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CAT 2020 Slot 3 DILR · Set 2 of 5Logical ReasoningHard DifficultyQ5–Q10 · 2 MCQ + 4 TITA

CAT 2020 Slot 3 DILR Set 2: Games & Tournaments (6 Questions) with Solutions

The Games & Tournaments set from the official CAT 2020 Slot 3 DILR paper: the caselet, all 6 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 2020 Slot 3 DILR · Questions 5–10
The Hi-Lo game is a four-player game played in six rounds. In every round, each player chooses to bid Hi or Lo. The bids are made simultaneously. If all four bid Hi, then all four lose 1 point each. If three players bid Hi and one bids Lo, then the players bidding Hi gain 1 point each and the player bidding Lo loses 3 points. If two players bid Hi and two bid Lo, then the players bidding Hi gain 2 points each and the players bidding Lo lose 2 points each. If one player bids Hi and three bid Lo, then the player bidding Hi gains 3 points and the players bidding Lo lose 1 point each. If all four bid Lo, then all four gain 1 point each.
Four players Arun, Bankim, Charu, and Dipak played the Hi-Lo game. The following facts are known about their game:
1
At the end of three rounds, Arun had scored 6 points, Dipak had scored 2 points, Bankim and Charu had scored -2 points each.
2
At the end of six rounds, Arun had scored 7 points, Bankim and Dipak had scored -1 point each, and Charu had scored -5 points.
3
Dipak's score in the third round was less than his score in the first round but was more than his score in the second round.
4
In exactly two out of the six rounds, Arun was the only player who bid Hi.

In the exam this set competed with 4 others for 40 minutes. Budget about 8 minutes if you attempt it.

Q5. Games & Tournaments

MCQ · +3 / −1
What were the bids by Arun, Bankim, Charu and Dipak, respectively in the first round?
  1. A) Lo, Lo, Lo, Hi
  2. B) Hi, Lo, Lo, Hi
  3. C) Hi, Hi, Lo, Lo
  4. D) Hi, Lo, Lo, Lo
Correct Answer
B) Hi, Lo, Lo, Hi
Step-by-step solution
📌 Core Concept
A round's payoff depends only on the number of Hi bids. So each option for round 1 can be tested against Dipak's clue (fact 3) and the score totals.
🔢 Step-by-Step Solution
1
Payoffs per player: 4 Hi gives -1 each; 3 Hi gives +1 to Hi and -3 to Lo; 2 Hi gives +2 to Hi and -2 to Lo; 1 Hi gives +3 to Hi and -1 to Lo; 0 Hi gives +1 each. A player's round score is never 0.
2
Option A has Dipak as the only Hi bidder. Arun then scores -1 in round 1, so he needs 7 from rounds 2 and 3 to reach 6. The maximum is 3+3=63+3=6, so A fails.
3
Option C gives Dipak -2 in round 1. Fact 3 needs D3<−2D_3 < -2, so D3=−3D_3=-3, and then D2<−3D_2 < -3, which is impossible. C fails.
4
Option D gives Dipak -1 in round 1. Fact 3 then forces D3=−2D_3=-2 and D2=−3D_2=-3. His total would be −1−3−2=−6-1-3-2=-6, not the 2 given in fact 1. D fails.
5
Option B has Arun and Dipak bidding Hi against two Lo bids, so the Hi players get +2 and the Lo players get -2. After round 1 the scores are Arun 2, Bankim -2, Charu -2, Dipak 2. Dipak then needs 0 over rounds 2 and 3, with D2<D3<2D_2 < D_3 < 2. This gives D2=−1D_2=-1 and D3=1D_3=1, which works and is consistent with the rest of the data.
Why Not the Others
A: Arun cannot reach 6 after three rounds.
C: Dipak's clue 3 cannot be satisfied.
D: Dipak's three-round total comes to -6, not 2.
Correct Answer: B

