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At the beginning of an introductory literature seminar the teacher ask

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At the beginning of an introductory literature seminar the teacher ask  [#permalink]

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New post 22 Mar 2017, 02:36
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A
B
C
D
E

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  35% (medium)

Question Stats:

75% (02:26) correct 25% (03:26) wrong based on 93 sessions

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At the beginning of an introductory literature seminar the teacher asked his students if anyone had read works from the three authors – Joyce, Goethe, or Hemmingway – that were to be covered in the course. Everyone had read at least one work by one of the authors, but no one had read works from all three. Fourteen students claimed to have read works from both Joyce and Hemmingway, while no one had read both Joyce and Goethe. If 3 people read only Goethe, and half the number of people who read both Joyce and Hemmingway read only Hemmingway, how many of the thirty students in the class read either only Joyce, or only Hemmingway and Goethe?

A. 6
B. 7
C. 9
D. 11
E. 14

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At the beginning of an introductory literature seminar the teacher ask  [#permalink]

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New post 22 Mar 2017, 09:41
Students who had read Only Joyce = J
Students who had read Only Goethe = 3
Students who had read Only Hemmingway = 7
Students who had read Both Joyce & Goethe = 0
Students who had read Both Goethe & Hemmingway = GH
Students who had read Both Joyce & Hemmingway = 14
Students who had read All Three = 0

Total number of students = J+3+7+0+GH+14+0 = 30

Number of students in the class who read either only Joyce, or only Hemmingway and Goethe = J+GH

J+GH = 30-24 = 6

Number of students in the class who read either only Joyce, or only Hemmingway and Goethe = 6

Answer is A. 6
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Re: At the beginning of an introductory literature seminar the teacher ask  [#permalink]

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New post 23 Mar 2017, 15:56
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Bunuel wrote:
At the beginning of an introductory literature seminar the teacher asked his students if anyone had read works from the three authors – Joyce, Goethe, or Hemmingway – that were to be covered in the course. Everyone had read at least one work by one of the authors, but no one had read works from all three. Fourteen students claimed to have read works from both Joyce and Hemmingway, while no one had read both Joyce and Goethe. If 3 people read only Goethe, and half the number of people who read both Joyce and Hemmingway read only Hemmingway, how many of the thirty students in the class read either only Joyce, or only Hemmingway and Goethe?

A. 6
B. 7
C. 9
D. 11
E. 14


We can divide the 30 students in the class into 7 subgroups:

1) Joyce only
2) Goethe only
3) Hemingway only
4) Joyce and Goethe only
5) Joyce and Hemingway only
6) Goethe and Hemingway only
7) All three authors

We can let x = the number of students who read Joyce only, y = the number of students who read Goethe and Hemingway only, and fill in the given information:

1) Joyce only = x
2) Goethe only = 3
3) Hemingway only = ½(14) = 7
4) Joyce and Goethe only = 0
5) Joyce and Hemingway only = 14
6) Goethe and Hemingway only = y
7) All three authors = 0

Since the total number of students is 30, we have:

x + 3 + 7 + 0 + 14 + y + 0 = 30

x + y + 24 = 40

x + y = 6

Since x + y is the number of students in the class who read either only Joyce or only Hemingway and Goethe, 6 students read either only Joyce or only Hemingway and Goethe.

Answer: A
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Re: At the beginning of an introductory literature seminar the teacher ask &nbs [#permalink] 23 Mar 2017, 15:56
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