CAT 2022 Slot 1 — DILR Question 16
Answer the next 5 questions based on the information given below:
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.
How many goals were scored in Match 7?
Answer & solution
- A
3
- B
2
- C
Cannot be determined
1
Total 12 goals were scored by 4 players such that each player scored at least one goal and distinct number of total goals.
There are two possibilities for this:
12 = 1 + 2 + 3 + 6
12 = 1 + 2 + 4 + 5
From (1): Only one goal was scored in every even numbered match.
From (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.
Let the number of goals scored in Match 3 and 7 be x each.
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From (6): The match in which the highest number of goals was scored was unique and it was not Match 5.
⇒ Highest goals were scored in Match 1.
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From (4): Bimla scored a goal in Match 1 and one each in three other consecutive matches.
From (2): Harita scored more goals than Bimla.
⇒ Bimla scored at least 4 goals while Harita scored at least 5 goals.
∴ 12 = 1 + 2 + 4 + 5
⇒ Bimla scored 4 goals while Harita scored at 5 goals.
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From (3): The highest goal scorer scored goals in exactly 3 matches including Match 4 and Match 8.
∴ Harita can score maximum 1 goal each in Match 4 and 5, hence she scores 3 goals in one more Match.
The only match Harita can score 3 goals is Match 1 since highest numbers of goals are scored in Match 1.
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From (4): Bimla scored a goal in Match 1 and one each in three other consecutive matches.
∴ Three consecutive matches Bimla can score in are Match 5, 6 and 7.
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Now, a + 1 + x + 1 + b + 1 + x + 1 = 12
⇒ a + b + 2x = 8
[Match 7: x has to be greater than or equal to 1.]
Case 1: x = 1
⇒ a + b = 6
⇒ a = 4 and b = 2 [a has to be uniquely highest and a, b ≠ x]
Case 2: x = 2
⇒ a + b = 4
Rejected as minimum value of a is 4 and that of b is 1.
∴ x = 1, a = 4 and b = 2
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Amla or Sarita could have scored 1 or 2 goal in any order.
Number of goals scored in Match 7 = 1.
Hence, option (d).