CAT 2025 Slot 3 DILR Paper with Solutions

Set 1CAT 2025 · Slot 3 · DILR Q1–Q44 questionsArrangements

Passing the Buck in a circle of seven

Seven children, Aarav, Bina, Chirag, Diya, Eshan, Farhan, and Gaurav, are sitting in a circle facing inside (not necessarily in the same order) and playing a game of 'Passing the Buck'.

The game is played over 10 rounds. In each round, the child holding the Buck must pass it directly to a child sitting in one of the following positions:

• Immediately to the left;

• Immediate to the right;

• Second to the left; or

• Second to the right.

The game starts with Bina passing the Buck and ends with Chirag receiving the Buck. The table below provides some information about the pass types and the child receiving the Buck. Some information is missing and labelled as '?'.

Data for this set (chart, table or figure)

Set solution: how to crack this set

Number the seats with Bina at 0 and "left" as $+1$ (so right is $-1$ ). A pass moves $\pm 1$ or $\pm 2$ seats.

Round 1 (left 1): Aarav $= 1$ . Round 2 (right 2): receiver at $-1 = 6$ . Round 3 (right 1): Diya $= 5$ .

Round 6: Aarav passes left 2 to seat 3. Round 7 (left 1): Gaurav $= 4$ . Round 8 (left 1): seat 5 = Diya.

Round 9: Diya (5) passes to Farhan, so Farhan is at 3 or 6. Round 10: Farhan passes to Chirag. From seat 6 no free seat is within 2 steps, so Farhan $= 3$ , Chirag $= 2$ , Eshan $= 6$ .

Seating (going left from Bina): Bina, Aarav, Chirag, Farhan, Gaurav, Diya, Eshan.

Rounds 4–5 (Diya → ? → Aarav): via Eshan (left 1, left 2), via Bina (left 2, left 1) or via Farhan (right 2, right 2).

Q1CAT 2025 · Slot 3 · DILR Q1MCQ

Who is sitting immediately to the right of Bina?

Q2CAT 2025 · Slot 3 · DILR Q2MCQ

Who is sitting third to the left of Eshan?

Q3CAT 2025 · Slot 3 · DILR Q3MCQ

For which of the following pass types can the total number of occurrences be uniquely determined?

Q4CAT 2025 · Slot 3 · DILR Q4MCQ

For which of the following children is it possible to determine how many times they received the Buck?

Set 2CAT 2025 · Slot 3 · DILR Q5–Q95 questionsQuant-based Sets

Travellers, currencies and travel costs

Aurevia, Brelosia, Cyrenia and Zerathania are four countries with their currencies being Aurels, Brins, Crowns, and Zentars, respectively. The currencies have different exchange values. Crown's currency exchange rate with Zentars = 0.5, i.e., 1 Crown is worth 0.5 Zentars.

Three travelers, Jano, Kira, and Lian set out from Zerathania visiting exactly two of the countries. Each country is visited by exactly two travelers. Each traveler has a unique Flight Cost, which represents the total cost of airfare in traveling to both the countries and back to Zerathania. The Flight Cost of Jano was 4000 Zentars, while that of the other two travelers were 5000 and 6000 Zentars, not necessarily in that order. When visiting a country, a traveler spent either 1000, 2000 or 3000 in the country's local currency. Each traveler had different spends (in the country's local currency) in the two countries he/she visited. Across all the visits, there were exactly two spends of 1000 and exactly one spend of 3000 (in the country's local currency).

The total “Travel Cost” for a traveler is the sum of his/her Flight Cost and the money spent in the countries visited.

The citizens of the four countries with knowledge of these travels made a few observations, with spends measured in their respective local currencies:

i. Aurevia citizen: Jano and Kira visited our country, and their Travel Costs were 3500 and 8000, respectively.

ii. Brelosia citizen: Kira and Lian visited our country, spending 2000 and 3000, respectively. Kira's Travel Cost was 4000.

iii. Cyrenia citizen: Lian visited our country and her Travel Cost was 36000.

Set solution: how to crack this set

Routes: Jano visits Aurevia and Cyrenia, Kira visits Aurevia and Brelosia, Lian visits Brelosia and Cyrenia.

Spends: Lian's 3000 in Brelosia is the only 3000 and Kira spent 2000 there. Each traveller's two spends differ, so Kira spent 1000 in Aurevia. There are only two 1000s and Jano needs one of them, so Lian spent 2000 in Cyrenia.

