# CAT Model Paper 6 Questions and Answers with Explanation Part 4

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__Questions 20 to 22: Answer these questions after going through the information given__

__below__:

In Imperial engineering college, each student is a member of at least one of the four clubs - Dramatics, Red Cross, Rotaract and Twisters. The number of students who are members of all the clubs except Dramatics is . The number of students who are members of all the clubs except Red Cross is . The number of students who are members of all the clubs except Twisters is . The number of students who are members of all the clubs except Rotaract is . The number of members of Red Cross and Rotaract alone is 10 more than twice the number of members of Dramatics and Twisters alone. The number of members of Rotaract and Twisters alone is 10 lesser than the number of members of Dramatics alone. The number of members of Red Cross and Twisters alone is 20 more than twice the number of members of Dramatics and Rotaract alone. The number of members of only Dramatics and Red Cross is equal to the number of members of Twisters alone. The number of students who are members of Dramatics club alone is which is more than the number of students who are members of Rotaract club alone and more than the number of students of Twisters alone. The number of members of all the four clubs is 30 less than thrice the number of members of Red Cross alone.

Q: 20. If the number of members of the Dramatics, Red Cross and Rotaract clubs are and respectively what is the number of members of the Twisters club?

(A) 375

(B) 445

(C) 390

(D) 430

Ans: B

Solution:

The correct choice is (B) .

The number of students who are members of all the clubs except Dramatics is . Hence,

The number of students who are members of all the clubs except Red Cross is . Hence,

The number of students who are members of all the clubs except Twisters is . Hence,

The number of students who are members of all the clubs except Rotaract is . Hence,

The number of students who are members of Dramatics club alone is 85 which is more than the number of students who are members of Rotaract club alone and more than the number of students of Twisters alone.

The number of members of Rotaract and Twisters alone is 10 lesser than the number of members of Dramatics alone. Hence,

The number of members of only Dramatics and Red Cross is equal to the number of members of Twisters alone. Hence,

The number of members of Red Cross and Rotaract alone is 10 more than twice the number of members of Dramatics and Twisters alone.

Hence,

The number of members of Red Cross and Twisters alone is more than twice the number of members of Dramatics and Rotaract alone. Hence,

The number of members of all the four clubs is less than thrice the number of members of Red Cross alone. Hence,

Substituting all the above values in the Venn diagram:

Number of members of Dramatics club

Number of members of Red Cross club

Number of members of Rotaract club

Number of members of Twisters club

Solving,

Number of members of Twisters club

Q: 21. The number of students who are members of at least one of the four clubs is . The number of members of Dramatics or Rotaract club is . The number of members of Twisters club is . Find the number of members of exactly two clubs.

(A)

(B)

(C)

(D)

Ans: C

Solution:

The correct choice is (C) .

The number of students who are members of all the clubs except Dramatics is 30. Hence,

The number of students who are members of all the clubs except Red Cross is 50. Hence,

The number of students who are members of all the clubs except Twisters is 40. Hence,

The number of students who are members of all the clubs except Rotaract is 45. Hence,

The number of students who are members of Dramatics club alone is 85 which is 30 more than the number of students who are members of Rotaract club alone and 50 more than the number of students of Twisters alone.

The number of members of Rotaract and Twisters alone is 10 lesser than the number of members of Dramatics alone. Hence,

The number of members of only Dramatics and Red Cross is equal to the number of members of Twisters alone. Hence,

The number of members of Red Cross and Rotaract alone is 10 more than twice the number of members of Dramatics and Twisters alone.

Hence,

The number of members of Red Cross and Twisters alone is more than twice the number of members of Dramatics and Rotaract alone. Hence,

The number of members of all the four clubs is 30 less than thrice the number of members of Red Cross alone. Hence,

Substituting all the above values in the Venn diagram:

Number of members of Dramatics club

Number of members of Red Cross club

Number of members of Rotaract club

Number of members of Twisters club

Total number of members in at Least one of the four clubs

Number of members of Dramatics or Rotaract club

Number of members of Twisters club

Solving the above three equations,

The number of members of exactly two clubs is highlighted in yellow:

Number of members

Q: 22. The number of members of Red Cross is 31 more than the number of members of Twisters. The number of members of Rotaract is 35 more than the number of members of Red Cross. The number of members of Red Cross is 24 more than the number of members of Dramatics. Find the number of students in Imperial engineering college.

(A)

(B)

(C)

(D)

Ans: D

Solution:

The correct choice is (D) .

The number of students who are members of all the clubs except Dramatics is 30. Hence, j = 30

The number of students who are members of all the clubs except Red Cross is . Hence,

The number of students who are members of all the clubs except Twisters is . Hence,

The number of students who are members of all the clubs except Rotaract is . Hence,

The number of students who are members of Dramatics club alone is 85 which is 30 more than the number of students who are members of Rotaract club alone and 50 more than the number of students of Twisters alone.

The number of members of Rotaract and Twisters alone is 10 lesser than the number of members of Dramatics alone. Hence,

The number of members of only Dramatics and Red Cross is equal to the number of members of Twisters alone. Hence,

The number of members of Red Cross and Rotaract alone is 10 more than twice the number of members of Dramatics and Twisters alone.

Hence,

The number of members of Red Cross and Twisters alone is 20 more than twice the number of members of Dramatics and Rotaract alone. Hence,

The number of members of all the four clubs is 30 less than thrice the number of members of Red Cross alone. Hence,

Substituting all the above values in the Venn diagram:

Number of members of Dramatics club

Number of members of Red Cross club

Number of members of Rotaract club

Number of members of Twisters club

The number of members of Red Cross is 31 less than the number of members of Twisters.

Simplifying, (1)

The number of members of Rotaract is 35 more than the number of members of Red

Cross.

5

Simplifying, Eqn (2)

The number of members of Red Cross is 24 more than the number of members of Dramatics.

Simplifying, (3)

Solving the three equations,

Total number of students in Imperial Engineering College