Question 1164085: Logic: Set and operations - Cardinal numbers and surveys
A director of Financial Aid for a small university inspected the records of 100 students and found the following:
49 receive government scholarships,
55 receive private scholarships,
43 receive college aid,
23 receive government scholarships and private scholarships,
18 receive scholarships. government and university aid,
28 receive private scholarships and university aid,
8 receive aid from all three sources.
a-How many of the students in the survey have only government scholarships?
b-How many of the students in the survey have a private scholarship but not a government scholarship?
c-How many of the students in the survey receive financial aid from only one of these sources?
d-How many of the students in the survey receive help from exactly two sources?
e-How many of the students in the survey do not receive financial aid from any of these sources?
f-How many of the students in the survey do not receive financial aid from the university or the government?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! If Venn diagrams are drawn,
16 are government only
of the 18 that are government and college, 10 are just those two; the other 8 are all three (center of the diagram)
of the 23 that are government and private, 15 are just those two; the other eight are all 3.
16+10+15+8=49
Private is 55.
12 are only, 15 and 8 are shared with government and all three, and 20 more shared with college.
of the 28 that are private and college, 20 are just those two, for again, the other 8 are all three.
College is 43
5 are college alone, 8 are all 3, 20 shared with private alone and 10 shared with government alone.
The sum of the seven different containers ,A, B, C, AB, AC, BC, and ABC, is 86.
Therefore, the answer to e, those who don't receive any from these sources, is 100-86 or 14.
a. is 16
b. is 32 private alone + private/college
c.from only one of these sources is 16+12+5=33
d. from exactly two sources is 10+15+20=45
f.this is how many are private alone, and that is 12.
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