13.a Overlapping Sets

Question 1

What is a good way of solving “overlapping sets”?

Answer 1

Set-Matrix

Question 2

Explain the layout of a set-matrix

Answer 2

15 boxes, the rows should be mutually-exclusive

Question 3

What is important to remember about the column/ rows?

Answer 3

The column 1 and 2 heading must be mutually-exclusive, and the row 1 and 2 headings must also be mutually-exclusive

Question 4

What does cell 7 equal?

Answer 4

Cell 1 + Cell 4 = Cell 7

Question 5

What does cell 3 equal?

Answer 5

Cell 1 + Cell 2 = Cell 3

Question 6

What does cell 9 equal?

Answer 6

Cell 3 + Cell 6 = Cell 9

or

Cell 7 + Cell 8 = Cell 9

Question 7

What does Cell 5 equal?

Answer 7

Cell 6 - Cell 4 = Cell 5

or

Cell 8 - Cell 2 = Cell 5

Question 8

In percent overlapping set problems, where the number of items is not given, what should you do?

Answer 8

Use a variable eg. n

or

Assume the total number of items is 100

Question 9

Solve:

Answer 9

Either!

Each is sufficient!

Question 10

In fraction overlapping set problems, when the number of items is not given, what should we do?

Answer 10

Assign a variable, eg. n

or

Assume the total number of items is the LCM of the denominators of the fractions

Question 11

What could the total number of items in the set be?

Answer 11

Either a variable (eg. x) for the total number of items

or

the lcm of 5/8, 2/3 and 1/4, which is 24

Question 12

What could you assume the total number of items could be?

Answer 12

LCM of the denominators!

= 40

Question 13

If 1/8th of dog owners own a cat, how would you express this and where?

Answer 13

Question 14

How would you find the sum of x + y?

Answer 14

Understand that 30 + 25 + x + y = 80

Question 15

If we know the total population of the group, and we know at least one of the 4 main values, then we can find the _____ of the other _____ values

Answer 15

If we know the total population of the group, and we know at least one of the 4 main values, then we can find the SUM of the other THREE values

Question 16

What does the sum of these 4 cells equal?

Answer 16

Question 17

What is the formula for calculating the number of items in either set?

Answer 17

items in either A or B = # items in A + # items in B - # items in both

Question 18

In a school, 120 students learn english, 140 students learn math, and 80 students learn both. What is the total number of students who learn either English or Math?

Answer 18

Question 19

Solve:

Answer 19

Question 20

If you maximize the value in Cell 4, what happens to Cell 5?

Answer 20

The value in cell 5 would be minimize

Question 21

For any two cells that sum to a total, if we minimize one cell, the adjacent cell will be _______________

Answer 21

For any two cells that sum to a total, if we minimize one cell, the adjacent cell will be MAXIMIZED

Question 22

How do you refit this into a set-matrix?

Answer 22

Increase/ Not increase

(not increase = decrease + unchanged)

And then residential/ bypass on the sides

Question 23

How do you refit this into a set-matrix?

Answer 23