Common Information
There are five boys in a certain school. Their names are Ram, Shyam, Ashok, John and Charit. Each of them represents the school in one of the following sports: Cricket, Table Tennis, Basketball, Lawn Tennis and Football. Their ages are 11, 12, 13, 14 and 15 in any order. Their coaches are Mr. Peter, Mr. Raju, Mr. Nehra, Mr. Jha and Mr. Abdul, not necessarily in the same order. The following information is also known.
Q31. 
Common Information Question: 1/5 What is the age (in years) of John? 
A.  11 

B.  12 

C.  13 

D.  14 

E.  15 
Solution:
Option(D) is correct
Let us analyse the information and prepare a matrix
Here, the objects are the boys and the properties to be determined are the sports played by each of them, their age and their coach.
We first choose short forms as follows:
Cricket, Table Tennis, Basketball, Lawn Tennis and Football: CK, TT, BB, LT and FB
Mr. Peter, Mr. Raju, Mr. Nehra, Mr. Jha and Mr. Abdul: P, R, N, J and A
1. Shyam plays Football. Neither Mr. Raju nor Mr. Nehra is his coach: So, we put a tick in the ‘FB’ column for Shyam (and put a cross in all the remaining boxes of that column and that row for the first five columns). Also put a cross in the R and N columns for Shyam.
2. John is neither the oldest nor the youngest. He plays Lawn Tennis: Thus, John cannot be 11 or 15 years old. We put a cross in the corresponding boxes. Also, he plays Lawn Tennis, so there will be a tick in that box and a cross in all other boxes in the same row and column.
3. Ram’s coach is Mr. Jha: Again, we put a tick in the corresponding box and a cross in other boxes in the same row and column.
4. The 13 year old boy plays Cricket: Thus, Shyam and John cannot be 13 years old because we know that they do not play cricket. We put a cross in the corresponding boxes.
5. Ashok’s age is the average of those of Shyam and John: This is slightly more complicated than our earlier conditions. Out of the five ages given, 12 is the average of 11 and 13, 13 is the average of 11 and 15, 13 is the average of 12 and 14 and 14 is the average of 13 and 15. Thus, Ashok has to be 12, 13 or 14 years old. We can put a cross in the ‘11’ and ‘15’ columns for Ashok.
But neither Shyam, nor John can be 13 years old. So Ashok cannot be 12 or 14 years old. So we put a cross in those boxes. Ashok is thus 13 years old. Thus, from condition 4 we know that Ashok plays cricket. So we put corresponding ticks and crosses accordingly. Since Ashok is 13 years old, John and Shyam have to be either 11 and 15 years old or 12 and 14 years old in any order.But, from condition 2 we know that John is not 11 or 15 years old. So they have to be 12 and 14 years old only. We put the crosses accordingly.
6. The youngest boy plays Table Tennis. Charit plays Basketball: As of now we do not know who the youngest boy is and who plays Table Tennis. But we know that Charit does not play TT, so we put a cross for him in the column of 11 years. We also put a tick in the BB column for Charit.
The only unfilled box left in the TT column is of Ram. So, Ram plays TT and is 11 years old. We put a tick in these two boxes and crosses in the remaining corresponding boxes. It can be observed now, that the only box unfilled in the column of 15 years is that of Charit’s. So Charit is 15 years old.
The matrix at this point looks like this:
We now analyse the last two conditions.
7. Mr. Peter and Mr. Raju are the coaches for Football and Cricket (not necessarily in that order): Since Shyam plays Football, and it is given that his coach cannot be R, his coach must be P. Thus, R is the coach for Cricket, and therefore of Ashok. We put ticks and crosses accordingly.
8. The second oldest boy plays Lawn Tennis, and is not coached by Mr. Nehra: We know that John plays LT. So he must be the second oldest boy i.e. 14 years old. It thus follows that Shyam is 12 years old. Also, we know from our matrix that John is coached either by N or A. Since N has been eliminated, John’s coach is A. Therefore, Charit’s coach is N.
The completed matrix is shown below:
From our completed matrix, we can see that John is 14 years old.
Hence, option D is the correct choice.
Q32. 
Common Information Question: 2/5 Which boy is coached by Mr. Abdul? 
A.  Ram 

