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CAT 2022 Slot 1 DILR · Set 1 of 4Logical ReasoningModerate DifficultyQ1–Q5 · 5 MCQ

CAT 2022 Slot 1 DILR Set 1: Arrangements (5 Questions) with Solutions

The Arrangements set from the official CAT 2022 Slot 1 DILR paper: the caselet, all 5 questions, the official answer key and a step-by-step solution for each. 100% free, no sign-up.

The Set: Read the Caselet First

CAT 2022 Slot 1 DILR · Questions 1–5
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.

In the exam this set competed with 3 others for 40 minutes. Budget about 10 minutes if you attempt it.

Q1. Arrangements

MCQ · +3 / −1
How many goals were scored in Match 7?
  1. A) 1
  2. B) 2
  3. C) 3
  4. D) Cannot be determined
Correct Answer
A) 1
Step-by-step solution
📌 Core Concept
Fix the goal totals from the distinct-total and 12-goal constraints, then place each player's goals match by match.
🔢 Step-by-Step Solution
1
Matches 2, 4, 6 and 8 have 1 goal each, so 4 goals are used. The other 8 goals are in matches 1, 3, 5 and 7.
2
Bimla scored in 4 matches, so she has at least 4 goals. Harita has more than Bimla, so Harita has at least 5. The totals are distinct and sum to 12, so the only split is Harita 5, Bimla 4, and 2 and 1 for Amla and Sarita.
3
The top scorer scored in exactly 3 matches. Bimla scored in 4 matches, so the top scorer is Harita with 5 goals. She scored 1 each in matches 4 and 8, so she scored 3 in one more match. Match 4 and match 8 each had only 1 goal, so Bimla did not score in them.
4
Bimla scored in match 1 and in three other consecutive matches. These cannot include 4 or 8, so they are matches 5, 6 and 7. Bimla scored 1 goal in each of matches 1, 5, 6 and 7.
5
Harita's 3-goal match is the unique highest and is not match 5. If it were match 3 or 7, the other of the two would have equal goals (match 3 equals match 7), so the maximum would not be unique. Hence it is match 1, and match 1 has at least 4 goals (Bimla's 1 plus Harita's 3).
6
Amla and Sarita have 3 goals in total: 1 in match 2 and 2 spread over matches 1, 3, 5 and 7. Match 3 needs a scorer, and only Amla or Sarita can supply it, so it gets at least 1 of those extra goals.
7
If match 3 had 2 goals, match 7 would also have 2, needing 2 + 1 = 3 extra goals, but only 2 are available. So match 3 has 1 goal and match 7 has 1 goal, which is Bimla's.
Quick Check
The remaining extra goal must go to match 5 (match 5 differs from match 3, so it cannot have 1 goal). The odd matches then have 4, 1, 2, 1 goals, which sum to 8.
Correct Answer: A

Q2. Arrangements

MCQ · +3 / −1
Which of the following is the correct sequence of goals scored in matches 1, 3, 5 and 7?
  1. A) 3, 1, 2, 1
  2. B) 5, 1, 0, 1
  3. C) 3, 2, 1, 2
  4. D) 4, 1, 2, 1
Correct Answer
D) 4, 1, 2, 1
Step-by-step solution
📌 Core Concept
Fix the goal totals from the distinct-total and 12-goal constraints, then place each player's goals match by match.
🔢 Step-by-Step Solution
1
Matches 2, 4, 6 and 8 have 1 goal each, so 4 goals are used. The other 8 goals are in matches 1, 3, 5 and 7.
2
Bimla scored in 4 matches, so she has at least 4 goals. Harita has more than Bimla, so Harita has at least 5. The totals are distinct and sum to 12, so the split is Harita 5, Bimla 4, and 2 and 1 for Amla and Sarita.
3
The top scorer scored in exactly 3 matches, so it is Harita, not Bimla. Harita scored 1 each in matches 4 and 8, and 3 goals in one more match. Bimla therefore did not score in matches 4 or 8.
4
Bimla scored in match 1 and in three other consecutive matches. These cannot include 4 or 8, so they are matches 5, 6 and 7. Bimla scored 1 goal in each of matches 1, 5, 6 and 7.
5
Harita's 3-goal match is the unique highest and is not match 5. It cannot be match 3 or 7, because those two have equal goals and the maximum would not be unique. So it is match 1, which then has 3 + 1 = 4 goals.
6
Amla and Sarita have 3 goals in total: 1 in match 2, and 2 more. Match 3 needs a scorer, so it gets at least 1 of them. If match 3 had 2 goals, match 7 would also need 2, requiring 3 extra goals when only 2 exist. So matches 3 and 7 have 1 goal each.
7
The last extra goal goes to match 5, which must differ from match 3, giving 2 goals in match 5.
8
The sequence for matches 1, 3, 5 and 7 is 4, 1, 2, 1.
Why Not the Others
A) Match 1 would have to be 4 because of Harita's 3 plus Bimla's 1, not 3.
B) Match 5 cannot be 0, since Bimla scored in it.
C) Matches 3 and 7 must be equal, but here they are 2 each, which needs too many goals.
Correct Answer: D

