Practice Exercise 1: In a “keep-fit” gymnasium class, there are fifteen females enrolled in a weight-loss program. They all have been grouped in any one of the five weight-groups W1, W2, W3, W4 or W5. One instructor is assigned to one weight-group only. Sonali, Shalini, Shubhra and Shahira belong to the same weight-group. Sonali and Rupa are in one weight-group, Rupali and Renuka are also in one weight-group.

Rupa, Radha, Renuka, Ruchika, and Ritu belong to different weight-groups. Somya cannot be with Ritu and Tara cannot be with Radha. Komal cannot be with Radha, Somya, or Ritu. Shahira is in W1 and Somya is in W4 with Ruchika. Sweta and Jyotika cannot be with Rupali, but are in a weight group with total membership of four. No weight group can have more than five or less than one member. Amita, Babita, Chandrika, Deepika, and Elina are instructors of weight groups with membership sizes 5, 4, 3, 2, and 1, respectively. Who is the instructor of Radha?

A. Babita

B. Elina

C. Chandrika

D. Deepika

We have groups with 5, 4, 3, 2, and 1 members. All we have to do is to go through the instructions and place the members in the right group.

> Sonali, Shalini, Shubhra and Shahira belong to the same weight-group. Sonali and Rupa are in one weight-group, Rupali and Renuka are also in one weight-group.

Group 1: Sonali, Shalini, Shubhra, Shahira, Rupa. This group won’t contain more members.

Group 2: Rupali, Renuka

> Rupa, Radha, Renuka, Ruchika, and Ritu belong to different weight-groups.

Group 1: Sonali, Shalini, Shubhra, Shahira, Rupa

Group 2: Rupali, Renuka

Group 3: Ruchika

Group 4: Radha

Group 5: Ritu

> Shahira is in W1 and Somya is in W4 with Ruchika.

Group 1 (W1): Sonali, Shalini, Shubhra, Shahira, Rupa

Group 2: Rupali, Renuka

Group 3 (W4): Ruchika, Somya

Group 4: Radha

Group 5: Ritu

> Komal cannot be with Radha, Somya, or Ritu.

This implies Komal is in the group that includes Rupali and Renuka.

Group 1 (W1): Sonali, Shalini, Shubhra, Shahira, Rupa

Group 2: Rupali, Renuka, Komal

Group 3 (W4): Ruchika, Somya

Group 4: Radha

Group 5: Ritu

> Somya cannot be with Ritu and Tara cannot be with Radha. Sweta and Jyotika cannot be with Rupali, but are in a weight group with a total membership of four.

Since Tara is not with Radha, group 4 cannot have four members. The only possibility for Sweta and Jyotika is that they are in the group that includes Ruchika and Somya. Then, Tara must be in the group that includes Ritu.

Group 1 (W1): Sonali, Shalini, Shubhra, Shahira, Rupa

Group 2: Rupali, Renuka, Komal

Group 3 (W4): Ruchika, Somya, Sweta, Jyotika

Group 4: Radha

Group 5: Ritu, Tara

We can see that Radha is in the group that includes only one member. Therefore, her instructor is Elina. So, B is the correct option.

Practice Exercise 2: A king has unflinching loyalty from eight of his ministers M1 to M8, but he has to select only four to make a cabinet committee. He decides to choose these four such that each selected person shares a liking with at least one of the other three selected. The selected persons must also hate at least one of the likings of any of the other three persons selected.

(i) M1 likes fishing and smoking, but hates gambling;

(ii) M2 likes smoking and drinking, but hates fishing;

(iii) M3 likes gambling, but hates fishing;

(iv) M4 likes mountaineering, but hates drinking;

(v) M5 likes drinking, but hates smoking and mountaineering;

(vi) M6 likes fishing, but hates smoking and mountaineering;

(vii) M7 likes gambling and mountaineering, but hates fishing;

(viii) M8 likes smoking and gambling, but hates mountaineering;

Who are the four people selected by the king?

A. M1, M2, M5, M6

B. M3, M4, M5, M6

C. M4, M5, M6, M8

D. M1, M2, M4, M7

Let’s check the options:

A. M1, M2, M5, M6

M1 hates gambling which is not liked by M2, M5, and M6. So, this option is not correct.

B. M3, M4, M5, M6

M3 likes gambling which is not liked by M4, M5, and M6. So, this option is also not correct.

C. M4, M5, M6, M8

M4 likes mountaineering which is not liked by M5, M6, and M8. So, this option is also not correct.

D. M1, M2, M4, M7

> M1 likes smoking which is liked by M2, and hates gambling which is liked by M7.

> M2 hates fishing which is liked by M1.

> M4 likes mountaineering which is liked by M7, and hates drinking which is liked by M2.

> M7 hates fishing which is liked by M1.

