CAT 2022 Slot 1 DILR Set 3 Q11–Q15

A DILR caselet from the Data Interpretation & Logical Reasoning (DILR) section of CAT 2022 Slot 1, with 5 questions (Quant-based Puzzles). Answers are CAT's official key.

The set

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.

Question 11

How many goals were scored in Match 7?
  1. A
    3
  2. B
    Cannot be determined
  3. C
    2
  4. D
    1

Answer: (D) 1 Quant-based Puzzles MCQ

Solution

  1. Distinct positive totals summing to 12 are \(\{1,2,3,6\}\) or \(\{1,2,4,5\}\). Bimla scores in at least 4 matches and Harita beats her, so the totals are Bimla 4, Harita 5 (top scorer), Amla and Sarita 1 and 2.
  2. Harita scores in exactly 3 matches including 4 and 8 (even matches: 1 goal each), so she has 1 in M4, 1 in M8 and 3 in one odd match. Bimla's three consecutive matches cannot include 4 or 8, so they are 5, 6, 7 (plus M1).
  3. Odd matches hold 8 goals. Harita's 3-goal match: M3 or M7 forces M3 = M7 = 3 (tie for highest) or is impossible; M5 would be the top match (not allowed). So it is M1, and with M3 = M7 and M5 different, the only fit is M1 = 4, M3 = 1, M5 = 2, M7 = 1.
  4. Amla and Sarita share the single goals in M2, M3 and M5 (one goal each), in some split of 1 and 2.
  5. Match 7 had 1 goal (Bimla's).

Question 12

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
    4, 1, 2, 1
  3. C
    5, 1, 0, 1
  4. D
    3, 2, 1, 2

Answer: (B) 4, 1, 2, 1 Quant-based Puzzles MCQ

Solution

  1. Distinct positive totals summing to 12 are \(\{1,2,3,6\}\) or \(\{1,2,4,5\}\). Bimla scores in at least 4 matches and Harita beats her, so the totals are Bimla 4, Harita 5 (top scorer), Amla and Sarita 1 and 2.
  2. Harita scores in exactly 3 matches including 4 and 8 (even matches: 1 goal each), so she has 1 in M4, 1 in M8 and 3 in one odd match. Bimla's three consecutive matches cannot include 4 or 8, so they are 5, 6, 7 (plus M1).
  3. Odd matches hold 8 goals. Harita's 3-goal match: M3 or M7 forces M3 = M7 = 3 (tie for highest) or is impossible; M5 would be the top match (not allowed). So it is M1, and with M3 = M7 and M5 different, the only fit is M1 = 4, M3 = 1, M5 = 2, M7 = 1.
  4. Amla and Sarita share the single goals in M2, M3 and M5 (one goal each), in some split of 1 and 2.
  5. Matches 1, 3, 5, 7: 4, 1, 2, 1.

Shortcut. A and D fail (M3=M7 tie or wrong); C has 0 in M5 though Bimla scored there.

Question 13

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
    Statement-1 only
  2. B
    Both the statements
  3. C
    None of the statements
  4. D
    Statement-2 only

Answer: (B) Both the statements Quant-based Puzzles MCQ

Solution

  1. Distinct positive totals summing to 12 are \(\{1,2,3,6\}\) or \(\{1,2,4,5\}\). Bimla scores in at least 4 matches and Harita beats her, so the totals are Bimla 4, Harita 5 (top scorer), Amla and Sarita 1 and 2.
  2. Harita scores in exactly 3 matches including 4 and 8 (even matches: 1 goal each), so she has 1 in M4, 1 in M8 and 3 in one odd match. Bimla's three consecutive matches cannot include 4 or 8, so they are 5, 6, 7 (plus M1).
  3. Odd matches hold 8 goals. Harita's 3-goal match: M3 or M7 forces M3 = M7 = 3 (tie for highest) or is impossible; M5 would be the top match (not allowed). So it is M1, and with M3 = M7 and M5 different, the only fit is M1 = 4, M3 = 1, M5 = 2, M7 = 1.
  4. Amla and Sarita share the single goals in M2, M3 and M5 (one goal each), in some split of 1 and 2.
  5. Amla and Sarita only score in M2, M3, M5, each of which has just one A/S goal, so they never share a match: Statement 1 true.
  6. Harita scores only in M1, M4, M8, none of which Sarita touches: Statement 2 true.

Question 14

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
    None of the statements
  2. B
    Statement-1 only
  3. C
    Statement-2 only
  4. D
    Both the statements

Answer: (A) None of the statements Quant-based Puzzles MCQ

Solution

  1. Distinct positive totals summing to 12 are \(\{1,2,3,6\}\) or \(\{1,2,4,5\}\). Bimla scores in at least 4 matches and Harita beats her, so the totals are Bimla 4, Harita 5 (top scorer), Amla and Sarita 1 and 2.
  2. Harita scores in exactly 3 matches including 4 and 8 (even matches: 1 goal each), so she has 1 in M4, 1 in M8 and 3 in one odd match. Bimla's three consecutive matches cannot include 4 or 8, so they are 5, 6, 7 (plus M1).
  3. Odd matches hold 8 goals. Harita's 3-goal match: M3 or M7 forces M3 = M7 = 3 (tie for highest) or is impossible; M5 would be the top match (not allowed). So it is M1, and with M3 = M7 and M5 different, the only fit is M1 = 4, M3 = 1, M5 = 2, M7 = 1.
  4. Amla and Sarita share the single goals in M2, M3 and M5 (one goal each), in some split of 1 and 2.
  5. Every match has at least one goal (4,1,1,1,2,1,1,1): Statement 1 true.
  6. Matches scored in: Bimla 4, Harita 3, and Amla/Sarita 1 and 2: all different, Statement 2 true. So neither is false.

Question 15

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
    None of the statements
  2. B
    Statement-1 only
  3. C
    Both the statements
  4. D
    Statement-2 only

Answer: (A) None of the statements Quant-based Puzzles MCQ

Solution

  1. Distinct positive totals summing to 12 are \(\{1,2,3,6\}\) or \(\{1,2,4,5\}\). Bimla scores in at least 4 matches and Harita beats her, so the totals are Bimla 4, Harita 5 (top scorer), Amla and Sarita 1 and 2.
  2. Harita scores in exactly 3 matches including 4 and 8 (even matches: 1 goal each), so she has 1 in M4, 1 in M8 and 3 in one odd match. Bimla's three consecutive matches cannot include 4 or 8, so they are 5, 6, 7 (plus M1).
  3. Odd matches hold 8 goals. Harita's 3-goal match: M3 or M7 forces M3 = M7 = 3 (tie for highest) or is impossible; M5 would be the top match (not allowed). So it is M1, and with M3 = M7 and M5 different, the only fit is M1 = 4, M3 = 1, M5 = 2, M7 = 1.
  4. Amla and Sarita share the single goals in M2, M3 and M5 (one goal each), in some split of 1 and 2.
  5. Harita played 3 scoring matches, so Sarita scored in 2 (total 2) and Amla in 1.
  6. Amla scores in only one match, so Statement 1 is not true. Sarita's two matches can be any two of M2, M3, M5 (e.g. 2 and 5), so Statement 2 is not necessary. Neither.

Same concept in other years

See every question on Small integer counts per entity per day/match under sum and ordering clues.

More Quant-based Puzzles questions from CAT

All 127 Quant-based Puzzles questions asked since 2017.