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When Professor Wang looked at the rosters for this term's [#permalink]
27 Nov 2012, 00:20

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Difficulty:

15% (low)

Question Stats:

68% (02:20) correct
32% (02:06) wrong based on 42 sessions

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?

Re: When Professor Wang looked at the rosters for this term's [#permalink]
27 Nov 2012, 02:48

Expert's post

saxenarahul021 wrote:

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?

Re: When Professor Wang looked at the rosters for this term's [#permalink]
15 Jan 2014, 19:11

Bunuel wrote:

saxenarahul021 wrote:

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?

Re: When Professor Wang looked at the rosters for this term's [#permalink]
15 Jan 2014, 20:40

Expert's post

prasannajeet wrote:

Bunuel wrote:

saxenarahul021 wrote:

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?

Also please solve through ven-diagram actually my i got wrong while solving in ven diagram....

Rgds 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 1177 times ]

Now add all the students in the venn diagram = 14 + 5 + 13 + 3+ 4 + 6 + 5 = 50 _________________

Re: When Professor Wang looked at the rosters for this term's [#permalink]
30 Sep 2014, 02:44

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

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