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CAT 2022 Slot 2 · DILR · Games and Tournaments · hard

CAT 2022 Slot 2 DILR: Debate Contest Judging

Five students — A, B, C, D and E — participated in an inter-college debate contest. Three judges, J1, J2 and J3, each independently scored the five participants. Each judge awarded the five participants five distinct integer scores from the set {6, 7, 8, 9, 10} — that is, each judge's five scores form a permutation of 6, 7, 8, 9 and 10, one score per participant. A participant's final score is the sum of the scores given by the three judges, and the participant with the highest final score is declared the winner (no two participants have the same final score).

The following is known about the scoring:
1. Under J1, A received the highest score (10) and C received the lowest (6).
2. Under J1, D scored higher than B, and B scored higher than E.
3. Under J2, B received the highest score (10) and D received the lowest (6).
4. Under J2, E scored higher than C, and C scored higher than A.
5. Under J3, C received the highest score (10) and E received the lowest (6).
6. Under J3, A scored higher than D, and D scored higher than B.

Question 1

Single correct option

Who wins the debate contest?
  1. A. A
  2. B. B
  3. C. C
  4. D. D
Show answer and solution

Answer: (A) A

From clue 1, J1: A=10, C=6; clue 2 forces the remaining scores {7,8,9} onto D,B,E as D>B>E, so D=9,B=8,E=7. From clue 3, J2: B=10,D=6; clue 4 forces {7,8,9} onto E,C,A as E>C>A, so E=9,C=8,A=7. From clue 5, J3: C=10,E=6; clue 6 forces {7,8,9} onto A,D,B as A>D>B, so A=9,D=8,B=7. Totals: A=10+7+9=26, B=8+10+7=25, C=6+8+10=24, D=9+6+8=23, E=7+9+6=22. A has the highest total and wins.

Question 2

Numerical answer

What score did E receive from judge J2?
Show answer and solution

Answer: 9

From clue 3, J2 gave D the lowest score (6) and B the highest (10). Clue 4 says, under J2, E>C>A, so the remaining scores {7,8,9} are assigned with E getting the highest of the three, i.e. E=9, C=8, A=7.

Question 3

Single correct option

Which participant received the lowest score from judge J1?
  1. A. B
  2. B. C
  3. C. D
  4. D. E
Show answer and solution

Answer: (B) C

Clue 1 directly states that under J1, C received the lowest score (6).

Question 4

Numerical answer

What is D's final score (sum over all three judges)?
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Answer: 23

D's scores: J1=9 (from D>B>E among {7,8,9} after A=10,C=6), J2=6 (clue 3, lowest), J3=8 (from A>D>B among {7,8,9} after C=10,E=6). Total = 9+6+8 = 23.

Question 5

Single correct option

What is the correct ranking of the five participants from highest to lowest final score?
  1. A. A, B, C, D, E
  2. B. B, A, C, D, E
  3. C. A, C, B, D, E
  4. D. A, B, D, C, E
Show answer and solution

Answer: (A) A, B, C, D, E

Using the fully solved grid: totals are A=26, B=25, C=24, D=23, E=22, which gives the descending order A, B, C, D, E.
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Original question written in the CAT 2022 Slot 2 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake