2. Solved Examples
Example Case 1
1)
The Bannerjees, the Sharmas, and the Pattabhiramans each have a tradition of eating Sunday lunch as a family. Each family serves a special meal at a certain time of day. Each family has a particular set of chinaware used for this meal. Use the clues below to answer the following question.
. The Sharma family eats at noon.
. The family that serves fried brinjal uses blue chinaware.
. The Bannerjee family eats at 2 o’clock.
. The family that serves sambar does not use red chinaware.
. The family that eats at 1 o’clock serves fried brinjal.
. The Pattabhiraman family does not use white chinaware.
. The family that eats last likes makkai-ki-roti.
Which one of the following statements is true?
[CAT 2001]
(1) The Bannerjees eat makkai-ki-roti at 2 o’clock, the Sharmas eat fried brinjal at 12 o’clock and the Pattabhiramans eat sambar from red chinaware
(2) The Sharmas eat sambar served in white chinaware, the Pattabhiramans eat fried brinjal at 1 o’clock, and the Bannerjees eat makkai-ki-roti served in blue chinaware
(3) The Sharmas eat sambar at noon, the Pattabhiramans eat fried brinjal served in blue chinaware, and the Bannerjees eat makkai-ki-roti served in red chinaware
(4) The Bannerjees eat makkai-ki-roti served in white chinaware, the Sharmas eat fried brinjal at 12 o’clock and the Pattabhiramans eat sambar from red chinaware
Start with the direct clues in statement 1) and 3).
Statement 5) says that the family that eats at 1 O’ clock serves fried brinjal. As the time for the two other families were filled, we can conclude that Pattabhiramans family is the one that eats at 1 O’ clock and serves fried brinjal.
Statement 2) says that the family serves fried brinjal uses blue chinaware. As Pattabhiramans family is serving fried brinjal, we can conclude that they use blue chinaware.
Statement 7) says that the family that eats last likes makkai-ki-roti. As Bannerjees family is eating last, we can conclude that they like makkai-ki-roti.
Statement 4) says that the family that serves sambar does not use red chinaware. As the blue china is already used, the only colour left is white. So we can conclude that the family serving sambar uses white chinaware. And as the meal for families other than the Sharmas were filled, the only place left to fill sambar is Sharma. As the Sharma family is serving sambar, they use white chinaware.
Red is remaining. So we can conclude that the Bannerjee family is the one that uses red chinaware.
Answer: (3) The Sharmas eat sambar at noon, the Pattabhiramans eat fried brinjal served in blue chinaware, and the Bannerjees eat makkai-ki-roti served in red chinaware
. The Sharma family eats at noon.
. The family that serves fried brinjal uses blue chinaware.
. The Bannerjee family eats at 2 o’clock.
. The family that serves sambar does not use red chinaware.
. The family that eats at 1 o’clock serves fried brinjal.
. The Pattabhiraman family does not use white chinaware.
. The family that eats last likes makkai-ki-roti.
Which one of the following statements is true?
[CAT 2001]
(1) The Bannerjees eat makkai-ki-roti at 2 o’clock, the Sharmas eat fried brinjal at 12 o’clock and the Pattabhiramans eat sambar from red chinaware
(2) The Sharmas eat sambar served in white chinaware, the Pattabhiramans eat fried brinjal at 1 o’clock, and the Bannerjees eat makkai-ki-roti served in blue chinaware
(3) The Sharmas eat sambar at noon, the Pattabhiramans eat fried brinjal served in blue chinaware, and the Bannerjees eat makkai-ki-roti served in red chinaware
(4) The Bannerjees eat makkai-ki-roti served in white chinaware, the Sharmas eat fried brinjal at 12 o’clock and the Pattabhiramans eat sambar from red chinaware
Solution
Let us form a table with the three families in different columns and then match the Meal, Time and Chinaware with them.Start with the direct clues in statement 1) and 3).
Statement 5) says that the family that eats at 1 O’ clock serves fried brinjal. As the time for the two other families were filled, we can conclude that Pattabhiramans family is the one that eats at 1 O’ clock and serves fried brinjal.
Statement 2) says that the family serves fried brinjal uses blue chinaware. As Pattabhiramans family is serving fried brinjal, we can conclude that they use blue chinaware.
Statement 7) says that the family that eats last likes makkai-ki-roti. As Bannerjees family is eating last, we can conclude that they like makkai-ki-roti.
Statement 4) says that the family that serves sambar does not use red chinaware. As the blue china is already used, the only colour left is white. So we can conclude that the family serving sambar uses white chinaware. And as the meal for families other than the Sharmas were filled, the only place left to fill sambar is Sharma. As the Sharma family is serving sambar, they use white chinaware.
