CAT - Logical Reasoning - Math Puzzles | Free Questions | AfterGrad

CAT Logical Reasoning > Math Puzzles PYQs

Filter & Analyse PYQs (Topic-Wise) →

No login required. No pop-ups. We have all previous-year questions with solutions for free!

Q1:

2025 Slot 3

Logical Reasoning > Math Puzzles

Hard

Three countries -- Pumpland (P), Xiland (X) and Cheeseland (C) -- trade among themselves and with the (other countries in) Rest of World (ROW). All trade volumes are given in IC (international currency). The following terminology is used: - Trade balance = Exports - Imports - Total trade = Exports + Imports - Normalized trade balance = Trade balance / Total trade, expressed in percentage terms The following information is known. 1. The normalized trade balances of P, X and C are 0%, 10%, and -20%, respectively. 2. 40% of exports of X are to P. 22% of imports of P are from X. 3. 90% of exports of C are to P; 4% are to ROW. 4. 12% of exports of ROW are to X, 40% are to P. 5. The export volumes of P, in IC, to X and C are 600 and 1200, respectively. P is the only country that exports to C.

How much is exported from C to X, in IC?

Entered answer:

Correct Answer

48

Correct Answer

Explanation →

Q2:

2025 Slot 3

Logical Reasoning > Math Puzzles

Hard

Three countries -- Pumpland (P), Xiland (X) and Cheeseland (C) -- trade among themselves and with the (other countries in) Rest of World (ROW). All trade volumes are given in IC (international currency). The following terminology is used: - Trade balance = Exports - Imports - Total trade = Exports + Imports - Normalized trade balance = Trade balance / Total trade, expressed in percentage terms The following information is known. 1. The normalized trade balances of P, X and C are 0%, 10%, and -20%, respectively. 2. 40% of exports of X are to P. 22% of imports of P are from X. 3. 90% of exports of C are to P; 4% are to ROW. 4. 12% of exports of ROW are to X, 40% are to P. 5. The export volumes of P, in IC, to X and C are 600 and 1200, respectively. P is the only country that exports to C.

How much is exported from P to ROW, in IC?

Entered answer:

Correct Answer

200

Correct Answer

Explanation →

Q3:

2025 Slot 3

Logical Reasoning > Math Puzzles

Hard

Three countries -- Pumpland (P), Xiland (X) and Cheeseland (C) -- trade among themselves and with the (other countries in) Rest of World (ROW). All trade volumes are given in IC (international currency). The following terminology is used: - Trade balance = Exports - Imports - Total trade = Exports + Imports - Normalized trade balance = Trade balance / Total trade, expressed in percentage terms The following information is known. 1. The normalized trade balances of P, X and C are 0%, 10%, and -20%, respectively. 2. 40% of exports of X are to P. 22% of imports of P are from X. 3. 90% of exports of C are to P; 4% are to ROW. 4. 12% of exports of ROW are to X, 40% are to P. 5. The export volumes of P, in IC, to X and C are 600 and 1200, respectively. P is the only country that exports to C.

How much is exported from ROW to ROW, in IC?

Entered answer:

Correct Answer

1008

Correct Answer

Explanation →

Q4:

2025 Slot 3

Logical Reasoning > Math Puzzles

Hard

Three countries -- Pumpland (P), Xiland (X) and Cheeseland (C) -- trade among themselves and with the (other countries in) Rest of World (ROW). All trade volumes are given in IC (international currency). The following terminology is used: - Trade balance = Exports - Imports - Total trade = Exports + Imports - Normalized trade balance = Trade balance / Total trade, expressed in percentage terms The following information is known. 1. The normalized trade balances of P, X and C are 0%, 10%, and -20%, respectively. 2. 40% of exports of X are to P. 22% of imports of P are from X. 3. 90% of exports of C are to P; 4% are to ROW. 4. 12% of exports of ROW are to X, 40% are to P. 5. The export volumes of P, in IC, to X and C are 600 and 1200, respectively. P is the only country that exports to C.

What is the trade balance of ROW?

