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CAT 2025 Slot 3 DILR · Set 5 of 5Logical ReasoningHard DifficultyQ18–Q22 · 2 MCQ + 3 TITA

CAT 2025 Slot 3 DILR Set 5: Math Puzzles (5 Questions) with Solutions

The Math Puzzles set from the official CAT 2025 Slot 3 DILR paper: the caselet, all 5 questions, the official answer key and a step-by-step solution for each. 100% free, no sign-up.

The Set: Read the Caselet First

CAT 2025 Slot 3 DILR · Questions 18–22
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.

In the exam this set competed with 4 others for 40 minutes. Budget about 8 minutes if you attempt it.

Q18. Math Puzzles

TITA · +3 / 0
What is the sum of Travel Costs for all travelers in Zentars?
Correct Answer
41000
Step-by-step solution
📌 Core Concept
Fix who visited which country, then use the local-currency Travel Costs to get the exchange rates and flight costs.
🔢 Step-by-Step Solution
1
Each country has exactly two visitors. Aurevia: Jano and Kira. Brelosia: Kira and Lian. So Cyrenia's two visitors must be Lian and Jano. Routes: Jano (Aurevia, Cyrenia), Kira (Aurevia, Brelosia), Lian (Brelosia, Cyrenia).
2
Kira spent 2000 in Brelosia and spends must differ within a country pair, so her Aurevia spend is not 2000. Lian's 3000 in Brelosia is the only 3000, so Kira's Aurevia spend is 1000.
3
Let 1 Aurel = aa Zentars, 1 Brin = bb Zentars, and Kira's flight cost = FF. Her total in Zentars is F+2000b+1000aF + 2000b + 1000a. Brelosia says this is 4000b4000b and Aurevia says it is 8000a8000a. So 4000b=8000a4000b = 8000a, giving b=2ab = 2a.
4
Then F=8000a−2000(2a)−1000a=3000aF = 8000a - 2000(2a) - 1000a = 3000a. Jano's flight is 4000, so FF is 5000 or 6000, giving a=5/3a = 5/3 or a=2a = 2.
5
Jano's cost is 3500a3500a Zentars, so his spends are worth 3500a−40003500a - 4000. For a=2a = 2 this is 3000, which is 2jA+0.5jC2j_A + 0.5j_C with jAj_A = 1000 or 2000 (3000 is taken). Only jA=1000j_A = 1000, jC=2000j_C = 2000 works. For a=5/3a = 5/3, jA=1000j_A = 1000 forces jC≈333j_C \approx 333 and jA=2000j_A = 2000 overshoots, so it fails. Hence a=2a = 2, b=4b = 4, Kira's flight is 6000, and Lian's is 5000.
6
Travel Costs in Zentars: Jano 3500×2=70003500 \times 2 = 7000; Kira 4000×4=160004000 \times 4 = 16000; Lian 36000×0.5=1800036000 \times 0.5 = 18000.
Quick Check
7000+16000+18000=410007000 + 16000 + 18000 = 41000.
Correct Answer: 41000

Q19. Math Puzzles

TITA · +3 / 0
How many Zentars did Lian spend in the two countries he visited?
Correct Answer
13000
Step-by-step solution
📌 Core Concept
Work out the routes and exchange rates, then convert Lian's two spends into Zentars.
🔢 Step-by-Step Solution
1
Aurevia has Jano and Kira, Brelosia has Kira and Lian, so Cyrenia has Lian and Jano. Lian visited Brelosia and Cyrenia.
2
Kira spent 2000 in Brelosia. Lian's 3000 in Brelosia is the only 3000, so Kira's Aurevia spend is 1000.
3
Let 1 Aurel = aa Zentars, 1 Brin = bb Zentars, and Kira's flight = FF. Kira's total is 4000b4000b (Brelosia) and also 8000a8000a (Aurevia), and both equal F+2000b+1000aF + 2000b + 1000a. So b=2ab = 2a and F=3000aF = 3000a.
4
FF is 5000 or 6000. Jano's total of 3500a3500a Zentars less his 4000 flight leaves 3500a−40003500a - 4000 for his spends. With a=2a = 2 this is 3000 and gives Jano 1000 in Aurevia and 2000 in Cyrenia. With a=5/3a = 5/3 no valid spends exist. So a=2a = 2, b=4b = 4, Kira's flight is 6000 and Lian's is 5000.
5
The two 1000 spends are now Kira's and Jano's in Aurevia, so Lian's Cyrenia spend cannot be 1000. It differs from her 3000, so it is 2000 Crowns.
6
Lian's spends in Zentars: Brelosia 3000×4=120003000 \times 4 = 12000; Cyrenia 2000×0.5=10002000 \times 0.5 = 1000. Total 13000.
Quick Check
5000+13000=18000=36000×0.55000 + 13000 = 18000 = 36000 \times 0.5, which matches Lian's Travel Cost.
Correct Answer: 13000