Red is remaining. So we can conclude that the Bannerjee family is the one that uses red chinaware.
Answer: (3) The Sharmas eat sambar at noon, the Pattabhiramans eat fried brinjal served in blue chinaware, and the Bannerjees eat makkai-ki-roti served in red chinaware
Example Case 2
2) Five persons with names P, M, U, T and X live separately in any one of the following: a palace, a hut, a fort, a house or a hotel. Each one likes two different colours from among the following: blue, black, red, yellow and green. U likes red and blue. T likes black. The person living in a palace does not like black or blue. P likes blue and red. M likes yellow. X lives in a hotel. M lives in a
[CAT 2000]
(1) hut
(2) palace
(3) fort
(4) house
U likes red and blue.
T likes black and ______ .
P likes blue and red.
M likes yellow and _______ .
X lives in a hotel.
There is one more clue saying that the person who lives in a palace does not like black or blue. X lives in a hotel. Every person other than M likes either black or blue. So we can conclude that M is the person living in the palace.
Answer: (2) palace
[CAT 2000]
(1) hut
(2) palace
(3) fort
(4) house
Solution
There are a few direct clues, so let us directly match the clues with the five persons.U likes red and blue.
T likes black and ______ .
P likes blue and red.
M likes yellow and _______ .
X lives in a hotel.
There is one more clue saying that the person who lives in a palace does not like black or blue. X lives in a hotel. Every person other than M likes either black or blue. So we can conclude that M is the person living in the palace.
Answer: (2) palace
Example Case 3
3) In a ‘keep-fit’ gymnasium class there are 15 females enrolled in a weight-loss programme. 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 weightgroup. 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 weightgroup 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?
[CAT 2001]
(1) Babita
(2) Elina
(3) Chandrika
(4) Deepika
Let us form a small table based on the weights.
Sonali, Shalini, Subhra and Shahira belong to the same weight-group.
Sonali and Rupa are in one weight-group. So Sonali, Shalini, Subhra, Shahira and Rupa are in same weight-group.
Rupali and Renuka are also in one weight-group.
Rupa, Radha, Renuka, Ruchika and Ritu belong to different weight-groups.
Shahira is in W1 and Somya is in W4 with Ruchika.
According to clue 5), Komal cannot be with Radha, Somya, or Ritu. As it is said that no weight-group can have more than 5 members, Komal cannot be in W1. So Komal must be with Rupali and Renuka.
Clue 6) says that Sweta and Jyotika cannot be with Rupali, but are in a weight group with a total membership of four. Therefore, Rupali, Renuka and Komal must be in the group with 3 members.
Sweta, Jyotika and Tara have to be added to their groups. According to clue 4), Tara cannot be with Radha. Clue 7) says that Sweta and Jyotika cannot be with Rupali, but are in a weight group with total membership of four. If we put Sweta and Jyotika with Radha, they would form a group with three members which is already there. Therefore, Radha must be in a group that has only 1 member. The Instructor for the group with 1 member is Elina, which is the correct answer.
Answer: (2) Elina
[CAT 2001]
(1) Babita
(2) Elina
(3) Chandrika
(4) Deepika
Solution
SolutionLet us form a small table based on the weights.
Sonali, Shalini, Subhra and Shahira belong to the same weight-group.
Sonali and Rupa are in one weight-group. So Sonali, Shalini, Subhra, Shahira and Rupa are in same weight-group.
Rupali and Renuka are also in one weight-group.
Rupa, Radha, Renuka, Ruchika and Ritu belong to different weight-groups.
Shahira is in W1 and Somya is in W4 with Ruchika.
According to clue 5), Komal cannot be with Radha, Somya, or Ritu. As it is said that no weight-group can have more than 5 members, Komal cannot be in W1. So Komal must be with Rupali and Renuka.
Clue 6) says that Sweta and Jyotika cannot be with Rupali, but are in a weight group with a total membership of four. Therefore, Rupali, Renuka and Komal must be in the group with 3 members.
Sweta, Jyotika and Tara have to be added to their groups. According to clue 4), Tara cannot be with Radha. Clue 7) says that Sweta and Jyotika cannot be with Rupali, but are in a weight group with total membership of four. If we put Sweta and Jyotika with Radha, they would form a group with three members which is already there. Therefore, Radha must be in a group that has only 1 member. The Instructor for the group with 1 member is Elina, which is the correct answer.
Answer: (2) Elina