B.  Charit 

C.  John 

D.  Shyam 

E.  Ashok 
Solution:
Option(C) is correct
Let us analyse the information and prepare a matrix
Here, the objects are the boys and the properties to be determined are the sports played by each of them, their age and their coach.
We first choose short forms as follows:
Cricket, Table Tennis, Basketball, Lawn Tennis and Football: CK, TT, BB, LT and FB
Mr. Peter, Mr. Raju, Mr. Nehra, Mr. Jha and Mr. Abdul: P, R, N, J and A
1. Shyam plays Football. Neither Mr. Raju nor Mr. Nehra is his coach: So, we put a tick in the ‘FB’ column for Shyam (and put a cross in all the remaining boxes of that column and that row for the first five columns). Also put a cross in the R and N columns for Shyam.
2. John is neither the oldest nor the youngest. He plays Lawn Tennis: Thus, John cannot be 11 or 15 years old. We put a cross in the corresponding boxes. Also, he plays Lawn Tennis, so there will be a tick in that box and a cross in all other boxes in the same row and column.
3. Ram’s coach is Mr. Jha: Again, we put a tick in the corresponding box and a cross in other boxes in the same row and column.
4. The 13 year old boy plays Cricket: Thus, Shyam and John cannot be 13 years old because we know that they do not play cricket. We put a cross in the corresponding boxes.
5. Ashok’s age is the average of those of Shyam and John: This is slightly more complicated than our earlier conditions. Out of the five ages given, 12 is the average of 11 and 13, 13 is the average of 11 and 15, 13 is the average of 12 and 14 and 14 is the average of 13 and 15. Thus, Ashok has to be 12, 13 or 14 years old. We can put a cross in the ‘11’ and ‘15’ columns for Ashok.
But neither Shyam, nor John can be 13 years old. So Ashok cannot be 12 or 14 years old. So we put a cross in those boxes. Ashok is thus 13 years old. Thus, from condition 4 we know that Ashok plays cricket. So we put corresponding ticks and crosses accordingly. Since Ashok is 13 years old, John and Shyam have to be either 11 and 15 years old or 12 and 14 years old in any order.But, from condition 2 we know that John is not 11 or 15 years old. So they have to be 12 and 14 years old only. We put the crosses accordingly.
6. The youngest boy plays Table Tennis. Charit plays Basketball: As of now we do not know who the youngest boy is and who plays Table Tennis. But we know that Charit does not play TT, so we put a cross for him in the column of 11 years. We also put a tick in the BB column for Charit.
The only unfilled box left in the TT column is of Ram. So, Ram plays TT and is 11 years old. We put a tick in these two boxes and crosses in the remaining corresponding boxes. It can be observed now, that the only box unfilled in the column of 15 years is that of Charit’s. So Charit is 15 years old.
The matrix at this point looks like this:
We now analyse the last two conditions.
7. Mr. Peter and Mr. Raju are the coaches for Football and Cricket (not necessarily in that order): Since Shyam plays Football, and it is given that his coach cannot be R, his coach must be P. Thus, R is the coach for Cricket, and therefore of Ashok. We put ticks and crosses accordingly.
8. The second oldest boy plays Lawn Tennis, and is not coached by Mr. Nehra: We know that John plays LT. So he must be the second oldest boy i.e. 14 years old. It thus follows that Shyam is 12 years old. Also, we know from our matrix that John is coached either by N or A. Since N has been eliminated, John’s coach is A. Therefore, Charit’s coach is N.
The completed matrix is shown below:
From our completed matrix, we can see that Mr. Abdul coaches John.
Hence, option C is the correct choice.
Q33. 
Common Information Question: 3/5 Who is the coach of the second youngest boy? 
A.  Mr. Abdul 

