CAT 2025 Slot 3 DILR Set 2 Q5–Q9

A DILR caselet from the Data Interpretation & Logical Reasoning (DILR) section of CAT 2025 Slot 3, with 5 questions (Quant-based Puzzles). Answers are CAT's official key.

The set

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

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

TITA: type in the answer. There are no options and no negative marking.

Answer: 41000 Quant-based Puzzles TITA

Solution

  1. Aurevia: Jano, Kira; Brelosia: Kira, Lian; Cyrenia gets two visitors and Kira is used up, so Cyrenia: Lian, Jano.
  2. Spends: one 3000 (Lian in B), two 1000s, three 2000s. Kira (2000 in B) must spend 1000 in A. Jano spends one 1000 and one 2000, so Lian spends 2000 in C.
  3. Kira's Travel Cost is 8000 Aurels \(=\) 4000 Brins, so 1 Brin \(= 2\) Aurels. With 1 Aurel \(= a\) Zentars, Kira's flight \(= 8000a - 1000a - 2000(2a) = 3000a\).
  4. Lian's Travel Cost \(= 36000\) Crowns \(= 18000\) Z \(=\) flight \(+ 3000(2a) + 1000\). If Kira's flight is 6000 then \(a = 2\), Lian's flight 5000 and \(5000 + 12000 + 1000 = 18000\) fits; Kira's flight 5000 fails.
  5. So 1 Aurel \(= 2\) Z, 1 Brin \(= 4\) Z, 1 Crown \(= 0.5\) Z. Jano: \(3500 \times 2 = 7000 = 4000 + 2x + 0.5y\) gives 1000 Aurels in A and 2000 Crowns in C.
  6. Travel Costs in Zentars: Jano 7000, Kira \(8000 \times 2 = 16000\), Lian 18000; total 41000.

Question 6

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

TITA: type in the answer. There are no options and no negative marking.

Answer: 13000 Quant-based Puzzles TITA

Solution

  1. Aurevia: Jano, Kira; Brelosia: Kira, Lian; Cyrenia gets two visitors and Kira is used up, so Cyrenia: Lian, Jano.
  2. Spends: one 3000 (Lian in B), two 1000s, three 2000s. Kira (2000 in B) must spend 1000 in A. Jano spends one 1000 and one 2000, so Lian spends 2000 in C.
  3. Kira's Travel Cost is 8000 Aurels \(=\) 4000 Brins, so 1 Brin \(= 2\) Aurels. With 1 Aurel \(= a\) Zentars, Kira's flight \(= 8000a - 1000a - 2000(2a) = 3000a\).
  4. Lian's Travel Cost \(= 36000\) Crowns \(= 18000\) Z \(=\) flight \(+ 3000(2a) + 1000\). If Kira's flight is 6000 then \(a = 2\), Lian's flight 5000 and \(5000 + 12000 + 1000 = 18000\) fits; Kira's flight 5000 fails.
  5. So 1 Aurel \(= 2\) Z, 1 Brin \(= 4\) Z, 1 Crown \(= 0.5\) Z. Jano: \(3500 \times 2 = 7000 = 4000 + 2x + 0.5y\) gives 1000 Aurels in A and 2000 Crowns in C.
  6. Lian: 3000 Brins \(= 12000\) Z and 2000 Crowns \(= 1000\) Z, total 13000 Zentars.

Question 7

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

TITA: type in the answer. There are no options and no negative marking.

