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CAT 2019 Slot 1 DILR · Set 6 of 8Logical ReasoningHard DifficultyQ21–Q24 · 4 MCQ

CAT 2019 Slot 1 DILR Set 6: Games & Tournaments (4 Questions) with Solutions

The Games & Tournaments set from the official CAT 2019 Slot 1 DILR paper: the caselet, all 4 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 2019 Slot 1 DILR · Questions 21–24
Six players - Tanzi, Umeza, Wangdu, Xyla, Yonita and Zeneca competed in an archery tournament. The tournament had three compulsory rounds, Rounds 1 to 3. In each round every player shot an arrow at a target. Hitting the centre of the target (called bull's eye) fetched the highest score of 5. The only other possible scores that a player could achieve were 4, 3, 2 and 1. Every bull's eye score in the first three rounds gave a player one additional chance to shoot in the bonus rounds, Rounds 4 to 6. The possible scores in Rounds 4 to 6 were identical to the first three.
A player's total score in the tournament was the sum of his/her scores in all rounds played by him/her. The table below presents partial information on points scored by the players after completion of the tournament. In the table, NP means that the player did not participate in that round, while a hyphen means that the player participated in that round and the score information is missing.
NameRound-1Round-2Round-3Round-4Round-5Round-6
Tanzi-4-5NPNP
Umeza---12NP
Wangdu-4-NPNPNP
Xyla---15-
Yonita--35NPNP
Zeneca---55NP
The following facts are also known.
1
Tanzi, Umeza and Yonita had the same total score.
2
Total scores for all players, except one, were in multiples of three.
3
The highest total score was one more than double of the lowest total score.
4
The number of players hitting bull's eye in Round 2 was double of that in Round 3.
5
Tanzi and Zeneca had the same score in Round 1 but different scores in Round 3.

In the exam this set competed with 7 others for 60 minutes. Budget about 8 minutes if you attempt it.

Q21. Games & Tournaments

MCQ · +3 / −1
What was the highest total score?
  1. A) 25
  2. B) 21
  3. C) 24
  4. D) 23
Correct Answer
A) 25
Step-by-step solution
📌 Core Concept
Every bull's eye in Rounds 1-3 earns exactly one bonus round. So the bonus rounds each player played tell how many bull's eyes they scored in Rounds 1-3.
🔢 Step-by-Step Solution
1
Bonus rounds played equal bull's eyes in Rounds 1-3. Tanzi and Yonita played one bonus round each, so they have 1 bull's eye. Umeza and Zeneca played two, so they have 2. Xyla played three, so Rounds 1-3 are all 5s. Wangdu played none, so he has no 5s.
2
Wangdu, Tanzi (4 in R2) and Yonita (3 in R3) have no bull's eye in the rounds where the table shows a lower score. Xyla is the only certain bull's eye in Round 3.
3
Fact 4 says the Round 2 bull's eyes are double the Round 3 ones. If Round 3 had only Xyla, then Round 2 would have two. Zeneca (R1 = 5 by fact 5 with Tanzi's R1) would then need R2 as her second 5. Umeza would be left with only R1 for two bull's eyes, which is impossible. So Round 3 has 2 bull's eyes and Round 2 has 4: Xyla, Umeza, Yonita, Zeneca.
4
The second Round 3 bull's eye cannot be Tanzi, since Tanzi's R1 would then be below 5 while Zeneca's R1 is 5. It cannot be Zeneca either, which forces a contradiction with fact 5. So it is Umeza. Hence Zeneca scored 5, 5 in R1 and R2, and Tanzi scored 5, 4 in R1 and R2.
5
Let Tanzi's R3 be tt. Tanzi's total is 14+t14+t. Umeza's total is 13+u113+u_1 and Yonita's is 13+y113+y_1. Equal totals give u1=y1=t+1≤4u_1=y_1=t+1\le 4.
6
Fact 2: three players share one total, so that total is a multiple of 3. Only 14+t=1514+t=15 works, so t=1t=1 and all three score 15.
7
Zeneca scores 20+a20+a and Xyla scores 21+x621+x_6. Wangdu scores at most 12.
8
Fact 3: highest =2×=2\times lowest +1+1. Wangdu is the lowest. Wangdu = 12 gives highest = 25, which Xyla reaches with x6=4x_6=4. Wangdu = 11 gives 23, but Zeneca and Xyla would then both need to be multiples of 3, and 24 is too high. Wangdu = 9 gives 19, which is too low.
9
So the highest total is 25.
Quick Check
Totals are 15, 15, 12, 25, 15, 24. Only 25 is not a multiple of 3, and 2×12+1=252\times12+1=25.
Correct Answer: A