B.  Mr. Nehra 

C.  Mr. Peter 

D.  Mr. Raju 

E.  Mr. Jha 
Solution:
Option(C) is correct
Let us analyse the information and prepare a matrix
Here, the objects are the boys and the properties to be determined are the sports played by each of them, their age and their coach.
We first choose short forms as follows:
Cricket, Table Tennis, Basketball, Lawn Tennis and Football: CK, TT, BB, LT and FB
Mr. Peter, Mr. Raju, Mr. Nehra, Mr. Jha and Mr. Abdul: P, R, N, J and A
1. Shyam plays Football. Neither Mr. Raju nor Mr. Nehra is his coach: So, we put a tick in the ‘FB’ column for Shyam (and put a cross in all the remaining boxes of that column and that row for the first five columns). Also put a cross in the R and N columns for Shyam.
2. John is neither the oldest nor the youngest. He plays Lawn Tennis: Thus, John cannot be 11 or 15 years old. We put a cross in the corresponding boxes. Also, he plays Lawn Tennis, so there will be a tick in that box and a cross in all other boxes in the same row and column.
3. Ram’s coach is Mr. Jha: Again, we put a tick in the corresponding box and a cross in other boxes in the same row and column.
4. The 13 year old boy plays Cricket: Thus, Shyam and John cannot be 13 years old because we know that they do not play cricket. We put a cross in the corresponding boxes.
5. Ashok’s age is the average of those of Shyam and John: This is slightly more complicated than our earlier conditions. Out of the five ages given, 12 is the average of 11 and 13, 13 is the average of 11 and 15, 13 is the average of 12 and 14 and 14 is the average of 13 and 15. Thus, Ashok has to be 12, 13 or 14 years old. We can put a cross in the ‘11’ and ‘15’ columns for Ashok.
But neither Shyam, nor John can be 13 years old. So Ashok cannot be 12 or 14 years old. So we put a cross in those boxes. Ashok is thus 13 years old. Thus, from condition 4 we know that Ashok plays cricket. So we put corresponding ticks and crosses accordingly. Since Ashok is 13 years old, John and Shyam have to be either 11 and 15 years old or 12 and 14 years old in any order.But, from condition 2 we know that John is not 11 or 15 years old. So they have to be 12 and 14 years old only. We put the crosses accordingly.
6. The youngest boy plays Table Tennis. Charit plays Basketball: As of now we do not know who the youngest boy is and who plays Table Tennis. But we know that Charit does not play TT, so we put a cross for him in the column of 11 years. We also put a tick in the BB column for Charit.
The only unfilled box left in the TT column is of Ram. So, Ram plays TT and is 11 years old. We put a tick in these two boxes and crosses in the remaining corresponding boxes. It can be observed now, that the only box unfilled in the column of 15 years is that of Charit’s. So Charit is 15 years old.
The matrix at this point looks like this:
We now analyse the last two conditions.
7. Mr. Peter and Mr. Raju are the coaches for Football and Cricket (not necessarily in that order): Since Shyam plays Football, and it is given that his coach cannot be R, his coach must be P. Thus, R is the coach for Cricket, and therefore of Ashok. We put ticks and crosses accordingly.
8. The second oldest boy plays Lawn Tennis, and is not coached by Mr. Nehra: We know that John plays LT. So he must be the second oldest boy i.e. 14 years old. It thus follows that Shyam is 12 years old. Also, we know from our matrix that John is coached either by N or A. Since N has been eliminated, John’s coach is A. Therefore, Charit’s coach is N.
The completed matrix is shown below:
The second youngest boy is the one who is 12 years old. According to our table, Shyam is 12 years old. His coach is Mr. Peter.
Hence, option C is the correct choice.
Q34. 
Common Information Question: 4/5 For which sport is Mr. Nehra the coach? 
A.  Table Tennis 

B.  Football 

C.  Cricket 

D.  Lawn Tennis 

E.  Basketball 
Solution:
Option(E) is correct
Let us analyse the information and prepare a matrix
Here, the objects are the boys and the properties to be determined are the sports played by each of them, their age and their coach.
We first choose short forms as follows:
Cricket, Table Tennis, Basketball, Lawn Tennis and Football: CK, TT, BB, LT and FB
Mr. Peter, Mr. Raju, Mr. Nehra, Mr. Jha and Mr. Abdul: P, R, N, J and A
1. Shyam plays Football. Neither Mr. Raju nor Mr. Nehra is his coach: So, we put a tick in the ‘FB’ column for Shyam (and put a cross in all the remaining boxes of that column and that row for the first five columns). Also put a cross in the R and N columns for Shyam.
2. John is neither the oldest nor the youngest. He plays Lawn Tennis: Thus, John cannot be 11 or 15 years old. We put a cross in the corresponding boxes. Also, he plays Lawn Tennis, so there will be a tick in that box and a cross in all other boxes in the same row and column.
3. Ram’s coach is Mr. Jha: Again, we put a tick in the corresponding box and a cross in other boxes in the same row and column.
4. The 13 year old boy plays Cricket: Thus, Shyam and John cannot be 13 years old because we know that they do not play cricket. We put a cross in the corresponding boxes.
5. Ashok’s age is the average of those of Shyam and John: This is slightly more complicated than our earlier conditions. Out of the five ages given, 12 is the average of 11 and 13, 13 is the average of 11 and 15, 13 is the average of 12 and 14 and 14 is the average of 13 and 15. Thus, Ashok has to be 12, 13 or 14 years old. We can put a cross in the ‘11’ and ‘15’ columns for Ashok.
But neither Shyam, nor John can be 13 years old. So Ashok cannot be 12 or 14 years old. So we put a cross in those boxes. Ashok is thus 13 years old. Thus, from condition 4 we know that Ashok plays cricket. So we put corresponding ticks and crosses accordingly. Since Ashok is 13 years old, John and Shyam have to be either 11 and 15 years old or 12 and 14 years old in any order.But, from condition 2 we know that John is not 11 or 15 years old. So they have to be 12 and 14 years old only. We put the crosses accordingly.
6. The youngest boy plays Table Tennis. Charit plays Basketball: As of now we do not know who the youngest boy is and who plays Table Tennis. But we know that Charit does not play TT, so we put a cross for him in the column of 11 years. We also put a tick in the BB column for Charit.
The only unfilled box left in the TT column is of Ram. So, Ram plays TT and is 11 years old. We put a tick in these two boxes and crosses in the remaining corresponding boxes. It can be observed now, that the only box unfilled in the column of 15 years is that of Charit’s. So Charit is 15 years old.
The matrix at this point looks like this:
We now analyse the last two conditions.
7. Mr. Peter and Mr. Raju are the coaches for Football and Cricket (not necessarily in that order): Since Shyam plays Football, and it is given that his coach cannot be R, his coach must be P. Thus, R is the coach for Cricket, and therefore of Ashok. We put ticks and crosses accordingly.
8. The second oldest boy plays Lawn Tennis, and is not coached by Mr. Nehra: We know that John plays LT. So he must be the second oldest boy i.e. 14 years old. It thus follows that Shyam is 12 years old. Also, we know from our matrix that John is coached either by N or A. Since N has been eliminated, John’s coach is A. Therefore, Charit’s coach is N.
The completed matrix is shown below:
From our completed matrix, we can see that Mr. Nehra is the Basketball coach.
Hence, option E is the correct choice.
Q35. 
Common Information Question: 5/5 What is the difference in age (in years) between the boy who plays Football and the boy whose coach is Mr. Raju? 
A.  0 

