Correct Answer: 41000

Explanation: Travel Cost equals Flight Cost plus total spending converted into Zentars. Jano’s Travel Cost is 4000 Z flight plus 2000 Z from 1000 Aurels and 1000 Z from 2000 Crowns, giving 7000 Z. Kira’s Travel Cost is 6000 Z flight plus 2000 Z from 1000 Aurels and 8000 Z from 2000 Brins, giving 16000 Z. Lian’s Travel Cost is 5000 Z flight plus 12000 Z from 3000 Brins and 1000 Z from 2000 Crowns, giving 18000 Z. Adding all three Travel Costs gives 7000 + 16000 + 18000 = 41000 Zentars.

Steps to complete the DILR Set

Step 0: Start with a completely blank table. No values are known yet except that the rows are fixed as Flight Cost, spends in Aurevia, Brelosia, Cyrenia, and totals, and the columns are Jano, Kira, and Lian.

Step 1: From the given information, Jano’s Flight Cost is 4000 Zentars, while Kira and Lian have Flight Costs of 5000 and 6000 Zentars in some order. Only Jano’s value can be fixed at this stage.

Step 2: Citizen observations fix travel routes. Aurevia was visited by Jano and Kira, Brelosia was visited by Kira and Lian, and Cyrenia was visited by Lian and exactly one other traveler. Since each country must be visited by exactly two travelers, Jano must also have visited Cyrenia. This fixes that Jano visited Aurevia and Cyrenia, Kira visited Aurevia and Brelosia, and Lian visited Brelosia and Cyrenia. The table structure is now constrained, though no new numbers are filled yet.

Step 3: From the Brelosia citizen’s statement, Kira spent 2000 Brins in Brelosia and Lian spent 3000 Brins in Brelosia. These are direct placements in the table.

Step 4: Across all six visits, there are exactly two spends of 1000, exactly one spend of 3000, and the rest are 2000. Since Lian already has a spend of 3000 Brins in Brelosia, no other visit can have a spend of 3000 in local currency. Therefore, all spends in Aurevia and Cyrenia must be either 1000 or 2000.

Step 5: Kira must have different local-currency spends in the two countries she visited. Since Kira spent 2000 Brins in Brelosia and 3000 is not allowed again, Kira must have spent 1000 Aurels in Aurevia.

Step 6: Kira’s Travel Cost is reported by Aurevia citizens as 8000 Aurels and by Brelosia citizens as 4000 Brins. These represent the same real cost, so 8000 Aurels equals 4000 Brins. This gives the exchange relation that 1 Brin equals 2 Aurels. Using the given fact that 1 Crown equals 0.5 Zentars, the consistent currency values become 1 Aurel equals 2 Zentars, 1 Brin equals 4 Zentars, and 1 Crown equals 0.5 Zentars.

Step 7: Using these exchange rates, Kira’s spending can be converted to Zentars. In Aurevia, 1000 Aurels equals 2000 Zentars. In Brelosia, 2000 Brins equals 8000 Zentars. So Kira’s total spend is 10000 Zentars. Her Travel Cost is 8000 Aurels, which converts to 16000 Zentars, so her Flight Cost must be 6000 Zentars. This fixes Lian’s Flight Cost as 5000 Zentars.

Step 8: Lian’s Travel Cost is reported by Cyrenia citizens as 36000 Crowns. Using the exchange rate, this equals 18000 Zentars. Lian’s Flight Cost is 5000 Zentars and her Brelosia spend is 3000 Brins, which equals 12000 Zentars. The remaining amount, 1000 Zentars, must be her spend in Cyrenia, which corresponds to 2000 Crowns.

Step 9: Jano’s Travel Cost is reported by Aurevia citizens as 3500 Aurels, which equals 7000 Zentars. After subtracting Jano’s Flight Cost of 4000 Zentars, his total spending must be 3000 Zentars. Since 3000 is already used elsewhere and local spends must be 1000 or 2000, the only possible split is 1000 Aurels in Aurevia, equal to 2000 Zentars, and 2000 Crowns in Cyrenia, equal to 1000 Zentars.

Correct Answer: 13000

Explanation: Lian spent money in Brelosia and Cyrenia. In Brelosia, 3000 Brins converts to 3000 × 4 = 12000 Zentars. In Cyrenia, 2000 Crowns converts to 2000 × 0.5 = 1000 Zentars. Adding these gives a total spending of 12000 + 1000 = 13000 Zentars. This also matches Lian’s Travel Cost reported in Crowns after subtracting her Flight Cost.

Steps to complete the DILR Set

Step 0: Start with a completely blank table. No values are known yet except that the rows are fixed as Flight Cost, spends in Aurevia, Brelosia, Cyrenia, and totals, and the columns are Jano, Kira, and Lian.

