Set Theory1
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Question 1 of 4
1. Question
Read the following passage and answer the question:
Each of 100 kids took at least one of the chocolates from Munch, Perk, KitKat and Toblerone. 40 kids took each of Munch, Perk, KitKat and Toblerone. An equal number of kids took only Munch, only Perk, only KitKat and only Toblerone. An equal number of kids took each pair of Munch, Perk, KitKat and Toblerone. An equal number of kids took each combination of three chocolates. 15 kids took all four chocolates.
Find the maximum possible number of kids who took only Toblerone.
Correct
a + 3e + 3f + 15 = 40
a + 3(e + f) = 25
a is maximum when e + f is minimum i.e., 0
max (a) = 25
The maximum possible number of students who participated in only the 400 m dash is 25.
Incorrect
a + 3e + 3f + 15 = 40
a + 3(e + f) = 25
a is maximum when e + f is minimum i.e., 0
max (a) = 25
The maximum possible number of students who participated in only the 400 m dash is 25.

Question 2 of 4
2. Question
Read the following passage and answer the question:
Each of 100 kids took at least one of the chocolates from Munch, Perk, KitKat and Toblerone. 40 kids took each of Munch, Perk, KitKat and Toblerone. An equal number of kids took only Munch, only Perk, only KitKat and only Toblerone. An equal number of kids took each pair of Munch, Perk, KitKat and Toblerone. An equal number of kids took each combination of three chocolates. 15 kids took all four chocolates.
Find the maximum possible number of kids who took all three: Munch, Perk and Toblerone.
Correct
The number of students who participated in the 100 m dash, 200 m dash and 150 dash = f + 15.
From the previous solution, a + 3(e + f) = 25.
f is maximum when e and a are both minimum.
Min (e) = 0, and min(a) = 1
∴ Max (f) = 8
The maximum possible number of students who participated in the 100 m dash and 400 m dash = 8 + 15 = 23.Incorrect
The number of students who participated in the 100 m dash, 200 m dash and 150 dash = f + 15.
From the previous solution, a + 3(e + f) = 25.
f is maximum when e and a are both minimum.
Min (e) = 0, and min(a) = 1
∴ Max (f) = 8
The maximum possible number of students who participated in the 100 m dash and 400 m dash = 8 + 15 = 23. 
Question 3 of 4
3. Question
Read the following passage and answer the question:
Each of 100 kids took at least one of the chocolates from Munch, Perk, KitKat and Toblerone. 40 kids took each of Munch, Perk, KitKat and Toblerone. An equal number of kids took only Munch, only Perk, only KitKat and only Toblerone. An equal number of kids took each pair of Munch, Perk, KitKat and Toblerone. An equal number of kids took each combination of three chocolates. 15 kids took all four chocolates.
If 16 kids took only Munch, find the number of kids who took Munch and at least one other.
Correct
16 students participated in only the 100 m dash.
All the other students who participated in the 100 m dash participated in at least one other.
24 students participated in the 100 m dash and at least one other.Incorrect
16 students participated in only the 100 m dash.
All the other students who participated in the 100 m dash participated in at least one other.
24 students participated in the 100 m dash and at least one other. 
Question 4 of 4
4. Question
Read the following passage and answer the question:
Each of 100 kids took at least one of the chocolates from Munch, Perk, KitKat and Toblerone. 40 kids took each of Munch, Perk, KitKat and Toblerone. An equal number of kids took only Munch, only Perk, only KitKat and only Toblerone. An equal number of kids took each pair of Munch, Perk, KitKat and Toblerone. An equal number of kids took each combination of three chocolates. 15 kids took all four chocolates.
Using the information in the previous question, find the maximum possible number of kids who took only Munch and Perk.
Correct
16 + 3(e + f)+ 15 = 40
e + f = 3
Number of students who participated in only the 100 m max (e) = 3.Incorrect
16 + 3(e + f)+ 15 = 40
e + f = 3
Number of students who participated in only the 100 m max (e) = 3.