 28, and the roster for her statistics class (S) had 18. When she compared the rosters, she saw that E and M had 9 names in common, E and S had 7, and M and S had 10. She also saw that 4 names were on all 3 rosters. If the rosters for Professor Wang's 3 classes are combined with no student's name listed more than once, how many names will be on the combined roster?
A. 30
B. 34
C. 42
D. 46
E. 50
A. 30
B. 34
C. 42
D. 46
E. 50
30 Sep 2014, 03:44
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it's easier and more efficient to use the formula rather than a venn diagram in the actual exam.
For this problem, the appropriate formula should be:
Total = Group 1 + Group 2 + Group 3 - (Sum of two group overlaps) + All three + Neither
Total = 26 + 28 + 18 - (9 + 7 + 10) + 4 + 0 = 50
FYI, if a question asks for "Exactly" two groups, the formula is slightly modified:
Total = Group 1 + Group 2 + Group 3 - (Sum of Exactly 2 group overlaps) - (2 x All Three) + Neither
For this problem, the appropriate formula should be:
Total = Group 1 + Group 2 + Group 3 - (Sum of two group overlaps) + All three + Neither
Total = 26 + 28 + 18 - (9 + 7 + 10) + 4 + 0 = 50
FYI, if a question asks for "Exactly" two groups, the formula is slightly modified:
Total = Group 1 + Group 2 + Group 3 - (Sum of Exactly 2 group overlaps) - (2 x All Three) + Neither
15 Jan 2014, 21:40
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prasannajeet
When making the Venn diagram here, start by putting in the number of students which are in all 3 sets i.e. 4
Next, E and M had 9 names in common so the overlap of E and M excluding the overlap of all 3 will be 9 - 4 = 5.
Similarly for the E and S overlap and M and S overlap.
Next, E has 26 people and after removing 5 + 4 + 3 = 12, we are left with 14 people who have taken only E. Similarly for M and S too.
Attachment:
Ques3.jpg [ 15.92 KiB | Viewed 83329 times ]
Now add all the students in the venn diagram = 14 + 5 + 13 + 3+ 4 + 6 + 5 = 50