Let 1 Aurel $= a$ Z and 1 Brin $= b$ Z (1 Crown $= 0.5$ Z). Kira's cost: $8000a = 4000b \Rightarrow b = 2a$ .

Kira: $F_K + 1000a + 2000b = 8000a \Rightarrow F_K = 3000a$ .

Lian: $36000 \times 0.5 = 18000 = F_L + 3000b + 2000 \times 0.5 \Rightarrow F_L = 17000 - 6000a$ .

$F_K, F_L \in \{5000, 6000\}$ : only $a = 2$ works ( $F_K = 6000$ , $F_L = 5000$ ). So $b = 4$ .

Jano: $3500 \times 2 = 7000 = 4000 + 2J_A + 0.5J_C$ , which gives $J_A = 1000$ Aurels and $J_C = 2000$ Crowns.

Q5CAT 2025 · Slot 3 · DILR Q5TITA

What is the sum of Travel Costs for all travelers in Zentars?

Q6CAT 2025 · Slot 3 · DILR Q6TITA

How many Zentars did Lian spend in the two countries he visited?

Q7CAT 2025 · Slot 3 · DILR Q7TITA

What was Jano's total spend in the two countries he visited, in Aurels?

Q8CAT 2025 · Slot 3 · DILR Q8MCQ

One Brin is equivalent to how many Crowns?

Q9CAT 2025 · Slot 3 · DILR Q9MCQ

Which of the following statements is NOT true about money spent in the local currency?

Set 3CAT 2025 · Slot 3 · DILR Q10–Q134 questionsCharts & Graphs

Puzzle competition progress charts

Anirbid, Chandranath, Koushik, and Suranjan participated in a puzzle solving competition. The competition comprised 10 puzzles that had to be solved in the same sequence, i.e., a competitor got access to a puzzle as soon as they solved the previous puzzle. Some of the puzzles were visual puzzles and the others were number-based puzzles. The winner of the competition was the one who solved all puzzles in the least time.

The following charts describe their progress in the competition. The chart on the left shows the number of puzzles solved by each competitor at a given time (in minutes) after the start of the competition. The chart on the right shows the number of visual puzzles solved by each competitor at a given time (in minutes) after the start of the competition.

Set solution: how to crack this set

Visual puzzles are the ones whose solve times show up as steps in the right chart. Suranjan's visual steps (5, 18, 28, 30 min) match his 1st, 4th, 8th and 9th solves.

So puzzles 1, 4, 8 and 9 are visual; 2, 3, 5, 6, 7 and 10 are number-based.

Anirbid solved puzzles at about 4, 9, 11, 14, 19, 22, 27, 29, 33 and 37 minutes.

Q10CAT 2025 · Slot 3 · DILR Q10MCQ

Who had solved the largest number of puzzles by the 20-th minute from the start of the competition?

Q11CAT 2025 · Slot 3 · DILR Q11TITA

How many minutes did Suranjan take to solve the third visual puzzle in the competition?

Q12CAT 2025 · Slot 3 · DILR Q12TITA

At what number in the sequence was the fourth number-based puzzle?

Q13CAT 2025 · Slot 3 · DILR Q13MCQ

Which of the following is the closest to the average time taken by Anirbid to solve the number-based puzzles in the competition?

Set 4CAT 2025 · Slot 3 · DILR Q14–Q185 questionsTables & Missing Data

Trade between Pumpland, Xiland, Cheeseland and ROW

Three countries — Pumpland (P), Xiland (X) and Cheeseland (C) — trade among themselves and with the (other countries in) Rest of World (ROW). All trade volumes are given in IC (international currency). The following terminology is used:

• Trade balance = Exports - Imports

• Total trade = Exports + Imports

• Normalized trade balance = Trade balance / Total trade, expressed in percentage terms

The following information is known.

1. The normalized trade balances of P, X and C are 0%, 10%, and -20%, respectively.

2. 40% of exports of X are to P. 22% of imports of P are from X.

3. 90% of exports of C are to P; 4% are to ROW.

4. 12% of exports of ROW are to X, 40% are to P.

5. The export volumes of P, in IC, to X and C are 600 and 1200, respectively. P is the only country that exports to C.

Set solution: how to crack this set

C imports only from P: 1200. Normalised balance $-20\%$ : $\dfrac{E_C - 1200}{E_C + 1200} = -0.2 \Rightarrow E_C = 800$ .