100

-200

0

200

Correct Answer

Option 4

Correct Answer

Explanation →

Q5:

2025 Slot 3

Logical Reasoning > Math Puzzles

Hard

Three countries -- Pumpland (P), Xiland (X) and Cheeseland (C) -- trade among themselves and with the (other countries in) Rest of World (ROW). All trade volumes are given in IC (international currency). The following terminology is used: - Trade balance = Exports - Imports - Total trade = Exports + Imports - Normalized trade balance = Trade balance / Total trade, expressed in percentage terms The following information is known. 1. The normalized trade balances of P, X and C are 0%, 10%, and -20%, respectively. 2. 40% of exports of X are to P. 22% of imports of P are from X. 3. 90% of exports of C are to P; 4% are to ROW. 4. 12% of exports of ROW are to X, 40% are to P. 5. The export volumes of P, in IC, to X and C are 600 and 1200, respectively. P is the only country that exports to C.

Which among the countries P, X, and C has/have the least total trade?

Only X

Only P

Both X and C

Only C

Correct Answer

Option 3

Correct Answer

Explanation →

Q6:

2025 Slot 3

Logical Reasoning > Math Puzzles

Hard

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.

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

Entered answer:

Correct Answer

41000

Correct Answer

Explanation →

Q7:

2025 Slot 3

Logical Reasoning > Math Puzzles

Hard

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.

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

Entered answer:

Correct Answer

13000

Correct Answer

Explanation →

Q8:

2025 Slot 3

Logical Reasoning > Math Puzzles

Hard

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.

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

Entered answer:

Correct Answer

1500

Correct Answer

Explanation →

Q9:

2025 Slot 3

Logical Reasoning > Math Puzzles

Hard

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.

One Brin is equivalent to how many Crowns?

0.125

4

0.5

8

Correct Answer

Option 4

Correct Answer

Explanation →

Q10:

2025 Slot 3

Logical Reasoning > Math Puzzles

Hard

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.

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

Lian spent 2000 in Cyrenia

Kira spent 1000 in Aurevia

Jano spent 2000 in Cyrenia

Jano spent 2000 in Aurevia

Correct Answer

Option 4

Correct Answer

Explanation →

Q11:

2025 Slot 2

Logical Reasoning > Math Puzzles

Hard

The two most populous cities and the non-urban region (NUR) of each of three states, Whimshire, Fogglia, and Humbleset, are assigned Pollution Measures (PMs). These nine PMs are all distinct multiples of 10, ranging from 10 to 90. The six cities in increasing order of their PMs are: Blusterburg, Noodleton, Splutterville, Quackford, Mumpypore, Zingaloo. The Pollution Index (PI) of a state is a weighted average of the PMs of its NUR and cities, with a weight of 50% for the NUR, and 25% each for its two cities. There is only one pair of an NUR and a city (considering all cities and all NURs) where the PM of the NUR is greater than that of the city. That NUR and the city both belong to Humbleset. The PIs of all three states are distinct integers, with Humbleset and Fogglia having the highest and the lowest PI respectively.

What is the PI of Whimshire?

Entered answer:

Correct Answer

45

Correct Answer

Explanation →

Q12:

2025 Slot 2

Logical Reasoning > Math Puzzles

Hard

The two most populous cities and the non-urban region (NUR) of each of three states, Whimshire, Fogglia, and Humbleset, are assigned Pollution Measures (PMs). These nine PMs are all distinct multiples of 10, ranging from 10 to 90. The six cities in increasing order of their PMs are: Blusterburg, Noodleton, Splutterville, Quackford, Mumpypore, Zingaloo. The Pollution Index (PI) of a state is a weighted average of the PMs of its NUR and cities, with a weight of 50% for the NUR, and 25% each for its two cities. There is only one pair of an NUR and a city (considering all cities and all NURs) where the PM of the NUR is greater than that of the city. That NUR and the city both belong to Humbleset. The PIs of all three states are distinct integers, with Humbleset and Fogglia having the highest and the lowest PI respectively.

What is the PI of Fogglia?

Entered answer:

Correct Answer

35

Correct Answer

Explanation →

Q13:

2025 Slot 2

Logical Reasoning > Math Puzzles

Hard

The two most populous cities and the non-urban region (NUR) of each of three states, Whimshire, Fogglia, and Humbleset, are assigned Pollution Measures (PMs). These nine PMs are all distinct multiples of 10, ranging from 10 to 90. The six cities in increasing order of their PMs are: Blusterburg, Noodleton, Splutterville, Quackford, Mumpypore, Zingaloo. The Pollution Index (PI) of a state is a weighted average of the PMs of its NUR and cities, with a weight of 50% for the NUR, and 25% each for its two cities. There is only one pair of an NUR and a city (considering all cities and all NURs) where the PM of the NUR is greater than that of the city. That NUR and the city both belong to Humbleset. The PIs of all three states are distinct integers, with Humbleset and Fogglia having the highest and the lowest PI respectively.

What is the PI of Humbleset?

Entered answer:

Correct Answer

50

Correct Answer

Explanation →

Q14:

2025 Slot 2

Logical Reasoning > Math Puzzles

Hard

The two most populous cities and the non-urban region (NUR) of each of three states, Whimshire, Fogglia, and Humbleset, are assigned Pollution Measures (PMs). These nine PMs are all distinct multiples of 10, ranging from 10 to 90. The six cities in increasing order of their PMs are: Blusterburg, Noodleton, Splutterville, Quackford, Mumpypore, Zingaloo. The Pollution Index (PI) of a state is a weighted average of the PMs of its NUR and cities, with a weight of 50% for the NUR, and 25% each for its two cities. There is only one pair of an NUR and a city (considering all cities and all NURs) where the PM of the NUR is greater than that of the city. That NUR and the city both belong to Humbleset. The PIs of all three states are distinct integers, with Humbleset and Fogglia having the highest and the lowest PI respectively.

Which pair of cities definitely belong to the same state?

Blusterburg, Mumpypore

Splutterville, Quackford

Noodleton, Quackford

Mumpypore, Zingaloo

Correct Answer

Option 3

Correct Answer

Explanation →

Q15:

2025 Slot 2

Logical Reasoning > Math Puzzles

Hard

The two most populous cities and the non-urban region (NUR) of each of three states, Whimshire, Fogglia, and Humbleset, are assigned Pollution Measures (PMs). These nine PMs are all distinct multiples of 10, ranging from 10 to 90. The six cities in increasing order of their PMs are: Blusterburg, Noodleton, Splutterville, Quackford, Mumpypore, Zingaloo. The Pollution Index (PI) of a state is a weighted average of the PMs of its NUR and cities, with a weight of 50% for the NUR, and 25% each for its two cities. There is only one pair of an NUR and a city (considering all cities and all NURs) where the PM of the NUR is greater than that of the city. That NUR and the city both belong to Humbleset. The PIs of all three states are distinct integers, with Humbleset and Fogglia having the highest and the lowest PI respectively.

For how many of the cities and NURs is it possible to identify their PM and the state they belong to?

Entered answer:

Correct Answer

9

Correct Answer

Explanation →

Q16:

2025 Slot 1

Logical Reasoning > Math Puzzles

Hard

A train travels from Station A to Station E, passing through stations B, C, and D, in that order. The train has a seating capacity of 200. A ticket may be booked from any station to any other station ahead on the route, but not to any earlier station. A ticket from one station to another reserves one seat on every intermediate segment of the route. For example, a ticket from B to E reserves a seat in the intermediate segments B – C, C – D, and D – E. The occupancy factor for a segment is the total number of seats reserved in the segment as a percentage of the seating capacity. The total number of seats reserved for any segment cannot exceed 200. The following information is known. 1. Segment C – D had an occupancy factor of 95%. Only segment B – C had a higher occupancy factor. 2. Exactly 40 tickets were booked from B to C and 30 tickets were booked from B to E. 3. Among the seats reserved on segment D – E, exactly four-sevenths were from stations before C. 4. The number of tickets booked from A to C was equal to that booked from A to E, and it was higher than that from B to E. 5. No tickets were booked from A to B, from B to D and from D to E. 6. The number of tickets booked for any segment was a multiple of 10.

What was the occupancy factor for segment D – E?

84%

70%

35%

77%

Correct Answer

Option 2

Correct Answer

Explanation →

Q17:

2025 Slot 1

Logical Reasoning > Math Puzzles

Hard

A train travels from Station A to Station E, passing through stations B, C, and D, in that order. The train has a seating capacity of 200. A ticket may be booked from any station to any other station ahead on the route, but not to any earlier station. A ticket from one station to another reserves one seat on every intermediate segment of the route. For example, a ticket from B to E reserves a seat in the intermediate segments B – C, C – D, and D – E. The occupancy factor for a segment is the total number of seats reserved in the segment as a percentage of the seating capacity. The total number of seats reserved for any segment cannot exceed 200. The following information is known. 1. Segment C – D had an occupancy factor of 95%. Only segment B – C had a higher occupancy factor. 2. Exactly 40 tickets were booked from B to C and 30 tickets were booked from B to E. 3. Among the seats reserved on segment D – E, exactly four-sevenths were from stations before C. 4. The number of tickets booked from A to C was equal to that booked from A to E, and it was higher than that from B to E. 5. No tickets were booked from A to B, from B to D and from D to E. 6. The number of tickets booked for any segment was a multiple of 10.

