Crossing The River With Dogs 2nd Edition, Chapter 12, question 6

Question

The Staff at TLC watched the eating habits of their 64 students during lunch, and this is what they saw:

59 kids at green beans

56 kids ate cauliflower

60 ate broccoli

55 ate beans and cauliflower

54 ate cauliflower and broccoli

56 ate beans and broccoli

53 ate all three

1.)How many didn't eat all any of the vegetables --1

2.)How many ate beans but not cauliflower -- 3

3.)How many didn't eat broccoli -- ???

4.)How many only at cauliflower -- 0

5.)how many ate exactly two of these three vegetables -- ???

How would you figure out questions 3 and 5? I can't understand this at all....

Answer 1

1.   A+E+D+G = 59 kids ate green beans

2.   B+E+F+G = 56 kids ate cauliflower

3.   C+D+F+G = 60 ate broccoli

4.   E+G = 55 ate beans and cauliflower

5.   F+G = 54 ate cauliflower and broccoli

6.   D+G = 56 ate beans and broccoli

7.   G = 53 ate all three

Clue 7 (usually, start at the end of the problem) is VERY IMPORTANT.

Putting G=53 into clues 4-5-6 gives:

      D=3

      E = 2

      F = 1

      G = 53

Now, use these values to solve clues 1-3.

Remember to calculate H.

Answer 2

#3 If 60 ate broccoli, then 64 - 60 = 4 did not.

#5 55 ate both beans and cauli, 54 ate both cauli and brocc, 56 ate beans and brocc

However, all three of these numbers include the 53 students who ate all three.

55 - 53 = 2 ate just beans and cauli without brocc

54 - 53 = 1 ate just cauli and brocc without beans

56 - 53 = 3 ate just beans and brocc without cauli

2 + 1 + 3 = 6 ate exactly two of the three vegetables.

Note: An helpful way to answer this question is using a Venn diagram with three overlapping circles.