A study was made of 200 preschoolers to determine if they watched some particular television shows. The choices were Little Galileo, Super Reader and Prehistoric Train. The results are
I. 22 preschoolers did not watch any of these shows
II. 73 preschoolers only watched Little Galileo
III. 136 preschoolers watched Little Galileo
IV. 14 preschoolers only watched Super Reader and Prehistoric Train
V. 31 preschoolers only watched Little Galileo and Prehistoric Train
VI. 63 preschoolers watch Super Reader
VII. 135 preschoolers do not watch Prehistoric Train
How many students are in the event Watches Little Galileo and Super Reader?
A)
23
B)
32
C)
167
D)
240
Ms sue. Can you help. I don’t know where to start to figure this out. Maybe a Venn diagram
Yes, a Venn diagram,
3 intersecting circles G, S, and T within a rectangle
We are not given the intersection of all 3 circles, so put in x in that intersection
- 22 preschoolers did not watch any of these shows, ... so put 22 outside the circles but inside the rectangle.
- 22 preschoolers did not watch any of these shows, .... so put 73 in the G circle part not intersecting with any of the others.
- 31 preschoolers only watched Little Galileo and Prehistoric Train, .... so you already have the intersection of all three marked as x, so the missing part of G and P is 31-x, put it in
- 136 preschoolers watched Little Galileo, ... label the intersection of G and S, but not P as y
y + x + 31-x + 73 = 136
y = 32 , put that in for y
- 14 preschoolers only watched Super Reader and Prehistoric Train, .... just as before put in
14-x for S and P, but not G
- 63 preschoolers watch Super Reader, let only S be k
k + x + 14-x + 32 = 63
k = 17 , put that in
continue in this way ....
Yay!!!!! Thanks so much.
Thanks for getting me started Reiny
To determine the number of students who watch both Little Galileo and Super Reader, you can use a Venn diagram.
Let's break down the given information and fill in the Venn diagram step by step:
I. 22 preschoolers did not watch any of these shows. This information represents the region outside the circles. Put 22 in this region.
II. 73 preschoolers only watched Little Galileo. This information represents the region inside the Little Galileo circle but not the Super Reader circle. Put 73 in this region.
III. 136 preschoolers watched Little Galileo. This information includes both the region inside the Little Galileo circle (73 from previous information) and the overlap region of both circles. So, subtract 73 from 136 to find the number of students in the overlap region. Put this number in the overlap region.
IV. 14 preschoolers only watched Super Reader and Prehistoric Train. This information represents the region inside the Super Reader circle but not the Little Galileo circle. Put 14 in this region.
V. 31 preschoolers only watched Little Galileo and Prehistoric Train. This information includes the overlap region (already filled in) and the region inside the Little Galileo circle but not the Super Reader circle. So, subtract the overlap region from 31 to find the number of students in this region only. Put this number in the Little Galileo circle but not the Super Reader circle.
VI. 63 preschoolers watch Super Reader. This information includes both the region inside the Super Reader circle (14 from previous information) and the overlap region. So, subtract 14 from 63 to find the number of students in the overlap region. Put this number in the overlap region.
VII. 135 preschoolers do not watch Prehistoric Train. This information represents the region outside the Prehistoric Train circle. Subtract the numbers in the Prehistoric Train circle from 200 (total number of preschoolers) to find the number outside the Prehistoric Train circle. Put this number in the region outside the Prehistoric Train circle.
Now, let's calculate the number of students who watch both Little Galileo and Super Reader by adding the numbers in the overlap region:
Number in overlap region: 136 (from III) + 14 (from VI) = 150
So, the answer is 150.
However, none of the options given (A, B, C, D) match 150, so the given options are incorrect.