Step 1: From the given information, Jano’s Flight Cost is 4000 Zentars, while Kira and Lian have Flight Costs of 5000 and 6000 Zentars in some order. Only Jano’s value can be fixed at this stage.

Step 2: Citizen observations fix travel routes. Aurevia was visited by Jano and Kira, Brelosia was visited by Kira and Lian, and Cyrenia was visited by Lian and exactly one other traveler. Since each country must be visited by exactly two travelers, Jano must also have visited Cyrenia. This fixes that Jano visited Aurevia and Cyrenia, Kira visited Aurevia and Brelosia, and Lian visited Brelosia and Cyrenia. The table structure is now constrained, though no new numbers are filled yet.

Step 3: From the Brelosia citizen’s statement, Kira spent 2000 Brins in Brelosia and Lian spent 3000 Brins in Brelosia. These are direct placements in the table.

Step 4: Across all six visits, there are exactly two spends of 1000, exactly one spend of 3000, and the rest are 2000. Since Lian already has a spend of 3000 Brins in Brelosia, no other visit can have a spend of 3000 in local currency. Therefore, all spends in Aurevia and Cyrenia must be either 1000 or 2000.

Step 5: Kira must have different local-currency spends in the two countries she visited. Since Kira spent 2000 Brins in Brelosia and 3000 is not allowed again, Kira must have spent 1000 Aurels in Aurevia.

Step 6: Kira’s Travel Cost is reported by Aurevia citizens as 8000 Aurels and by Brelosia citizens as 4000 Brins. These represent the same real cost, so 8000 Aurels equals 4000 Brins. This gives the exchange relation that 1 Brin equals 2 Aurels. Using the given fact that 1 Crown equals 0.5 Zentars, the consistent currency values become 1 Aurel equals 2 Zentars, 1 Brin equals 4 Zentars, and 1 Crown equals 0.5 Zentars.

Step 7: Using these exchange rates, Kira’s spending can be converted to Zentars. In Aurevia, 1000 Aurels equals 2000 Zentars. In Brelosia, 2000 Brins equals 8000 Zentars. So Kira’s total spend is 10000 Zentars. Her Travel Cost is 8000 Aurels, which converts to 16000 Zentars, so her Flight Cost must be 6000 Zentars. This fixes Lian’s Flight Cost as 5000 Zentars.

Step 8: Lian’s Travel Cost is reported by Cyrenia citizens as 36000 Crowns. Using the exchange rate, this equals 18000 Zentars. Lian’s Flight Cost is 5000 Zentars and her Brelosia spend is 3000 Brins, which equals 12000 Zentars. The remaining amount, 1000 Zentars, must be her spend in Cyrenia, which corresponds to 2000 Crowns.

Step 9: Jano’s Travel Cost is reported by Aurevia citizens as 3500 Aurels, which equals 7000 Zentars. After subtracting Jano’s Flight Cost of 4000 Zentars, his total spending must be 3000 Zentars. Since 3000 is already used elsewhere and local spends must be 1000 or 2000, the only possible split is 1000 Aurels in Aurevia, equal to 2000 Zentars, and 2000 Crowns in Cyrenia, equal to 1000 Zentars.

Correct Answer: 1500

Explanation: Jano spent 1000 Aurels in Aurevia and 2000 Crowns in Cyrenia. Since 1 Crown equals 0.25 Aurels, 2000 Crowns equals 500 Aurels. Adding the spends in both countries gives 1000 + 500 = 1500 Aurels. This is consistent with Jano’s Travel Cost being 3500 Aurels and his Flight Cost being 4000 Zentars.

Steps to complete the DILR Set

Step 0: Start with a completely blank table. No values are known yet except that the rows are fixed as Flight Cost, spends in Aurevia, Brelosia, Cyrenia, and totals, and the columns are Jano, Kira, and Lian.

Step 1: From the given information, Jano’s Flight Cost is 4000 Zentars, while Kira and Lian have Flight Costs of 5000 and 6000 Zentars in some order. Only Jano’s value can be fixed at this stage.

Step 2: Citizen observations fix travel routes. Aurevia was visited by Jano and Kira, Brelosia was visited by Kira and Lian, and Cyrenia was visited by Lian and exactly one other traveler. Since each country must be visited by exactly two travelers, Jano must also have visited Cyrenia. This fixes that Jano visited Aurevia and Cyrenia, Kira visited Aurevia and Brelosia, and Lian visited Brelosia and Cyrenia. The table structure is now constrained, though no new numbers are filled yet.

Step 3: From the Brelosia citizen’s statement, Kira spent 2000 Brins in Brelosia and Lian spent 3000 Brins in Brelosia. These are direct placements in the table.

Step 4: Across all six visits, there are exactly two spends of 1000, exactly one spend of 3000, and the rest are 2000. Since Lian already has a spend of 3000 Brins in Brelosia, no other visit can have a spend of 3000 in local currency. Therefore, all spends in Aurevia and Cyrenia must be either 1000 or 2000.