Q6. Games & Tournaments

TITA · +3 / 0
In how many rounds did Arun bid Hi?
Correct Answer
4
Step-by-step solution
📌 Core Concept
Work out the bids round by round from the payoff table. The scores after 3 rounds and after 6 rounds, together with Dipak's clue, fix every round.
🔢 Step-by-Step Solution
1
Round 1: only Arun and Dipak bidding Hi fits the data (Arun +2, Bankim -2, Charu -2, Dipak +2). Dipak's clue then gives D2=−1D_2=-1 and D3=1D_3=1. Rounds 2 and 3 must give Arun a total of 6−2=46-2=4 and Bankim and Charu a total of 0 each.
2
Round 2 has D2=−1D_2=-1. Either all four bid Hi (everyone gets -1), or Dipak is Lo in a round with exactly one Hi bidder. If all bid Hi, Arun would need 5 in round 3, which is impossible. If Bankim or Charu were the only Hi bidder, Arun would again get -1 and need 5. So Arun is the only Hi bidder in round 2: Arun +3, the others -1.
3
Round 3: Arun, Bankim, Charu and Dipak all need +1. That happens only when all four bid Lo, because a 3-Hi round would give Dipak -3 if he were Lo. Arun bids Lo.
4
Rounds 4 to 6 must give Arun +1, Bankim +1, Charu -3 and Dipak -3, a team total of −4-4. Only a 4-Hi round gives -4 in total, with the other two rounds summing to 0 overall. After one all-Hi round, the remaining two rounds need Arun -1, Bankim +3, Charu -1 and Dipak -1. That fits the one-Hi round with Bankim bidding Hi, and then fact 4 is met by Arun being the only Hi bidder in the other round (+3, others -1).
5
Arun's bids: Hi in round 1, Hi in round 2, Lo in round 3, then Hi in his sole-Hi round, Hi in the all-Hi round, Lo in the round where Bankim is the only Hi bidder. That is 4 Hi rounds.
Quick Check
Arun: 2+3+1+3−1−1=72+3+1+3-1-1=7 ✓.
Correct Answer: 4

Q7. Games & Tournaments

TITA · +3 / 0
In how many rounds did Bankim bid Lo?
Correct Answer
4
Step-by-step solution
📌 Core Concept
Rebuild the six rounds from the payoff table, the totals after 3 and 6 rounds, and Dipak's clue. Then count Bankim's Lo bids.
🔢 Step-by-Step Solution
1
Round 1: Arun and Dipak bid Hi, Bankim and Charu bid Lo (scores +2, -2, -2, +2). Dipak's clue then forces D2=−1D_2=-1 and D3=1D_3=1.
2
Round 2: Arun needs 4 across rounds 2 and 3. With D2=−1D_2=-1, the only workable case is Arun as the sole Hi bidder (+3, others -1). Bankim is Lo.
3
Round 3: Arun, Bankim, Charu and Dipak all need +1, so all four bid Lo. Bankim is Lo.
4
Rounds 4 to 6 total Arun +1, Bankim +1, Charu -3, Dipak -3. That works as three rounds: Arun as sole Hi bidder (Bankim Lo), one all-Hi round (Bankim Hi), and one round where Bankim is the sole Hi bidder (+3, others -1).
5
Bankim bids Lo in round 1, round 2, round 3 and in Arun's sole-Hi round in rounds 4 to 6. He bids Hi in the other two. That is 4 Lo rounds.
Quick Check
Bankim's scores: −2−1+1−1−1+3=−1-2-1+1-1-1+3=-1 ✓.
Correct Answer: 4