Q20. Math Puzzles

TITA · +3 / 0
What was Jano's total spend in the two countries he visited, in Aurels?
Correct Answer
1500
Step-by-step solution
📌 Core Concept
Find Jano's spends from his Travel Cost, then express both in Aurels using the exchange rates.
🔢 Step-by-Step Solution
1
Each country has two visitors, so Jano (Aurevia) and Lian (with Kira in Brelosia) force Jano's route to be Aurevia and Cyrenia.
2
Kira spent 2000 in Brelosia and Lian 3000, so Kira's Aurevia spend is 1000 (the only 3000 is already used).
3
Let 1 Aurel = aa Zentars, 1 Brin = bb Zentars, and Kira's flight = FF. Kira's total is 4000b=8000a=F+2000b+1000a4000b = 8000a = F + 2000b + 1000a. So b=2ab = 2a and F=3000aF = 3000a. Since FF is 5000 or 6000, aa is 5/35/3 or 2.
4
Jano's Travel Cost is 3500a3500a Zentars and his flight is 4000, so his spends are worth 3500a−40003500a - 4000. His Aurevia spend jAj_A is 1000 or 2000, and 2jA2j_A... in Zentars it is a⋅jAa \cdot j_A, while Cyrenia gives 0.5jC0.5 j_C.
5
For a=2a = 2: spends are worth 3000, so 2jA+0.5jC=30002j_A + 0.5j_C = 3000. Only jA=1000j_A = 1000, jC=2000j_C = 2000 fits. For a=5/3a = 5/3 no valid pair exists. So a=2a = 2.
6
Convert to Aurels: 1 Crown = 0.5 Zentars = 0.25 Aurel, so 2000 Crowns = 500 Aurels. Jano's total is 1000+500=15001000 + 500 = 1500 Aurels.
Quick Check
1500×2=30001500 \times 2 = 3000 Zentars, and 3000+4000=7000=3500×23000 + 4000 = 7000 = 3500 \times 2.
Correct Answer: 1500

Q21. Math Puzzles

MCQ · +3 / −1
One Brin is equivalent to how many Crowns?
  1. A) 0.125
  2. B) 4
  3. C) 0.5
  4. D) 8
Correct Answer
D) 8
Step-by-step solution
📌 Core Concept
Kira's Travel Cost is stated in two currencies, which links the Brin and the Aurel. The Crown is then linked through Jano's and Lian's data.
🔢 Step-by-Step Solution
1
Each country has two visitors: Aurevia has Jano and Kira, Brelosia has Kira and Lian, so Cyrenia has Lian and Jano.
2
Kira's Aurevia spend is 1000, since she spent 2000 in Brelosia and the only 3000 is Lian's in Brelosia.
3
Let 1 Aurel = aa Zentars, 1 Brin = bb Zentars, and Kira's flight = FF. Her total is 4000b4000b and also 8000a8000a. So b=2ab = 2a. Also F+2000b+1000a=8000aF + 2000b + 1000a = 8000a gives F=3000aF = 3000a, so a=5/3a = 5/3 or 2 for FF = 5000 or 6000.
4
Jano's spends are worth 3500a−40003500a - 4000 Zentars. For a=2a = 2 that is 3000, met only by 1000 Aurels and 2000 Crowns (2000+1000=30002000 + 1000 = 3000). For a=5/3a = 5/3 no valid spends fit. So a=2a = 2 and b=4b = 4.
5
1 Brin = 4 Zentars. Since 1 Crown = 0.5 Zentars, 1 Brin = 4/0.5=84 / 0.5 = 8 Crowns.
Why Not the Others
A) 0.125 is the inverse: Crowns per Brin flipped.
B) 4 is the Brin in Zentars, not in Crowns.
C) 0.5 is the Crown in Zentars.
Correct Answer: D

Q22. Math Puzzles

MCQ · +3 / −1
Which of the following statements is NOT true about money spent in the local currency?
  1. A) Lian spent 2000 in Cyrenia
  2. B) Kira spent 1000 in Aurevia
  3. C) Jano spent 2000 in Cyrenia
  4. D) Jano spent 2000 in Aurevia
Correct Answer
D) Jano spent 2000 in Aurevia
Step-by-step solution
📌 Core Concept
Derive each traveler's route and local-currency spends, then test each statement against them.
🔢 Step-by-Step Solution
1
Aurevia has Jano and Kira, Brelosia has Kira and Lian, so Cyrenia has Lian and Jano.
2
Kira spent 2000 in Brelosia and Lian spent 3000, so Kira's Aurevia spend is 1000 (the only 3000 is already used, and 2000 repeats her other spend).
3
Let 1 Aurel = aa Zentars, 1 Brin = bb Zentars, and Kira's flight = FF. Her total gives 4000b=8000a=F+2000b+1000a4000b = 8000a = F + 2000b + 1000a, so b=2ab = 2a and F=3000aF = 3000a. Then aa is 5/35/3 or 2.
4
Jano's spends are worth 3500a−40003500a - 4000 Zentars. For a=2a = 2 this is 3000, and 2jA+0.5jC=30002j_A + 0.5j_C = 3000 gives jA=1000j_A = 1000, jC=2000j_C = 2000. The case a=5/3a = 5/3 yields no valid spends. So a=2a = 2, b=4b = 4.
5
The two 1000 spends are Kira's and Jano's, both in Aurevia. So Lian's Cyrenia spend is 2000, using the cost relation 5000+12000+0.5j=180005000 + 12000 + 0.5 j = 18000.
6
Checking the options:
A) Lian spent 2000 in Cyrenia: true.
B) Kira spent 1000 in Aurevia: true.
C) Jano spent 2000 in Cyrenia: true.
D) Jano spent 1000, not 2000, in Aurevia: false.
Why Not the Others
A, B and C all match the derived spends, so only D is not true.
Correct Answer: D
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CAT 2025 Slot 3 DILR at a Glance

Sets in this section5
Questions in this section22
Section time40 minutes
Convenor IIMIIM Kozhikode

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