Classicists' Favorite Epic Poets: Survey Results

[thaneshsan]

A number of classicists were asked to identify their favorite epic poets. The results are
summarized below. 62 appreciate Homer, 40 appreciate Virgil, 5 appreciate Gomer, 2
appreciate Homer and Virgil and Gomer, 3 appreciate Virgil and Gomer, 20 appreciate
Homer and Virgil, 42 appreciate Homer and neither of the other two, 12 appreciate none
of these three epic poets .
a) How many were surveyed?
b) How many don’t appreciate Gomer?
c) How many appreciate Homer or Gomer?
d) How many appreciate exactly one of the three epic poets?

 

[Joppy]

Hi thaneshsan, welcome to MHB!

What have you tried so far? As your title suggests, a Venn diagram can be useful for these sorts of questions.

 

[HOI]

Start by drawing three overlapping circles and label them "H", for Homer, "V" for Virgil, and "G" for Gomer (never heard of him!). That should make 7 different areas- one that is inside "H" only, one inside "V" only, one inside "G" only, one where only "H" and "V" overlap, one where only "H" and "G" overlap, one where only "G" and "V" overlap, and one where all three overlap.

You are told "12 appreciate none of these three epic poets". So write the number "12" outside all three circles.

You are told "2 appreciate Homer and Virgil and Gomer" so write "2" in that little area where all three circles overlap.

You are told "3 appreciate Virgil and Gomer" but that includes the 2 who appreciate all three so write 3- 2= "1" in the area where only "V" and "G" overlap.

Continue in that way to separate out those that are included in more than one statement.

 

[thaneshsan]

Thank you Mr.Joppy and Country Boy. I figured the answer for this question.