B.  1 

C.  2 

D.  3 

E.  4 
Solution:
Option(B) is correct
Let us analyse the information and prepare a matrix
Here, the objects are the boys and the properties to be determined are the sports played by each of them, their age and their coach.
We first choose short forms as follows:
Cricket, Table Tennis, Basketball, Lawn Tennis and Football: CK, TT, BB, LT and FB
Mr. Peter, Mr. Raju, Mr. Nehra, Mr. Jha and Mr. Abdul: P, R, N, J and A
1. Shyam plays Football. Neither Mr. Raju nor Mr. Nehra is his coach: So, we put a tick in the ‘FB’ column for Shyam (and put a cross in all the remaining boxes of that column and that row for the first five columns). Also put a cross in the R and N columns for Shyam.
2. John is neither the oldest nor the youngest. He plays Lawn Tennis: Thus, John cannot be 11 or 15 years old. We put a cross in the corresponding boxes. Also, he plays Lawn Tennis, so there will be a tick in that box and a cross in all other boxes in the same row and column.
3. Ram’s coach is Mr. Jha: Again, we put a tick in the corresponding box and a cross in other boxes in the same row and column.
4. The 13 year old boy plays Cricket: Thus, Shyam and John cannot be 13 years old because we know that they do not play cricket. We put a cross in the corresponding boxes.
5. Ashok’s age is the average of those of Shyam and John: This is slightly more complicated than our earlier conditions. Out of the five ages given, 12 is the average of 11 and 13, 13 is the average of 11 and 15, 13 is the average of 12 and 14 and 14 is the average of 13 and 15. Thus, Ashok has to be 12, 13 or 14 years old. We can put a cross in the ‘11’ and ‘15’ columns for Ashok.
But neither Shyam, nor John can be 13 years old. So Ashok cannot be 12 or 14 years old. So we put a cross in those boxes. Ashok is thus 13 years old. Thus, from condition 4 we know that Ashok plays cricket. So we put corresponding ticks and crosses accordingly. Since Ashok is 13 years old, John and Shyam have to be either 11 and 15 years old or 12 and 14 years old in any order.But, from condition 2 we know that John is not 11 or 15 years old. So they have to be 12 and 14 years old only. We put the crosses accordingly.
6. The youngest boy plays Table Tennis. Charit plays Basketball: As of now we do not know who the youngest boy is and who plays Table Tennis. But we know that Charit does not play TT, so we put a cross for him in the column of 11 years. We also put a tick in the BB column for Charit.
The only unfilled box left in the TT column is of Ram. So, Ram plays TT and is 11 years old. We put a tick in these two boxes and crosses in the remaining corresponding boxes. It can be observed now, that the only box unfilled in the column of 15 years is that of Charit’s. So Charit is 15 years old.
The matrix at this point looks like this:
We now analyse the last two conditions.
7. Mr. Peter and Mr. Raju are the coaches for Football and Cricket (not necessarily in that order): Since Shyam plays Football, and it is given that his coach cannot be R, his coach must be P. Thus, R is the coach for Cricket, and therefore of Ashok. We put ticks and crosses accordingly.
8. The second oldest boy plays Lawn Tennis, and is not coached by Mr. Nehra: We know that John plays LT. So he must be the second oldest boy i.e. 14 years old. It thus follows that Shyam is 12 years old. Also, we know from our matrix that John is coached either by N or A. Since N has been eliminated, John’s coach is A. Therefore, Charit’s coach is N.
The completed matrix is shown below:
The boy who plays Football is Shyam (age 12). The boy who is coached by Mr. Raju is Ashok (age 13). The difference of their ages is 1 year.
Hence, option B is the correct choice.