2. 0 2 4 6 8 10 12 14 16 18
OTHERS
SOCIAL SCIENCE
PHYSICAL SCIENCE
HUMANITIES
HEALTH SCIENCE
FINE ARTS
ENGINEERING
biological science
BUSINESS
LOGICAL SCIENCE
MALE FEMALE
3. Question 1
Total male faculty = 250
Total female faculty = 200
There are 275 students in the field of engineering. What is the ratio of the number
of students in engineering to the number of faculty in engineering
Male faculty =
12
100
× 250 = 30
Female faculty =
2
100
× 200 = 4
Ratio of number of students in engineering to faculty in engineering =
275
34
= 𝑎𝑝𝑝𝑟𝑜𝑥 8 ∶ 1
4. Approximately what % of the faculty in humanities is male
Question 2
In humanities, female =
17
100
× 200 = 34
13
100
× 250 = 33Male =
Total = 67
% of male =
33
67
× 100% = 50 %
5. Question 3
For the biological and health sciences combined 1/3 of female and 2/9 of male faculty are tenured
professors. What fraction of the faculty members in these 2 fields are tenured professors
For biological sciences , female faculty =
5
100
× 200 = 10
Male faculty =
10
100
× 250 = 25
For health sciences, male faculty =
8
100
× 250 = 20
Female faculty =
16
100
× 200 = 32
6. Tenured professors: female faculty =
1
3
× 42 = 14
Male faculty = 2
9
× 45 = 10
Total number of tenured professors = 24
Total faculty in biological and health sciences = 87
Fraction of tenured professors =
24
87
7. Question 4
The following is a record of the performance of a team for the first 7 weeks of the season
Games won Games lost Total no of games
played
1st week 5 3 8
2nd week 4 4 16
3rd week 5 2 23
4th week 6 3 32
5th week 4 2 38
6th week 3 3 44
7th week 2 4 50
8. i) How many games did the team lose during the 1st 7 weeks
Ans = 3 +4 +2+ 3 +2 +3 +4 = 21
ii) What percentage of games did the team win
The team won 29 games
% won = 29
50
× 100% = 58 %
9. iii) Which week was worst for the team
The 7th week since they lost more games than they won
iv) Which week was best for the team
The 3rd week since they won 3 and lost 2
Note: not the 4th week since they won 3 and lost 3
10. v) If there are 50 more games to play in the season, how many more games must the team win to
end up winning 60% of the games
Out of 100, the team must win 60
Already won 29
Remaining = 60 -29 = 31
Need to win 31 games
11. Question 5
Let $ x be defined as $ x = (x+3)(x-3). If $ a = a +3, what is one possible value for a
(a+3)(a-3)=(a+3)
a-3 = 1
a = 4
*******************************
