sets problems

Question

in a school 120 students are participating in game A or game B or both. if students are participating in game A is 50% and 30% to 60% of these students are participating in both A and B . what % of the students are participating only in A.

 

(a)20%

(b)40%

(c)25%

(d)30%

(e)50%

Answer 1

Wow!  What a great question.  There will some thinking here.

 

Why is 120 students given if the whole problem and the answer are in terms of %  ??  (ans:  because the %’s must be whole students).

 

Why isn’t the number of students only participating in game B important?   (ans: because we are interested only in a % of a % that must be whole students).

 

Solution:

 

There are 120 students and 50% of them participate in game A (50% of 120 is 60).

 

Now, 30% to 60% of these (who are “these?” – the 60) is 18 to 36 students, so we have some number from 42 to 24 to choose from for the % participating only in A (and the possible answers are given).

 

Both A and B        Only A                  % only A

18                             42                             35

19                             41                             34.16667

20                             40                             33.33333

21                             39                             32.5

22                             38                             31.66667

23                             37                             30.83333

24                             36                             30

25                             35                             29.16667

26                             34                             28.33333

27                             33                             27.5

28                             32                             26.66667

29                             31                             25.83333

30                             30                             25

31                             29                             24.16667

32                             28                             23.33333

33                             27                             22.5

34                             26                             21.66667

35                             25                             20.83333

36                             24                             20

 

Here is the information about the choices:

 

(a)  Of 120 students, if 50% (60) participate in game A, and 36 of those (60%) participate in both A and B, then 24 (20% of the total 120) participate only in game A.

 

(b)  Of 120 students, if 50% (60) participate in game A, and 12 of those (20%) participate in both A and B, then 48 (40% of the total 120) participate only in game A.  But 20% is not allowed!

 

(c)  Of 120 students, if 50% (60) participate in game A, and 30 of those (50%) participate in both A and B, then 30 (25% of the total 120) participate only in game A.

 

(d)  Of 120 students, if 50% (60) participate in game A, and 24 of those (40%) participate in both A and B, then 36 (30% of the total 120) participate only in game A.

 

(e)  Of 120 students, if 50% (60) participate in game A, and 0 of those (0%) participate in both A and B, then 60 (50% of the total 120) participate only in game A.   But 0% is not allowed!

 

REVISED

REVISED more

Answer 2

120 students

Two games A, B (or both)

 

50% A

30-60% of 50% are also in B

= 15-30% of all students are in A&B

 

So those only in A will be 50 - (15 to 30)

 

50-15 = 35% in A (30% of A students in both)

50-30 = 20% in A (60% of A students in both)

 

Thus, we know that since 30-60% of A students are also in B, the % of only A students will be 20-35%. However, it cannot be less than 20, so even though (c) 25 and (d) 30 are in the range, they will not be true in all cases.

 

Answer would be (a) 20%
(Although this question is a bit unusual, I would look at the wording carefully again. "30% to 60% of these students" is highly unusual)

 

Hope this helps