Q8. Games & Tournaments

TITA · +3 / 0
In how many rounds did all four players make identical bids?
Correct Answer
2
Step-by-step solution
📌 Core Concept
Once every round's bids are reconstructed from the payoff table and the score data, count the rounds where all four bids match.
🔢 Step-by-Step Solution
1
Round 1: Arun and Dipak bid Hi, Bankim and Charu bid Lo. This is the only option consistent with Dipak's clue and the 3-round totals. The bids are not identical.
2
Round 2: Arun is the only Hi bidder (needed so that Arun reaches 4 across rounds 2 and 3 while Dipak scores -1). The bids are not identical.
3
Round 3: Arun, Bankim, Charu and Dipak all need +1, which is possible only if all four bid Lo. The bids are identical.
4
Rounds 4 to 6 must total Arun +1, Bankim +1, Charu -3, Dipak -3, a team total of -4. That needs exactly one all-Hi round (-1 each). The other two rounds are Arun as sole Hi bidder (fact 4) and Bankim as sole Hi bidder, neither of which is identical.
5
Identical bids occur in round 3 (all Lo) and in the all-Hi round: 2 rounds.
Correct Answer: 2

Q9. Games & Tournaments

TITA · +3 / 0
In how many rounds did Dipak gain exactly 1 point?
Correct Answer
1
Step-by-step solution
📌 Core Concept
Reconstruct all six rounds, then read off Dipak's score in each round.
🔢 Step-by-Step Solution
1
Round 1: Arun and Dipak bid Hi, Bankim and Charu bid Lo. Dipak gets +2.
2
Fact 3 gives D2<D3<D1=2D_2 < D_3 < D_1=2 and D1+D2+D3=2D_1+D_2+D_3=2, so D2+D3=0D_2+D_3=0. A round score is never 0, so D2=−1D_2=-1 and D3=1D_3=1.
3
Round 2: Arun is the only Hi bidder, so Dipak (Lo) gets -1.
4
Round 3: all four bid Lo, so Dipak gets +1.
5
Rounds 4 to 6: Dipak must total -3. The rounds are Arun as sole Hi bidder (Dipak -1), one all-Hi round (Dipak -1), and Bankim as sole Hi bidder (Dipak -1).
6
Dipak's scores in order of round: +2, -1, +1, then -1, -1, -1 in rounds 4 to 6. Only round 3 gives exactly 1 point.
Quick Check
2−1+1−1−1−1=−12-1+1-1-1-1=-1, matching fact 2.
Correct Answer: 1

Q10. Games & Tournaments

MCQ · +3 / −1
In which of the following rounds, was Arun DEFINITELY the only player to bid Hi?
  1. A) Second
  2. B) Fourth
  3. C) Third
  4. D) First
Correct Answer
A) Second
Step-by-step solution
📌 Core Concept
Reconstruct the bids round by round. Fact 4 says Arun is the sole Hi bidder in exactly two rounds, so find the rounds where this is forced.
🔢 Step-by-Step Solution
1
Round 1: Arun and Dipak bid Hi, Bankim and Charu bid Lo. Arun is not alone. Dipak's clue (fact 3) then gives D2=−1D_2=-1 and D3=1D_3=1.
2
Round 2: Arun needs 4 across rounds 2 and 3, and Dipak scores -1 in round 2. If all four bid Hi, Arun would need 5 in round 3. If Bankim or Charu were the only Hi bidder, Arun would get -1 and again need 5. So Arun is the only Hi bidder in round 2, which is forced.
3
Round 3: all four need +1, so all bid Lo. Arun is not alone.
4
Rounds 4 to 6 consist of three rounds: Arun as sole Hi bidder, an all-Hi round, and Bankim as sole Hi bidder. Fact 4 requires exactly one more sole-Hi round for Arun, but nothing fixes which of rounds 4 to 6 it is. The order of these three rounds is not determined.
5
So the only round where Arun is definitely the only Hi bidder is the second round.
Why Not the Others
B (Fourth): the sole-Hi round could be the fifth or sixth.
C (Third): all four bid Lo.
D (First): Dipak also bids Hi.
Correct Answer: A
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CAT 2020 Slot 3 DILR at a Glance

Sets in this section5
Questions in this section24
Section time40 minutes
Convenor IIMIIM Indore

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