Q22. Games & Tournaments

MCQ · +3 / −1
What was Zeneca's total score?
  1. A) 21
  2. B) 22
  3. C) 23
  4. D) 24
Correct Answer
D) 24
Step-by-step solution
📌 Core Concept
Bonus rounds played show how many bull's eyes each player had in Rounds 1-3. Combine that with the multiple-of-3 and highest/lowest conditions.
🔢 Step-by-Step Solution
1
Zeneca played two bonus rounds, so she has two bull's eyes in Rounds 1-3. Fact 4 forces 4 bull's eyes in Round 2 and 2 in Round 3. Zeneca is one of the four in Round 2.
2
Fact 5 gives Tanzi and Zeneca the same R1 score. Tanzi's single bull's eye must then be in Round 1, since a Round 3 bull's eye would leave her R1 below 5 against Zeneca's. So Zeneca's R1 is 5, and her R1 and R2 are 5, 5. Her R3 is not 5.
3
Zeneca's total is 5+5+a+5+5=20+a5+5+a+5+5=20+a, where aa is her Round 3 score (a≤4a\le 4).
4
Tanzi, Umeza and Yonita share the same total. Only one total is not a multiple of 3, so that common total is a multiple of 3. This gives 15, with Tanzi's R3 equal to 1. Then a≠1a\ne1 by fact 5.
5
Xyla's total is 21+x621+x_6 and Wangdu's is at most 12. Fact 3 gives highest =2×lowest+1=2\times\text{lowest}+1, so Wangdu = 12 and the highest = 25, which is Xyla.
6
Xyla's 25 is the one non-multiple of 3. So Zeneca's total must be a multiple of 3: 20+a=2420+a=24 gives a=4a=4.
Quick Check
5+5+4+5+5=245+5+4+5+5=24, which is a multiple of 3, and below Xyla's 25.
Correct Answer: D

Q23. Games & Tournaments

MCQ · +3 / −1
Which of the following statements is true?
  1. A) Xyla's score was 23
  2. B) Xyla was the highest scorer
  3. C) Zeneca was the highest scorer
  4. D) Zeneca's score was 23
Correct Answer
B) Xyla was the highest scorer
Step-by-step solution
📌 Core Concept
Fix every player's total from the bonus-round counts and the five facts, then compare the statements.
🔢 Step-by-Step Solution
1
Bonus rounds played equal bull's eyes in Rounds 1-3. Xyla played three bonus rounds, so she scored 5 in all of Rounds 1-3. Her total is 15+1+5+x6=21+x615+1+5+x_6=21+x_6.
2
Fact 4 forces 4 bull's eyes in Round 2 and 2 in Round 3. Combined with fact 5, this gives Zeneca 5, 5 in R1, R2 and Umeza a bull's eye in R2 and R3. Tanzi's R3 comes out as 1, so Tanzi, Umeza and Yonita each total 15, a multiple of 3.
3
Zeneca's total is 20+a20+a. Wangdu, with no bonus rounds, totals at most 12.
4
Fact 3: highest =2×lowest+1=2\times\text{lowest}+1. The lowest is Wangdu. Wangdu = 12 gives a highest of 25, so Xyla has x6=4x_6=4 and 25.
5
Only one total may be a non-multiple of 3. Xyla's 25 is that one, so Zeneca's total must be a multiple of 3: she totals 24.
6
Check the statements. Xyla's score is 25, not 23, so A is false. Xyla is the highest scorer at 25 over Zeneca's 24, so B is true. Zeneca is not the highest, so C is false. Zeneca's score is 24, not 23, so D is false.
Correct Answer: B

Q24. Games & Tournaments

MCQ · +3 / −1
What was Tanzi's score in Round 3?
  1. A) 5
  2. B) 4
  3. C) 1
  4. D) 3
Correct Answer
C) 1
Step-by-step solution
📌 Core Concept
Bull's eyes in Rounds 1-3 equal bonus rounds played. Equal totals for Tanzi, Umeza and Yonita, together with fact 2, then fix Tanzi's Round 3 score.
🔢 Step-by-Step Solution
1
Tanzi played one bonus round, so she has one bull's eye in R1-3. Her R2 is 4, so it is in R1 or R3. Umeza and Zeneca each have two. Yonita has one, with R3 = 3. Xyla has all three.
2
Fact 4 forces 4 bull's eyes in Round 2 (Xyla, Umeza, Yonita, Zeneca) and 2 in Round 3. Round 3's two are Xyla and one other. Testing the options, only Umeza fits. If it were Tanzi or Zeneca, fact 5 (same R1 score for Tanzi and Zeneca) breaks.
3
So Tanzi's bull's eye is in Round 1, not Round 3, and Tanzi's R3 is below 5. Her total is 5+4+t+5=14+t5+4+t+5=14+t, where tt is her Round 3 score.
4
Umeza scores u1+5+5+1+2=13+u1u_1+5+5+1+2=13+u_1, so u1=t+1≤4u_1=t+1\le4. Yonita similarly scores 13+y113+y_1 with y1=t+1y_1=t+1.
5
Fact 2 allows only one total that is not a multiple of 3. Three players share this common total, so it must be a multiple of 3. With t≤3t\le3, the options are 15, 16 and 17, so the total is 15 and t=1t=1.
Quick Check
Tanzi: 5+4+1+5=155+4+1+5=15. Umeza: 4+5+5+1+2=174+5+5+1+2=17 would break equality, but u1=2u_1=2 gives 2+5+5+1+2=152+5+5+1+2=15.
Correct Answer: C
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CAT 2019 Slot 1 DILR at a Glance

Sets in this section8
Questions in this section32
Section time60 minutes
Convenor IIMIIM Kozhikode

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