Step 5: Kira must have different local-currency spends in the two countries she visited. Since Kira spent 2000 Brins in Brelosia and 3000 is not allowed again, Kira must have spent 1000 Aurels in Aurevia.

Step 6: Kira’s Travel Cost is reported by Aurevia citizens as 8000 Aurels and by Brelosia citizens as 4000 Brins. These represent the same real cost, so 8000 Aurels equals 4000 Brins. This gives the exchange relation that 1 Brin equals 2 Aurels. Using the given fact that 1 Crown equals 0.5 Zentars, the consistent currency values become 1 Aurel equals 2 Zentars, 1 Brin equals 4 Zentars, and 1 Crown equals 0.5 Zentars.

Step 7: Using these exchange rates, Kira’s spending can be converted to Zentars. In Aurevia, 1000 Aurels equals 2000 Zentars. In Brelosia, 2000 Brins equals 8000 Zentars. So Kira’s total spend is 10000 Zentars. Her Travel Cost is 8000 Aurels, which converts to 16000 Zentars, so her Flight Cost must be 6000 Zentars. This fixes Lian’s Flight Cost as 5000 Zentars.

Step 8: Lian’s Travel Cost is reported by Cyrenia citizens as 36000 Crowns. Using the exchange rate, this equals 18000 Zentars. Lian’s Flight Cost is 5000 Zentars and her Brelosia spend is 3000 Brins, which equals 12000 Zentars. The remaining amount, 1000 Zentars, must be her spend in Cyrenia, which corresponds to 2000 Crowns.

Step 9: Jano’s Travel Cost is reported by Aurevia citizens as 3500 Aurels, which equals 7000 Zentars. After subtracting Jano’s Flight Cost of 4000 Zentars, his total spending must be 3000 Zentars. Since 3000 is already used elsewhere and local spends must be 1000 or 2000, the only possible split is 1000 Aurels in Aurevia, equal to 2000 Zentars, and 2000 Crowns in Cyrenia, equal to 1000 Zentars.

Correct Answer: 8

Explanation: One Brin equals 4 Zentars, and one Zentar equals 2 Crowns because 1 Crown equals 0.5 Zentars. Therefore, 1 Brin equals 4 × 2 = 8 Crowns, making option 2 the correct choice.

Steps to complete the DILR Set

Step 0: Start with a completely blank table. No values are known yet except that the rows are fixed as Flight Cost, spends in Aurevia, Brelosia, Cyrenia, and totals, and the columns are Jano, Kira, and Lian.

Step 1: From the given information, Jano’s Flight Cost is 4000 Zentars, while Kira and Lian have Flight Costs of 5000 and 6000 Zentars in some order. Only Jano’s value can be fixed at this stage.

Step 2: Citizen observations fix travel routes. Aurevia was visited by Jano and Kira, Brelosia was visited by Kira and Lian, and Cyrenia was visited by Lian and exactly one other traveler. Since each country must be visited by exactly two travelers, Jano must also have visited Cyrenia. This fixes that Jano visited Aurevia and Cyrenia, Kira visited Aurevia and Brelosia, and Lian visited Brelosia and Cyrenia. The table structure is now constrained, though no new numbers are filled yet.

Step 3: From the Brelosia citizen’s statement, Kira spent 2000 Brins in Brelosia and Lian spent 3000 Brins in Brelosia. These are direct placements in the table.

Step 4: Across all six visits, there are exactly two spends of 1000, exactly one spend of 3000, and the rest are 2000. Since Lian already has a spend of 3000 Brins in Brelosia, no other visit can have a spend of 3000 in local currency. Therefore, all spends in Aurevia and Cyrenia must be either 1000 or 2000.

Step 5: Kira must have different local-currency spends in the two countries she visited. Since Kira spent 2000 Brins in Brelosia and 3000 is not allowed again, Kira must have spent 1000 Aurels in Aurevia.

Step 6: Kira’s Travel Cost is reported by Aurevia citizens as 8000 Aurels and by Brelosia citizens as 4000 Brins. These represent the same real cost, so 8000 Aurels equals 4000 Brins. This gives the exchange relation that 1 Brin equals 2 Aurels. Using the given fact that 1 Crown equals 0.5 Zentars, the consistent currency values become 1 Aurel equals 2 Zentars, 1 Brin equals 4 Zentars, and 1 Crown equals 0.5 Zentars.

Step 7: Using these exchange rates, Kira’s spending can be converted to Zentars. In Aurevia, 1000 Aurels equals 2000 Zentars. In Brelosia, 2000 Brins equals 8000 Zentars. So Kira’s total spend is 10000 Zentars. Her Travel Cost is 8000 Aurels, which converts to 16000 Zentars, so her Flight Cost must be 6000 Zentars. This fixes Lian’s Flight Cost as 5000 Zentars.

