CAT 2025 Slot 3 · DILR · Set 2: Travellers and Exchange Rates
The full set and all 5 questions (Q5–Q9) from CAT 2025 Slot 3, with answers and solutions.
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.
Question 5 · Quant Based Puzzles and Optimisation
What is the sum of Travel Costs for all travelers in Zentars?
Answer & solution
Answer: 41000
Who went where: three travellers make 6 visits, and each country gets exactly 2, so the three countries visited are Aurevia, Brelosia and Cyrenia. Aurevia: Jano, Kira. Brelosia: Kira, Lian. Jano's second country must be Cyrenia, so Cyrenia: Jano, Lian.
Spends (local currency): Lian spent 3000 in Brelosia (the only 3000) and Kira 2000 there. Kira's two spends differ, so Kira spent 1000 in Aurevia. That leaves one more 1000 and two more 2000s among Jano–Aurevia, Jano–Cyrenia and Lian–Cyrenia. Jano's two spends must differ, so Jano has one 1000 and one 2000, and Lian spent 2000 in Cyrenia.
Exchange rates: let 1 Aurel = a Zentars and 1 Brin = b Zentars; 1 Crown = 0.5 Zentars.
Kira's Travel Cost is 8000 Aurels and also 4000 Brins, so 8000a = 4000b, giving b = 2a. In Zentars: Flight(K) + 1000a + 2000b = 8000a, so Flight(K) = 8000a − 1000a − 4000a = 3000a.
Lian's Travel Cost is 36000 Crowns = 18000 Zentars: Flight(L) + 3000b + 2000 × 0.5 = 18000, so Flight(L) = 17000 − 6000a.
Flight(K) and Flight(L) are 5000 and 6000. Flight(K) = 3000a gives a = 5/3 or 2; a = 5/3 makes Flight(L) = 7000 (not allowed), so a = 2, b = 4, Flight(K) = 6000, Flight(L) = 5000.
Jano's Travel Cost is 3500 Aurels = 7000 Zentars, so his spends total 7000 − 4000 = 3000 Zentars. Aurevia 1000 (= 2000 Z) + Cyrenia 2000 (= 1000 Z) = 3000 Z works; the reverse (4000 Z + 500 Z) does not.
Travel Costs in Zentars: Jano 7000, Kira 8000 × 2 = 16000, Lian 18000. Sum = 41000.
Shortcut: Kira's cost in two currencies gives b = 2a at once; the flight-cost options then force a = 2.
Hence, the answer is 41000.
Question 6 · Quant Based Puzzles and Optimisation
How many Zentars did Lian spend in the two countries he visited?
Answer & solution
Answer: 13000
Lian spent 3000 Brins in Brelosia and 2000 Crowns in Cyrenia.
With 1 Brin = 4 Zentars and 1 Crown = 0.5 Zentars: 3000 × 4 + 2000 × 0.5 = 12000 + 1000 = 13000 Zentars.
Check: Flight 5000 + 13000 = 18000 Zentars = 36000 Crowns, as stated.
Shortcut: Lian's Travel Cost is 18000 Z and her flight 5000 Z, so her spends are 13000 Z.
Hence, the answer is 13000.
Question 7 · Quant Based Puzzles and Optimisation
What was Jano's total spend in the two countries he visited, in Aurels?
Answer & solution
Answer: 1500
Jano spent 1000 Aurels in Aurevia (= 2000 Zentars) and 2000 Crowns in Cyrenia (= 1000 Zentars), a total of 3000 Zentars.
With 1 Aurel = 2 Zentars, 3000 Zentars = 1500 Aurels.
Check: Travel Cost 3500 Aurels = 7000 Zentars = flight 4000 + spends 3000.
Shortcut: Jano's total spend = Travel Cost − Flight Cost = 3500 Aurels − 2000 Aurels = 1500 Aurels.
Hence, the answer is 1500.
Question 8 · Quant Based Puzzles and Optimisation
One Brin is equivalent to how many Crowns?
- A
8
- B
0.125
- C
0.5
- D
4
Answer & solution
Answer: Option A
1 Brin = 4 Zentars (from b = 2a with a = 2), and 1 Crown = 0.5 Zentars.
So 1 Brin = 4 ÷ 0.5 = 8 Crowns.
Shortcut: convert both currencies to Zentars and divide.
Hence, the answer is option 1.
Question 9 · Quant Based Puzzles and Optimisation
Which of the following statements is NOT true about money spent in the local currency?
- A
Jano spent 2000 in Aurevia
- B
Lian spent 2000 in Cyrenia
- C
Jano spent 2000 in Cyrenia
- D
Kira spent 1000 in Aurevia
Answer & solution
Answer: Option A
Spends (local currency): Jano – Aurevia 1000, Cyrenia 2000; Kira – Aurevia 1000, Brelosia 2000; Lian – Brelosia 3000, Cyrenia 2000.
Option 1 is not true: Jano spent 1000 in Aurevia, not 2000.
Options 2, 3 and 4 are all true.
Shortcut: Jano's Travel Cost leaves exactly 3000 Zentars for spends, which only works with 1000 in Aurevia and 2000 in Cyrenia.
Hence, the answer is option 1.
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