At the beginning of an introductory literature seminar the teacher ask

Question

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

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

quantumliner · Answer

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

JeffTargetTestPrep · Answer

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

rachana_shukla · Answer

Isn't the formula for 3 overlapping sets below -

Total=A+B+C−(AnB+AnC+BnC)+AnBnC+Neither

Can someone please clarify why are we adding 0 + 14 + y rather than subtracting in below equation -

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

As per the formula, it should be -

x + 3 + 7 - ( 0 + 14 + y ) + 0 = 30

diva_jaxn · Answer

The overlap of J and H should only be 7 righht, if 7 is H only and then the overlap should be 7 only?

egmat · Answer

diva_jaxn  If I may explain:

Let's look at what the problem actually states:

Key statement from the problem:   "Fourteen students claimed to have read works from both Joyce and Hemingway, while... half the number of people who read both Joyce and Hemingway read only Hemingway"
 
This tells us:
 
  Given directly:  Joyce AND Hemingway =  14  students 
  Derived from this:  Only Hemingway =  \frac{1}{2} 	imes 14 = 7  students

Where the Confusion Arises:   You're thinking: "If  7  read only Hemingway, shouldn't the overlap also be  7 ?"
 
But the problem states it the  other way around :
 
 The overlap (Joyce ∩ Hemingway) =  14   (given first)  
 Only Hemingway =  \frac{14}{2} = 7   (calculated from the overlap)

Think of it this way: The problem is saying "Take the number who read both Joyce and Hemingway ( 14 ), and half of that number ( 7 ) is how many read only Hemingway."

I hope this helps? Let me know if you still have any confusion!

At the beginning of an introductory literature seminar the teacher ask

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