Step 8: Lian’s Travel Cost is reported by Cyrenia citizens as 36000 Crowns. Using the exchange rate, this equals 18000 Zentars. Lian’s Flight Cost is 5000 Zentars and her Brelosia spend is 3000 Brins, which equals 12000 Zentars. The remaining amount, 1000 Zentars, must be her spend in Cyrenia, which corresponds to 2000 Crowns.

Step 9: Jano’s Travel Cost is reported by Aurevia citizens as 3500 Aurels, which equals 7000 Zentars. After subtracting Jano’s Flight Cost of 4000 Zentars, his total spending must be 3000 Zentars. Since 3000 is already used elsewhere and local spends must be 1000 or 2000, the only possible split is 1000 Aurels in Aurevia, equal to 2000 Zentars, and 2000 Crowns in Cyrenia, equal to 1000 Zentars.

Correct Answer: 2

Explanation: From the completed table, Jano spent 2000 Crowns in Cyrenia, so statement 1 is true. Jano spent only 1000 Aurels in Aurevia, not 2000, so statement 2 is false. Lian spent 2000 Crowns in Cyrenia, making statement 3 true. Kira spent 1000 Aurels in Aurevia, making statement 4 true. Hence, statement 2 is the incorrect one.

Steps to complete the DILR Set

Step 0: Start with a completely blank table. No values are known yet except that the rows are fixed as Flight Cost, spends in Aurevia, Brelosia, Cyrenia, and totals, and the columns are Jano, Kira, and Lian.

Step 1: From the given information, Jano’s Flight Cost is 4000 Zentars, while Kira and Lian have Flight Costs of 5000 and 6000 Zentars in some order. Only Jano’s value can be fixed at this stage.

Step 2: Citizen observations fix travel routes. Aurevia was visited by Jano and Kira, Brelosia was visited by Kira and Lian, and Cyrenia was visited by Lian and exactly one other traveler. Since each country must be visited by exactly two travelers, Jano must also have visited Cyrenia. This fixes that Jano visited Aurevia and Cyrenia, Kira visited Aurevia and Brelosia, and Lian visited Brelosia and Cyrenia. The table structure is now constrained, though no new numbers are filled yet.

Step 3: From the Brelosia citizen’s statement, Kira spent 2000 Brins in Brelosia and Lian spent 3000 Brins in Brelosia. These are direct placements in the table.

Step 4: Across all six visits, there are exactly two spends of 1000, exactly one spend of 3000, and the rest are 2000. Since Lian already has a spend of 3000 Brins in Brelosia, no other visit can have a spend of 3000 in local currency. Therefore, all spends in Aurevia and Cyrenia must be either 1000 or 2000.

Step 5: Kira must have different local-currency spends in the two countries she visited. Since Kira spent 2000 Brins in Brelosia and 3000 is not allowed again, Kira must have spent 1000 Aurels in Aurevia.

Step 6: Kira’s Travel Cost is reported by Aurevia citizens as 8000 Aurels and by Brelosia citizens as 4000 Brins. These represent the same real cost, so 8000 Aurels equals 4000 Brins. This gives the exchange relation that 1 Brin equals 2 Aurels. Using the given fact that 1 Crown equals 0.5 Zentars, the consistent currency values become 1 Aurel equals 2 Zentars, 1 Brin equals 4 Zentars, and 1 Crown equals 0.5 Zentars.

Step 7: Using these exchange rates, Kira’s spending can be converted to Zentars. In Aurevia, 1000 Aurels equals 2000 Zentars. In Brelosia, 2000 Brins equals 8000 Zentars. So Kira’s total spend is 10000 Zentars. Her Travel Cost is 8000 Aurels, which converts to 16000 Zentars, so her Flight Cost must be 6000 Zentars. This fixes Lian’s Flight Cost as 5000 Zentars.

Step 8: Lian’s Travel Cost is reported by Cyrenia citizens as 36000 Crowns. Using the exchange rate, this equals 18000 Zentars. Lian’s Flight Cost is 5000 Zentars and her Brelosia spend is 3000 Brins, which equals 12000 Zentars. The remaining amount, 1000 Zentars, must be her spend in Cyrenia, which corresponds to 2000 Crowns.

Step 9: Jano’s Travel Cost is reported by Aurevia citizens as 3500 Aurels, which equals 7000 Zentars. After subtracting Jano’s Flight Cost of 4000 Zentars, his total spending must be 3000 Zentars. Since 3000 is already used elsewhere and local spends must be 1000 or 2000, the only possible split is 1000 Aurels in Aurevia, equal to 2000 Zentars, and 2000 Crowns in Cyrenia, equal to 1000 Zentars.