CAT 2019 Slot 2 — DILR Question 21
Answer the following questions based on the information given below.
Ten players, as listed in the table below, participated in a rifle shooting competition comprising of 10 rounds. Each round had 6 participants. Players numbered 1 through 6 participated in Round 1, players 2 through 7 in Round 2,..., players 5 through 10 in Round 5, players 6 through 10 and 1 in Round 6, players 7 through 10, 1 and 2 in Round 7 and so on. The top three performances in each round were awarded 7, 3 and 1 points respectively. There were no ties in any of the 10 rounds. The table below gives the total number of points obtained by the 10 players after Round 6 and Round 10.
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The following information is known about Rounds 1 through 6:
- Gordon did not score consecutively in any two rounds.
- Eric and Fatima both scored in a round.
The following information is known about Rounds 7 through 10:
- Only two players scored in three consecutive rounds. One of them was Chen. No other player scored in any two consecutive rounds.
- Joshin scored in Round 7, while Amita scored in Round 10.
- No player scored in all the four rounds.
What were the scores of Chen, David, and Eric respectively after Round 3?
Answer & solution
- A
3, 0, 3
- B
3, 3, 0
3, 3, 3
- D
3, 6, 3
âââââââAs the top three performances in each round were awarded 7, 3 and 1 respectively, remaining all performances were awarded 0 points.
Amita was participant in round 1 and in rounds 6 through 10.
âââââââSo, in all she scored 8(= 1 + 7) points in round 1 and round 6. Also she scored 10 points in rounds 7 through 10 together.
Bala was participant in rounds 1 and 2 and also in rounds 7 through 10.
As he scored 2 points in first two rounds, he must have scored 1 point in each of the two rounds. He scored 3(= 3 or 1+1+1) points in rounds 7 through 10.
Chen scored 3 points in first three rounds and as he scored in three consecutive rounds among 7 through 10, he must have scored 1 point each in round 8, 9 and 10.
David scored 6 points in first four rounds together and 0 (i.e., 6 – 6) each in 9th and 10th rounds.
Eric scored 3(= 3 or 1+1+1) points in five rounds together and hence 10 – 3 = 7 points in the 10th round.
Gordon scored 17 points in rounds 2 through 6 together and hence, 17 – 17 = 0 points in the 7th round.
As he did not scored consecutively in any two rounds, he must have scored 0 in 3rd and 5th round and 7, 7, and 3 points in 2nd, 4th and 6th rounds, not necessarily in the given sequence.
Hansa scored 1 point in one of the rounds 3-6. So, she must have scored 4 – 1 = 3 points in either 7th or 8th rounds.
Ikea scored 2 points in 4th, 5th and 6th rounds together. Therefore, remaining 15 points must have been scored in 7th, 8th and 9th round in some order.
As Chen scored 1 point in the 8th and 9th round, Ikea must have scored 1 point in 7th round and 7 points each in the 8th and 9th round.
Joshin scored 14 points in 5th and 6th rounds. So he scored 7 points in each of 5th and 6th rounds.
Now we need to decide about remaining 3 points in the last four rounds.
As Joshin scored in round 7, and Chen has scored 1 point in each of the last three rounds, Joshin must have scored all 3 points in the 7th round and 0 points in the last three rounds.
Therefore, we can tabulate this information as
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As Joshin scored 3 points in the 7th round, Hansa must have scored 3 in 8th round and 0 in the 7th round. Now consider 7th round. Only Amita must have scored 7 in the 7th round.
As she has scored in round 10, the remaining 3 points she must have scored in round 10. Thus, we can now conclude that Bala scored 3 points in the 9th round.
As Joshin scored 7 points in the 6th round Amita must have scored 1 point in this round and hence7 points in the first round.
Gordon scored 7, 7 and 3 points in 2nd, 4th and 6th rounds. Joshin scored 7 points in the 6th round so, Gordon scored 7, 7 and 3 points in 2nd, 4th and 6th rounds respectively.
So we can fill remaining values as 0 in the table for the 6th round.
Thus, Ikea scored 1 point each in 4th and 5th rounds. And hence, Hansa scored 1 point in the 3rd round.
So far we have entered values 1 and 7 for all the rounds. Now we have to enter 3 points of each of Bala, Chen, David and Fatima and 7 points for Fatima.
Eric and Fatima both scored in a round. This is possible only when Fatima scored 7 points and Eric scored 3 points. This must be round 3.
No one other than Fatima scored 3 points in round 5. Similarly, David scored 3 points in the 4th round. Chen and David scored 3 points in 1st and 2nd round in some order.
Thus we have
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After round 3, the scores of Chen, David and Eric were 3, 3, 3.
Hence, option (c).