Q3. Arrangements

MCQ · +3 / −1
Which of the following statement(s) is/are true?
Statement-1: Amla and Sarita never scored goals in the same match.
Statement-2: Harita and Sarita never scored goals in the same match.
  1. A) None of the statements
  2. B) Statement-1 only
  3. C) Both the statements
  4. D) Statement-2 only
Correct Answer
C) Both the statements
Step-by-step solution
📌 Core Concept
Work out the full goal distribution and then check which pairs of players share a match.
🔢 Step-by-Step Solution
1
Matches 2, 4, 6 and 8 have 1 goal each. The totals are distinct and sum to 12, with Bimla in at least 4 matches and Harita above her. This gives Harita 5, Bimla 4, and 2 and 1 for Amla and Sarita.
2
Harita is the top scorer and scored in exactly 3 matches: 1 each in matches 4 and 8, and 3 in match 1. This follows because the 3-goal match is unique and not match 5, and matches 3 and 7 have equal goals.
3
Bimla scored 1 goal each in matches 1, 5, 6 and 7.
4
The goals of Amla and Sarita are 1 in match 2, 1 in match 3, and 1 in match 5. These matches have exactly one such goal each, because the match totals are 1, 1 and 2 (match 5 is 1 from Bimla plus 1 more).
5
Statement-1: Amla and Sarita each take goals from matches 2, 3 and 5, one goal per match, so they never score in the same match. True.
6
Statement-2: Harita scored only in matches 1, 4 and 8, while Sarita scored only in some of matches 2, 3 and 5. They never overlap. True.
Correct Answer: C

Q4. Arrangements

MCQ · +3 / −1
Which of the following statement(s) is/are false?
Statement-1: In every match at least one player scored a goal.
Statement-2: No two players scored goals in the same number of matches.
  1. A) Statement-2 only
  2. B) None of the statements
  3. C) Both the statements
  4. D) Statement-1 only
Correct Answer
B) None of the statements
Step-by-step solution
📌 Core Concept
Use the full distribution of goals to test each statement.
🔢 Step-by-Step Solution
1
The totals are Harita 5, Bimla 4, and 2 and 1 for Amla and Sarita. This follows from the 12-goal total, the distinct totals, Bimla scoring in 4 matches, and Harita being the top scorer in exactly 3 matches.
2
Match by match, the scorers are as follows.
Match 1: Harita 3 and Bimla 1.
Match 2: one goal from Amla or Sarita.
Match 3: one goal from Amla or Sarita.
Match 4: Harita 1.
Match 5: Bimla 1 and one goal from Amla or Sarita.
Match 6: Bimla 1.
Match 7: Bimla 1.
Match 8: Harita 1.
3
Statement-1: every match has at least one scoring player. Matches 1 to 8 each have a scorer in the list above. So the statement is true, not false.
4
Statement-2: the numbers of matches in which the players scored are Harita 3, Bimla 4, and 2 and 1 for Amla and Sarita. All four counts are different. So the statement is true, not false.
5
Neither statement is false.
Correct Answer: B

Q5. Arrangements

MCQ · +3 / −1
If Harita scored goals in one more match as compared to Sarita, which of the following statement(s) is/are necessarily true?
Statement-1: Amla scored goals in consecutive matches.
Statement-2: Sarita scored goals in consecutive matches.
  1. A) Statement-1 only
  2. B) Statement-2 only
  3. C) Both the statements
  4. D) None of the statements
Correct Answer
D) None of the statements
Step-by-step solution
📌 Core Concept
Use the fixed goal distribution and the extra condition about Sarita's matches to see what must hold.
🔢 Step-by-Step Solution
1
The totals are Harita 5, Bimla 4, and 2 and 1 for Amla and Sarita. Harita scored in exactly 3 matches: 1, 4 and 8. Bimla scored in 1, 5, 6 and 7.
2
The goals of Amla and Sarita are 1 each in matches 2, 3 and 5, with no two of those goals in the same match.
3
Harita scored in 3 matches. If she scored in one more match than Sarita, Sarita scored in 2 matches, so Sarita has 2 goals and Amla has 1 goal.
4
Statement-1: Amla scored in only one match, so she did not score in consecutive matches. Statement-1 is false.
5
Statement-2: Sarita scored in two of matches 2, 3 and 5. She may have scored in matches 2 and 3, which are consecutive. She may also have scored in matches 2 and 5, or in matches 3 and 5, which are not consecutive. So Statement-2 is not necessarily true.
6
Neither statement is necessarily true.
Correct Answer: D
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CAT 2022 Slot 1 DILR at a Glance

Sets in this section4
Questions in this section20
Section time40 minutes
Convenor IIMIIM Bangalore

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