CATSprint

CAT 2025Slot 3DILRQues & Sol

Data InterpretationHard

Data 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 1

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

Solution

Setup: Countries: Aurevia (Aurels), Brelosia (Brins), Cyrenia (Crowns), Zerathania (Zentars). One Crown = (0.5) Zentars. Jano's flight cost = (4000Z); Kira and Lian have flight costs (5000Z) and (6000Z) in some order. Each traveler visits two countries, and each of the three visited countries is visited by two travelers.

CountryVisitors
AureviaJano, Kira
BrelosiaKira, Lian
CyreniaJano, Lian
TravelerAureviaBrelosiaCyrenia
Jano(1000A)—(2000C)
Kira(1000A)(2000B)—
Lian—(3000B)(2000C)

Steps:

  1. Country allocation: From the three-country/two-visitors condition, A is visited by Jano and Kira; B by Kira and Lian; C by Jano and Lian.

  2. Spending pattern: The six spends contain two (1000)'s, one (3000), and therefore three (2000)'s.

  3. Determine individual spends: Kira spends (2000B) in Brelosia. Since Kira's two spends differ, Kira's Aurevia spend is (1000A). Lian's Brelosia spend is (3000B), so Lian's Cyrenia spend is (2000C). Jano consequently uses (1000A) and (2000C).

  4. Determine currency values: Let Aurel = $aZ$ and Brin = $bZ$. Kira's Brelosia travel cost is $4000B$:

$$ \text{Flight cost} + 2000B = 4000B $$

The Aurevia observation gives Kira's travel cost as $8000A$. Solving with Kira's unique flight cost gives:

$$ 1A = 2Z,\qquad 1B = 4Z $$

Hence, Lian's flight cost is $5000Z$.

Jano's total cost:

$$ 4000 + 1000 \times 2 + 2000 \times 0.5 = 7000Z $$

Kira's total cost:

$$ 8000A = 8000 \times 2 = 16,000Z $$

Lian's total cost:

$$ 5000 + 3000 \times 4 + 2000 \times 0.5 = 18,000Z $$

Total cost:

$$ 7000 + 16000 + 18000 = 41,000Z $$

Final Answer: 41,000 Zentars

Question 2

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

Solution

  1. Lian's spends: Lian spends 3000 Brins in Brelosia and 2000 Crowns in Cyrenia.

  2. Currency values: 1 Brin = 4 Z and 1 Crown = 0.5 Z.

  3. Total spend:

$$ 3000 \times 4 + 2000 \times 0.5 = 12,000 + 1,000 = 13,000Z $$

Final Answer: 13,000 Zentars

Question 3

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

Solution

  1. Jano's spends: Jano spends 1000 Aurels and 2000 Crowns.

  2. Convert to Zentars: $$ 1000 \times 2 + 2000 \times 0.5 = 3000Z $$

  3. Convert back to Aurels: Since 1 Aurel = 2 Z

$$ 3000Z \div 2 = 1500A $$

Final Answer: 1500 Aurels

Question 4

One Brin is equivalent to how many Crowns?

Solution

  1. Currency values: 1 Brin = 4 Z and 1 Crown = 0.5 Z.

  2. Convert Brins to Crowns:

$$ 1\text{ Brin} = \frac{4}{0.5} = 8\text{ Crowns} $$

Final Answer: 1 Brin = 8 Crowns

Question 5

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

Solution

  1. Actual spend matrix: Jano = 1000 A + 2000 C; Kira = 1000 A + 2000 B; Lian = 3000 B + 2000 C.

  2. Evaluate the statements: Thus, B is true, C is true, and D is true, while A is false.

Final Answer: B, C and D are true; A is false.