find the number of students who read only sports illustrated

Question

in a survey of 224 students at a large university, the following data are collected:

95 students read time magazine

101 students read sports illustrated

80 students read readers digest

30 students read times and sports illustrated

25 students read times and readers digest

28 students read sports illustrated and readers digest

10 students read all three magazines

 

Answer 1

T=Time, S=Sports Illustrated, R=Reader's Digest

 

T=95

S=101

R=80

T&S=30, which means T=65 now and S=71 now (95-30 and 101-30 otherwise you have duplicates)

T&R=25 which means T=40 now and R=55 now (65-25 and 80-25 otherwise you have duplicates)

S&R=28 which means S=43 now and R=27 now (71-28 and 55-28 otherwise...)

T&S&R=10 which means T=30, S=33, R=17 now (40-10, 43-10, 27-10)

33 read Sports Illustrated

Draw two intersecting circles.

Draw a third intersecting circle under the first two.

Label the left one Time, label the right one Sports Illustrated , and label the bottom one Reader's Digest.

put 95 in the largest part of circle Time, put 101 in the largest part of circle Sports, and put 80 in the largest part of circle Reader's

put 30 in the intersection of Time and Reader's but not in the middle

subtract 30 from 90 to get T=65 and subtract 30 from 101 to get S=71

put 25 in the intersection of Time and Reader's but not in the middle

subtract 25 from 65 to get T=40 and subtract 25 from 80 to get R=55

put 28 in the intersection of Sports and Reader's but not in the middle

subtract 28 from 55 to get R=27 and subtract 28 from 71 to get S=43

put 10 in the middle(intersection of all 3 circles)

subtract 10 from 40 to get T=30

subtract 10 from 43 to get S=33

subtract 10 from 27 to get R=17

Answer 2

This is a great one for a Venn diagram - the kind with three interlocking circles.  That's really clumsy here, because the forum collapses spaces and doesn't provide a fixed-width font.  

 

If you copy the below diagram and paste it into notepad or any other word processing program, you'll be able to see a Venn diagram you could quickly draw for yourself with three circles.  

The T border is time, R is reader's digest, S is sports illustrated. Each region has been assigned a letter (the particular letter isn't important)to make it easy to reference.

.......TTTTTTTTTTTTTTTTTTTTTTT
.......T.....................T
.......T...........C.........T
.......T.....................T
SSSSSSSSSSSSSSSSSSSSSSS......T
S......T..............S......T
S......T...B..........S......T
S......T..............S......T
S..A...T......RRRRRRRRRRRRRRRRRRRRRRR
S......T......R.......S......T......R
S......T......R...D...S...E..T......R
S......T......R.......S......T......R
S......T......R.......S......T......R
S......TTTTTTTRTTTTTTTSTTTTTTT......R
S.............R.......S.............R
S.............R...F...S.............R
S.............R.......S.............R
SSSSSSSSSSSSSSRSSSSSSSS.............R
..............R..............G......R
..............R.....................R
..............R.....................R
..............RRRRRRRRRRRRRRRRRRRRRRR

95 students read time magazine...........................(B+C+D+E)
101 students read sports illustrated.....................(A+B+D+F)
80 students read readers digest..........................(D+E+F+G)
30 students read times and sports illustrated............(B)
25 students read times and readers digest................(E)
28 students read sports illustrated and readers digest...(F)
10 students read all three magazines.....................(D)

Using this, to find out the value of region G, for example, you take the number given for all reader's digest students, then subtract the given numbers of the regions that AREN'T region G. (80 - 25 - 28 - 10 = 17)

 

See how that works?

 

 

  

Answer 3

101 students read sports illustrated.

 

Of those students 30 also read time, 28 also read readers digest, and 10 also read both

 

Of the 101 students that read SI, 68 students read other magazines also.

 

33 students read only SI.