CAT - Set Theory - Practice Assignment#2

Quant Master Set Theory Practice Problems#2

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1. In a survey of political preference, 78% of those asked were in favor of at least one of the proposals: I, II and III. 50% of

those asked favored proposal I, 30% favored proposal II, and 20% favored proposal III. If 5% of those asked favored all three

of the proposals, what percentage of those asked favored more than one of the 3 proposals. [CAT 1999]

a. 10 b. 12 c. 17 d. 22

2. In a hospital there were 200 diabetes, 150 hyperglycaemia and 150 gastro-enteritis patients. Of these, 80 patients were

treated for both diabetics and hyperglycaemia. Sixty patients were treated for gastro-enteritis and hyperglycaemia, while 70

were treated for diabetes and gastroenteritis. Some of these patients have all the three diseases. Dr. Dennis treats patients

with only Diabetes. Doctor Hormis treats patients with only Hyperglycaemia and Doctor Gerard treats patients with only

gastro-enteritis. Dr. Paul is a generalist. Therefore, he can treat patients with multiple diseases. Patients always prefer a

specialist for their disease. If Dr. Dennis had 80 patients, then the other three doctors can be arranged in terms of the

number of patients treated as: [CAT 2002]

a. Paul > Gerard > Hormis b. Paul > Hormis > Gerard c. Gerard > Paul > Hormis d. None of these

Choose 1 if the question can be answered by one of the statement alone but not by the other.

Choose 2 if the question can be answered by using either statement alone.

Choose 3 if the question can be answered by using both the statements together, but cannot be answered by using either

statement alone.

Choose 4 if the question cannot be answered by either of the statements.

3. People in a club either speak French or Russian or both. Find the number of people in a club who speak only French. [CAT

2002]

A. There are 300 people in the club and the number of people who speak both French and Russian is 196.

B. The number of people who speak only Russian is 58.

a. 1 b. 2 c. 3 d. 4

Directions (4-5): Answer the questions on the basis of the information given below.

New Age Consultants have three consultants Gyani, Medha and Buddhi. The sum of the number of projects handled by Gyani

and Buddhi individually is equal to the number of projects in which Medha is involved. All three consultants are involved

together in 6 projects. Gyani works with Medha in 14 projects. Buddhi has 2 projects with Medha but without Gyani, and 3

projects with Gyani but without Medha. The total number of projects for New Age Consultants is one less than twice the

number of projects in which more than one consultant is involved. [CAT 2003]




4. What is the number of projects in which Gyani alone is involved?

a. Uniquely equal to zero b. Uniquely equal to 1 c. Uniquely equal to 4 d. Cannot be determined uniquely

5. What is the number of projects in which Medha alone is involved?

a. Uniquely equal to zero b. Uniquely equal to 1 c. Uniquely equal to 4 d. Cannot be determined

DIRECTIONS for Questions 6 to 8: Answer the questions on the basis of the information given below.

Table A below provides data about ages of children in a school. For the age given in the first column, the second column

gives the number of children not exceeding that age. For example, first entry indicates that there are 9 children aged 4 years

or less. Tables B and C provide data on the heights and weights respectively of the same group of children in a similar format.

Assume that an older child is always taller and weighs more than a younger child, answer the following questions. [CAT

2003]

6. What is the number of children of age 9 years or less whose height does not exceed 135 cm?

a. 48 b. 45 c. 3 d. Cannot be determined.

7. How many children of age more than 10 years are taller than 150 cm. and do not weigh more than 48 kg.?


8. Among the children older than 6 years but not exceeding 12 years, how many weigh more than 38 kg.?





Read the following and answer questions 9 to 12 based on the same.

Eight sets A, B, C, D, E, F, G and H are such that

A is a superset of B, but subset of C.

B is a subset of D, but superset of E.

F is a subset of A, but superset of B.

G is a superset of D, but subset of F.

H is a subset of B.

N(A), N(B), N(C), N(D), N(E), N(F), N(G) and N(H) are the number of elements in the sets A, B, C, D, E, F, G and H respectively.

[XAT 2005]

9. Which one of the following could be FALSE, but not necessarily FALSE?

a. E is a subset of D

b. E is a subset of C

c. E is a subset of A

d. E is a subset of H

10. If P is a new set and P is a superset of A and N(P) is the number of elements in P, then which of the following must be

true?

a. N(G) is smaller than only four numbers

b. N(C) is the greatest

c. N(B) is the smallest

d. N(P) is the greatest

11. If Q and Z are two new sets superset of H and N(Q) and N(Z) is the number of elements of the sets Q and

Z respectively, then:

a. N(H) is the smallest of all

b. N(E) is the smallest of all

c. N(C) is the greatest of all

d. Either N(H) or N(E) is the smallest

12. Which of the following could be TRUE, but not necessarily TRUE?

a. N(A) is the greatest of all.

b. N(G) is greater than N(D).

c. N(H) is the least of all.

d. N(F) is less than or equal to N(H).

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CAT - Set Theory - Practice Assignment#2