CAT 2025 Lesson : Selections - Case 5

Directions for questions 10 to 14: Answer the questions on the basis of the information given below:

K, L, M, N, P, Q, R, S, U and W are the only ten members in a department. There is a proposal to form a team from within the members of the department, subject to the following conditions:

1. A team must include exactly one among P, R, and S.
2. A team must include either M or Q, but not both.
3. If a team includes K, then it must also include L, and vice versa.
4. If a team includes one among S, U, and W then it must also include the other two.
5. L and N cannot be members of the same team.
6. L and U cannot be members of the same team.

The size of a team is defined as the number of members in the team.
[CAT 2006]

10) Who cannot be a member of a team of size 3?

(1) L
(2) M
(3) N
(4) P
(5) Q

11) Who can be a member of a team of size 5?

(1) K
(2) L
(3) M
(4) P
(5) R

12) What would be the size of the largest possible team?

(1) 8
(2) 7
(3) 6
(4) 5
(5) Cannot be determined

13) What could be the size of a team that includes K?

(1) 2 or 3
(2) 2 or 4
(3) 3 or 4
(4) Only 2
(5) Only 4

14) In how many ways can a team be constituted so that the team includes N?

(1) 2
(2) 3
(3) 4
(4) 5
(5) 6

Solution

10)
Notes:
(Conditions given)
1. One from (P/R/S)
2. One from (M/Q) and not (M & Q)
3. (K & L) or (L & K)
4. If one among S/U/W then (S & U & W)
5. $L \varpropto N$
6. $L \varpropto U$

For a team of size 3,

(S & U & W) cannot be selected as one from (M/Q) must be selected.
One from P/R must be selected.
If (K & L) or (L & K) is selected, then the team becomes 4 in size which is rejected,
The only person left is N who is to be selected.


Hence, option 1 is the answer.

Answer: (1) L

11)
Notes:
(Conditions given)
1. One from (P/R/S)
2. One from (M/Q) and not (M & Q)
3. (K & L) or (L & K)
4. If one among S/U/W, then (S & U & W)
5. $L \varpropto N$
6. $L \varpropto U$

For a team of size 5,

Start with a maximum pair size. Here from condition 1 & 4, we can conclude if (S & U & W) is selected, then both conditions are satisfied.
One person should be selected from (M/Q).
K & L or L & K cannot be selected as the team size becomes six, which is rejected.
The only person left is N who is to be selected.


On considering the options, option 3 is the answer.

Answer: (3) M

12)
Notes:
(Conditions given)
1. One from (P/R/S)
2. One from (M/Q) and not (M & Q)
3. (K & L) or (L & K)
4. If one among (S/U/W) then (S & U & W)
5. $L \varpropto N$
6. $L \varpropto U$

For a team of maximum size,

Start with a maximum pair size. Here from condition 1 & 4, We can conclude that if (S & U & W) are selected then both conditions are satisfied.
One person should be selected from (M/Q).
K & L or L & K cannot be selected as the team size becomes six, which is rejected.
The only person left is N who is to be selected.


From condition 1 & 4, we can conclude if (S & U & W) is not selected then,
One person should be selected from (M/Q).
K & L or L & K can be selected.
From condition 5, N cannot be selected. Thus the group size is 4.


Hence, the maximum team size can be 5.

Answer: (4) 5

13)
Notes:
(Conditions given)
1. One from (P/R/S)
2. One from (M/Q) and not (M & Q)
3. (K & L) or (L & K)
4. If one among S/U/W then (S & U & W)
5. $L \varpropto N$
6. $L \varpropto U$

As mentioned, K should be included in the team which is accompanied with L (Condition 3). One from (M/Q) should be selected. One from P/R should be selected.


This is the only possibility satisfying all the given conditions.

Hence the size of the team with K included is 4.

Answer:(5) Only 4

14)
Notes:
(Conditions given)
1. One from (P/R/S)
2. One from (M/Q) and not (M & Q)
3. (K & L) or (L & K)
4. If one among S/U/W then (S & U & W)
5. $L \varpropto N$
6. $L \varpropto U$

As said, N should be included in the team (K & L) cannot be selected because of condition 6.


Based on conditions 1 & 4 {one from (P/R/S & U & W)}, there are a total of 3 ways in which a team can be formed with N included.

Based on condition 2 {one from (M/Q)}, there are a total of 2 ways in which a team can be formed with N included.

Total ways $= 3 \times 2 = 6$ ways.

Hence, option 5 is the answer.

Answer: (5) 6

Answer:
10) (1) L
11) (3) M
12) (4) 5
13) (5) Only 4
14) (5) 6