Therefore, the combination in option (D) satisfies all the constraints. Hence, D is the correct option.

Practice Exercise 3: Answer the following questions based on the passage below.

A group of three or four has to be selected from seven persons. Among the seven are two women: Fiza and Kavita and five men: Ram, Shyam, David, Peter, and Rahim. Ram would not like to be in the group if Shyam is also selected. Shyam and Rahim want to be selected together in the group. Kavita would like to be in the group only if David is also there. David, if selected, would not like Peter in the group. Ram would like to be in the group only if Peter is also there. David insists that Fiza be selected in case he is there in the group.

1. Which of the following is a feasible group of three?

A. David, Ram, Rahim

B. Peter, Shyam, Rahim

C. Kavita, David, Shyam

D. Fiza, David, Ram

2. Which of the following is a feasible group of four?

A. Ram, Peter, Fiza, Rahim

B. Shyam, Rahim, Kavita, David

C. Shyam, Rahim, Fiza, David

D. Fiza, David, Ram, Peter

3. Which of the following statements is true?

A. Kavita and Ram can be part of a group of four.

B. A group of four can have two women.

C. A group of four can have all four men.

D. None of the above

Constraints:

> Ram would not like to be in the group if Shyam is also selected. Shyam and Rahim want to be selected together in the group.

Group:

(i) Ram or (Shyam and Rahim)

> Kavita would like to be in the group only if David is also there. David, if selected, would not like Peter in the group.

Group:

(ii) Kavita if David is there.

(iii) David or Peter

> Ram would like to be in the group only if Peter is also there. David insists that Fiza be selected in case he is there in the group.

Group:

(iv) Ram if Peter is there and David if Fiza is there.

Now let’s answer the questions:

1. 

Let’s analyze the options:

> A: David, Ram, Rahim

David would be included if Fiza is there in the group. So, this combination is not correct.

> B: Peter, Shyam, Rahim

This combination is possible.

> C: Kavita, David, Shyam

 This combination is not possible for the same reason as in the case of option (A).

> D: Fiza, David, Ram

Ram would be included if Peter is there in the group. So, this combination is not correct.

Therefore, B is the correct option.

2.

Let’s analyze the options:

> A: Ram, Peter, Fiza, Rahim

Ram and Rahim must not be included together in the group. So, this combination is not correct.

> B: Shyam, Rahim, Kavita, David

David would be included if Fiza is there in the group. So, this combination is not correct.

> C: Shyam, Rahim, Fiza, David

This combination is possible.

> D: Fiza, David, Ram, Peter

David and Peter must not be included together in the group. So, this combination is not correct.

Therefore, C is the correct option.

3. 

Let’s analyze the options:

> A: Kavita and Ram can be part of a group of four.

Kavita would be included if David is there in the group and Ram would be included if Peter is there in the group. But David and Peter cannot be together in the group. So, this statement is not true.

> B: A group of four can have two women

In that case, Kavita, Fiza, and David would be included in the group. The fourth person can’t be Peter because David is included in the group. Since Peter is not included in the group, Ram cannot be included in the group as well. Rahim and Shyam are included in the group together. So, it is not possible to include either of them in the group. Therefore, a group of four can’t have two women. So, this statement is false.

> C: A group of four can have all four men.

This is also not possible. So, D is the correct option.

Practice Exercise 4: Eight people carrying food baskets are going for a picnic on motorcycles. Their names are A, B, C, D, E, F, G, and H. They have four motorcycles M1, M2, M3, and M4 among them. They also have four food baskets O, P, Q, and R of different sizes and shapes and each of them can be carried only on motorcycles M1, M2, M3, or M4, respectively.

No more than two persons can travel on a motorcycle and no more than one basket can be carried on a motorcycle. There are two husband-wife pairs in this group of eight people and each pair will ride on a motorcycle together. C cannot travel with A or B. E cannot travel with B or F. G cannot travel with F, H or D. The husband-wife pairs must carry baskets O and P. Q  is with A and P is with D. F travels on M1 and E travels on M2 motorcycles. G is with Q, and B cannot go with R. Who is traveling with H?

(a) A

(b) B

(c) C

(d) D

No more than two persons can travel on a motorcycle and no more than one basket can be carried on a motorcycle.

> The four food baskets O, P, Q, and R of different sizes and shapes and each of them can be carried only on motorcycles M1, M2, M3, or M4, respectively.

M1 (O)

M2 (P)

M3 (Q)

M4 (R)

> Q  is with A and P is with D. F travels on M1 and E travels on M2 motorcycles. G is with Q.

M1 (O): F

M2 (P): D, E

M3 (Q): A, G

M4 (R)

> B cannot go with R.

M1 (O): F, B

M2 (P): D, E

M3 (Q): A, G

M4 (R): C, H

Hence, C is traveling with H. So, (c) is the correct option.