C's exports: P 720, ROW 32, X 48.

Let $E_X$ , $E_R$ be the total exports of X and ROW. X's imports $= 600 + 48 + 0.12E_R$ , and its balance gives $E_X = \dfrac{11}{9}(648 + 0.12E_R)$ .

P's imports $= 0.4E_X + 720 + 0.4E_R$ , and X supplies 22% of them: $0.4E_X = 0.22 \times$ P's imports.

Solving: $E_R = 2100$ , $E_X = 1100$ , P's imports $= 2000 =$ P's exports.

P → ROW $= 2000 - 600 - 1200 = 200$ . ROW → ROW $= 48\%$ of 2100 $= 1008$ .

Q14CAT 2025 · Slot 3 · DILR Q14TITA

How much is exported from C to X, in IC?

Q15CAT 2025 · Slot 3 · DILR Q15TITA

How much is exported from P to ROW, in IC?

Q16CAT 2025 · Slot 3 · DILR Q16TITA

How much is exported from ROW to ROW, in IC?

Q17CAT 2025 · Slot 3 · DILR Q17MCQ

What is the trade balance of ROW?

Q18CAT 2025 · Slot 3 · DILR Q18MCQ

Which among the countries P, X, and C has/have the least total trade?

Set 5CAT 2025 · Slot 3 · DILR Q19–Q224 questionsTables & Missing Data

Call minutes between friends on two operators

Anu, Bijay, Chetan, Deepak, Eshan, and Faruq are six friends. Each of them uses a mobile number from exactly one of the two mobile operators - Xitel and Yocel. During the last month, the six friends made several calls to each other. Each call was made by one of these six friends to another. The table below summarizes the number of minutes of calls that each of the six made to (outgoing minutes) and received from (incoming minutes) these friends, grouped by the operators. Some of the entries are missing.

It is known that the duration of calls from Faruq to Eshan was 200 minutes. Also, there were no calls from:

i. Bijay to Eshan,

ii. Chetan to Anu and Chetan to Deepak,

iii. Deepak to Bijay and Deepak to Faruq,

iv. Eshan to Chetan and Eshan to Deepak.

Set solution: how to crack this set

Xitel: Anu, Bijay. Yocel: Chetan, Deepak, Eshan, Faruq.

Anu's 100 outgoing Xitel minutes all go to Bijay, and Anu's 50 incoming Xitel minutes come from Bijay.

Chetan → Bijay $= 50$ (Chetan → Anu is 0). Deepak → Anu $= 100$ (Deepak → Bijay is 0).

Eshan's Yocel calls can only go to Faruq: Eshan → Faruq $= 100$ .

Faruq receives 150 from Yocel: Chetan → Faruq $= 50$ , so Chetan → Eshan $= 125$ .

Eshan receives 375 from Yocel: $125 + D + 200 = 375 \Rightarrow$ Deepak → Eshan $= 50$ , so Deepak → Chetan $= 100$ .

Deepak receives 100 from Yocel, all from Faruq. Chetan receives 150 from Yocel: $100 + F = 150 \Rightarrow$ Faruq → Chetan $= 50$ .

Q19CAT 2025 · Slot 3 · DILR Q19TITA

What was the duration of calls (in minutes) from Bijay to Anu?

Q20CAT 2025 · Slot 3 · DILR Q20TITA

What was the total duration of calls (in minutes) made by Anu to friends having mobile numbers from Operator Yocel?

Q21CAT 2025 · Slot 3 · DILR Q21TITA

What was the total duration of calls (in minutes) made by Faruq to friends having mobile numbers from Operator Yocel?

Q22CAT 2025 · Slot 3 · DILR Q22MCQ

What was the duration of calls (in minutes) from Deepak to Chetan?

CAT 2025 Slot 3 DILR paper with solutions

Passing the Buck in a circle of seven

Solution

Solution

Solution

Solution

Travellers, currencies and travel costs

Solution

Solution

Solution

Solution

Solution

Puzzle competition progress charts

Solution

Solution

Solution

Solution

Trade between Pumpland, Xiland, Cheeseland and ROW

Solution

Solution

Solution

Solution

Solution

Call minutes between friends on two operators

Solution

Solution

Solution

Solution