CAT 2022 Slot 1 · DILR · Question 2
CAT 2022 Slot 1 previous year question on Caselet DI, with the answer and a step-by-step solution.
Set 1: Goals Scored by Four Hockey Players — this question belongs to a set. Read the full set with all 5 questions →
The management of a university hockey team was evaluating performance of four women players - Amla, Bimla, Harita and Sarita for their possible selection in the university team for next year. For this purpose, the management was looking at the number of goals scored by them in the past 8 matches, numbered 1 through 8. The four players together had scored a total of 12 goals in these matches. In the 8 matches, each of them had scored at least one goal. No two players had scored the same total number of goals.
The following facts are known about the goals scored by these four players only. All the questions refer only to the goals scored by these four players.
1. Only one goal was scored in every even numbered match.
2. Harita scored more goals than Bimla.
3. The highest goal scorer scored goals in exactly 3 matches including Match 4 and Match 8.
4. Bimla scored a goal in Match 1 and one each in three other consecutive matches.
5. An equal number of goals were scored in Match 3 and Match 7, which was different from the number of goals scored in either Match 1 or Match 5.
6. The match in which the highest number of goals was scored was unique and it was not Match 5.
- A5, 1, 0, 1
- B3, 1, 2, 1
- C3, 2, 1, 2
- D4, 1, 2, 1
Answer & solution
Answer: Option D
Solving the set
Step 1 – Goals per player. Four different positive totals adding to 12: {1, 2, 3, 6} or {1, 2, 4, 5}.
Step 2 – Even matches (2, 4, 6, 8) have 1 goal each (fact 1), so 4 goals; the odd matches (1, 3, 5, 7) have 8 goals.
Step 3 – Bimla. She scores in Match 1 and exactly one goal in each of three other consecutive matches (fact 4), so she has at least 4 goals; with Harita above her (fact 2), Bimla = 4 and Harita = 5. Amla and Sarita have 1 and 2.
Step 4 – Harita is the top scorer: she scores in exactly 3 matches including 4 and 8 (fact 3). Those two even matches give her 1 goal each, so her third match gives 3 goals – an odd match. Matches 4 and 8 are 'used up' by Harita, so Bimla's run of three consecutive matches avoids 4 and 8 and excludes Match 1: it must be Matches 5, 6, 7.
Step 5 – Match totals. Matches 1, 5 and 7 each have at least Bimla's goal; Match 3 = Match 7 and both differ from Matches 1 and 5 (fact 5); the largest match total is unique and is not Match 5 (fact 6). Where is Harita's 3-goal match?
• Match 3 or Match 7: then Match 3 = Match 7 ≥ 3 and the odd matches already need 1 + 3 + 1 + 3 = 8 goals, so the top total (3) is shared by Matches 3 and 7 – not unique.
• Match 5: then Match 5 ≥ 4, and the other odd matches share at most 4 goals with Match 3 = Match 7, so Match 5 would be the unique maximum – not allowed.
• So it is Match 1 (at least 4 goals). With Match 1 + 2 × Match 3 + Match 5 = 8 and Match 5 ≠ Match 3, the only option is Match 1 = 4, Match 3 = Match 7 = 1, Match 5 = 2. Amla and Sarita's 3 goals therefore fall in Matches 2, 3 and 5 (Match 6's goal is Bimla's, Matches 4 and 8 are Harita's).
Match | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | Total |
Bimla | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 4 |
Harita | 3 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 5 |
Amla + Sarita | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 3 |
Goals in match | 4 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 12 |
Step 6 – Amla and Sarita's 3 goals (one player 1, the other 2) are spread over Matches 2, 3 and 5 in six possible ways:
Case | Amla scored in | Sarita scored in | Totals (A, S) |
1 | Match 5 | Matches 2, 3 | 1, 2 |
2 | Match 3 | Matches 2, 5 | 1, 2 |
3 | Matches 3, 5 | Match 2 | 2, 1 |
4 | Match 2 | Matches 3, 5 | 1, 2 |
5 | Matches 2, 5 | Match 3 | 2, 1 |
6 | Matches 2, 3 | Match 5 | 2, 1 |
This question
From the match table, Matches 1, 3, 5 and 7 had 4, 1, 2 and 1 goals.
Hence, the answer is option 4.
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