Answer: 1500 Quant-based Puzzles TITA

Solution

  1. Aurevia: Jano, Kira; Brelosia: Kira, Lian; Cyrenia gets two visitors and Kira is used up, so Cyrenia: Lian, Jano.
  2. Spends: one 3000 (Lian in B), two 1000s, three 2000s. Kira (2000 in B) must spend 1000 in A. Jano spends one 1000 and one 2000, so Lian spends 2000 in C.
  3. Kira's Travel Cost is 8000 Aurels \(=\) 4000 Brins, so 1 Brin \(= 2\) Aurels. With 1 Aurel \(= a\) Zentars, Kira's flight \(= 8000a - 1000a - 2000(2a) = 3000a\).
  4. Lian's Travel Cost \(= 36000\) Crowns \(= 18000\) Z \(=\) flight \(+ 3000(2a) + 1000\). If Kira's flight is 6000 then \(a = 2\), Lian's flight 5000 and \(5000 + 12000 + 1000 = 18000\) fits; Kira's flight 5000 fails.
  5. So 1 Aurel \(= 2\) Z, 1 Brin \(= 4\) Z, 1 Crown \(= 0.5\) Z. Jano: \(3500 \times 2 = 7000 = 4000 + 2x + 0.5y\) gives 1000 Aurels in A and 2000 Crowns in C.
  6. Jano: 1000 Aurels in A plus 2000 Crowns \(= 1000\) Z \(= 500\) Aurels in C; total 1500 Aurels.

Question 8

One Brin is equivalent to how many Crowns?
  1. A
    4
  2. B
    0.5
  3. C
    8
  4. D
    0.125

Answer: (C) 8 Quant-based Puzzles MCQ

Solution

  1. Aurevia: Jano, Kira; Brelosia: Kira, Lian; Cyrenia gets two visitors and Kira is used up, so Cyrenia: Lian, Jano.
  2. Spends: one 3000 (Lian in B), two 1000s, three 2000s. Kira (2000 in B) must spend 1000 in A. Jano spends one 1000 and one 2000, so Lian spends 2000 in C.
  3. Kira's Travel Cost is 8000 Aurels \(=\) 4000 Brins, so 1 Brin \(= 2\) Aurels. With 1 Aurel \(= a\) Zentars, Kira's flight \(= 8000a - 1000a - 2000(2a) = 3000a\).
  4. Lian's Travel Cost \(= 36000\) Crowns \(= 18000\) Z \(=\) flight \(+ 3000(2a) + 1000\). If Kira's flight is 6000 then \(a = 2\), Lian's flight 5000 and \(5000 + 12000 + 1000 = 18000\) fits; Kira's flight 5000 fails.
  5. So 1 Aurel \(= 2\) Z, 1 Brin \(= 4\) Z, 1 Crown \(= 0.5\) Z. Jano: \(3500 \times 2 = 7000 = 4000 + 2x + 0.5y\) gives 1000 Aurels in A and 2000 Crowns in C.
  6. 1 Brin \(= 4\) Z \(= 8\) Crowns.

Question 9

Which of the following statements is NOT true about money spent in the local currency?
  1. A
    Kira spent 1000 in Aurevia
  2. B
    Jano spent 2000 in Aurevia
  3. C
    Jano spent 2000 in Cyrenia
  4. D
    Lian spent 2000 in Cyrenia

Answer: (B) Jano spent 2000 in Aurevia Quant-based Puzzles MCQ

Solution

  1. Aurevia: Jano, Kira; Brelosia: Kira, Lian; Cyrenia gets two visitors and Kira is used up, so Cyrenia: Lian, Jano.
  2. Spends: one 3000 (Lian in B), two 1000s, three 2000s. Kira (2000 in B) must spend 1000 in A. Jano spends one 1000 and one 2000, so Lian spends 2000 in C.
  3. Kira's Travel Cost is 8000 Aurels \(=\) 4000 Brins, so 1 Brin \(= 2\) Aurels. With 1 Aurel \(= a\) Zentars, Kira's flight \(= 8000a - 1000a - 2000(2a) = 3000a\).
  4. Lian's Travel Cost \(= 36000\) Crowns \(= 18000\) Z \(=\) flight \(+ 3000(2a) + 1000\). If Kira's flight is 6000 then \(a = 2\), Lian's flight 5000 and \(5000 + 12000 + 1000 = 18000\) fits; Kira's flight 5000 fails.
  5. So 1 Aurel \(= 2\) Z, 1 Brin \(= 4\) Z, 1 Crown \(= 0.5\) Z. Jano: \(3500 \times 2 = 7000 = 4000 + 2x + 0.5y\) gives 1000 Aurels in A and 2000 Crowns in C.
  6. Jano spent 1000, not 2000, in Aurevia, so B is false; A, C and D are all true.

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