Directions: Answer the questions based on the information given below.
During the recent India- Australia bilateral 7 one-day international matches series Dhawan, Rohit and Kohli were in tremendous form and combinedly scored 7 centuries in these 7 games. Further, it is also known about their scores in the series:
1. In each game exactly one batsman scored a century.
2. Each of these three players scored at least one century and no two batsmen scored equal number of centuries.
3. Rohit did not score a century in the 2nd game and Kohli scored a century in the last game.
4. Dhawan did not score a century in the 1st and 4th game.
5 The player who scored a century in the 2nd game did not score a century in the 5th game.
6. The player who scored a century in the 4th game also scored a century in the 6th game.
7. The player who scored a century in the 3rd game did not score a century in the 1st game.
If Rohit scored a century in the 3rd game in which game/s did Dhawan score a century?
Directions: Answer the questions based on the information given below.
During the recent India- Australia bilateral 7 one-day international matches series Dhawan, Rohit and Kohli were in tremendous form and combinedly scored 7 centuries in these 7 games. Further, it is also known about their scores in the series:
1. In each game exactly one batsman scored a century.
2. Each of these three players scored at least one century and no two batsmen scored equal number of centuries.
3. Rohit did not score a century in the 2nd game and Kohli scored a century in the last game.
4. Dhawan did not score a century in the 1st and 4th game.
5 The player who scored a century in the 2nd game did not score a century in the 5th game.
6. The player who scored a century in the 4th game also scored a century in the 6th game.
7. The player who scored a century in the 3rd game did not score a century in the 1st game.
If Rohit scored a century in the 3rd game in which game/s did Dhawan score a century?
The correct option is A 2nd
From statement 1 and 2 it is clear that these three batsmen scored, 1, 2, 4 centuries in any order. From the remaining information we could from the following table:
1234567DhawnN N NNRohit N NKohli C
'N, represents a less than 100 score 'C' represents a century.
It is given that Rohit scored a century in the 3rd game, therefore, he did not score a century in the 1st game. Hence Kohli scored a century in the 1st game. Now Dhawan scored a 100+ in either the 2nd or the 5th game.
1234567DhawnN NN NNRohitNNC NKohliC N C
Case I: Dhawan scored a century in the 5th game.
In this case, it is not possible that he scored a century in the 2nd game (according to the 5th condition), hence Kohli scored a century in the 2nd game. If Kohli scored a century in the 4th game he must score a 100 in 6th game as well, which is not possible because in this case, he scored 5 centuries, which is not possible. If Rohit scored a 100 in the 4th game then he must score a century in the 6th game as well which is again not possible because in this case, two batsmen scored an equal number of centuries. (Kohli and Rohit would have 3 centuries each). Thus, we reject Dhawan scoring a century in game 5. He could not have scored a century in game 5.
Case 2: Dhawan scored a century in the 2nd game. In such a case, the table would look as below:
1234567DhawnNNNNNNNRohitNNC NKohliCNN C
From the above table it is clear that out of the 4th, 5th and 6th games, Kohli scored a century in either 0 or 2 games and Rohit scored a century in either I or 3 games.
Case 2(a): When Kohli did not score a century in 4th, 5th, 6th games. Then Rohit scored centuries in all three games (4th, 5th, 6th).
1234567DhawnNNNNNNNRohitNNCCCCNKohliCNNNNNC
Case 2(b): When Kohli scored centuries in the 4th and 6th games: Note- It is not possible that Kohli scored a 100 in the 4th , 5th or 5th, 6th games that contradicts clue 6. Then Rohit scored a century in the 5th game, The become as follows:
1234567DhawnNCNNNNNRohitNNCNCNNKohliCNNCNCC
Therefore, Dhawan scored a 100 in only the 2nd game.
Option (a) is correct.
2nd
From statement 1 and 2 it is clear that these three batsmen scored, 1, 2, 4 centuries in any order. From the remaining information we could from the following table:
1234567DhawnN N NNRohit N NKohli C
'N, represents a less than 100 score 'C' represents a century.
It is given that Rohit scored a century in the 3rd game, therefore, he did not score a century in the 1st game. Hence Kohli scored a century in the 1st game. Now Dhawan scored a 100+ in either the 2nd or the 5th game.
1234567DhawnN NN NNRohitNNC NKohliC N C
Case I: Dhawan scored a century in the 5th game.
In this case, it is not possible that he scored a century in the 2nd game (according to the 5th condition), hence Kohli scored a century in the 2nd game. If Kohli scored a century in the 4th game he must score a 100 in 6th game as well, which is not possible because in this case, he scored 5 centuries, which is not possible. If Rohit scored a 100 in the 4th game then he must score a century in the 6th game as well which is again not possible because in this case, two batsmen scored an equal number of centuries. (Kohli and Rohit would have 3 centuries each). Thus, we reject Dhawan scoring a century in game 5. He could not have scored a century in game 5.
Case 2: Dhawan scored a century in the 2nd game. In such a case, the table would look as below:
1234567DhawnNNNNNNNRohitNNC NKohliCNN C
From the above table it is clear that out of the 4th, 5th and 6th games, Kohli scored a century in either 0 or 2 games and Rohit scored a century in either I or 3 games.
Case 2(a): When Kohli did not score a century in 4th, 5th, 6th games. Then Rohit scored centuries in all three games (4th, 5th, 6th).
1234567DhawnNNNNNNNRohitNNCCCCNKohliCNNNNNC
Case 2(b): When Kohli scored centuries in the 4th and 6th games: Note- It is not possible that Kohli scored a 100 in the 4th , 5th or 5th, 6th games that contradicts clue 6. Then Rohit scored a century in the 5th game, The become as follows:
1234567DhawnNCNNNNNRohitNNCNCNNKohliCNNCNCC
Therefore, Dhawan scored a 100 in only the 2nd game.
Option (a) is correct.