How many tickets were booked from Station A to Station E?

Entered answer:

Correct Answer

50

Correct Answer

Explanation →

Q18:

2025 Slot 1

Logical Reasoning > Math Puzzles

Hard

A train travels from Station A to Station E, passing through stations B, C, and D, in that order. The train has a seating capacity of 200. A ticket may be booked from any station to any other station ahead on the route, but not to any earlier station. A ticket from one station to another reserves one seat on every intermediate segment of the route. For example, a ticket from B to E reserves a seat in the intermediate segments B – C, C – D, and D – E. The occupancy factor for a segment is the total number of seats reserved in the segment as a percentage of the seating capacity. The total number of seats reserved for any segment cannot exceed 200. The following information is known. 1. Segment C – D had an occupancy factor of 95%. Only segment B – C had a higher occupancy factor. 2. Exactly 40 tickets were booked from B to C and 30 tickets were booked from B to E. 3. Among the seats reserved on segment D – E, exactly four-sevenths were from stations before C. 4. The number of tickets booked from A to C was equal to that booked from A to E, and it was higher than that from B to E. 5. No tickets were booked from A to B, from B to D and from D to E. 6. The number of tickets booked for any segment was a multiple of 10.

How many tickets were booked from Station C?

Entered answer:

Correct Answer

80

Correct Answer

Explanation →

Q19:

2025 Slot 1

Logical Reasoning > Math Puzzles

Hard

A train travels from Station A to Station E, passing through stations B, C, and D, in that order. The train has a seating capacity of 200. A ticket may be booked from any station to any other station ahead on the route, but not to any earlier station. A ticket from one station to another reserves one seat on every intermediate segment of the route. For example, a ticket from B to E reserves a seat in the intermediate segments B – C, C – D, and D – E. The occupancy factor for a segment is the total number of seats reserved in the segment as a percentage of the seating capacity. The total number of seats reserved for any segment cannot exceed 200. The following information is known. 1. Segment C – D had an occupancy factor of 95%. Only segment B – C had a higher occupancy factor. 2. Exactly 40 tickets were booked from B to C and 30 tickets were booked from B to E. 3. Among the seats reserved on segment D – E, exactly four-sevenths were from stations before C. 4. The number of tickets booked from A to C was equal to that booked from A to E, and it was higher than that from B to E. 5. No tickets were booked from A to B, from B to D and from D to E. 6. The number of tickets booked for any segment was a multiple of 10.

What is the difference between the number of tickets booked to Station C and the number of tickets booked to Station D?

Entered answer:

Correct Answer

40

Correct Answer

Explanation →

Q20:

2025 Slot 1

Logical Reasoning > Math Puzzles

Hard

A train travels from Station A to Station E, passing through stations B, C, and D, in that order. The train has a seating capacity of 200. A ticket may be booked from any station to any other station ahead on the route, but not to any earlier station. A ticket from one station to another reserves one seat on every intermediate segment of the route. For example, a ticket from B to E reserves a seat in the intermediate segments B – C, C – D, and D – E. The occupancy factor for a segment is the total number of seats reserved in the segment as a percentage of the seating capacity. The total number of seats reserved for any segment cannot exceed 200. The following information is known. 1. Segment C – D had an occupancy factor of 95%. Only segment B – C had a higher occupancy factor. 2. Exactly 40 tickets were booked from B to C and 30 tickets were booked from B to E. 3. Among the seats reserved on segment D – E, exactly four-sevenths were from stations before C. 4. The number of tickets booked from A to C was equal to that booked from A to E, and it was higher than that from B to E. 5. No tickets were booked from A to B, from B to D and from D to E. 6. The number of tickets booked for any segment was a multiple of 10.

How many tickets were booked to travel in exactly one segment?

Entered answer:

Correct Answer

60

Correct Answer

Explanation →

Q21:

2025 Slot 1

Logical Reasoning > Math Puzzles

Hard

Alia, Badal, Clive, Dilshan, and Ehsaan played a game in which each asks a unique question to all the others and they respond by tapping their feet, either once or twice or thrice. One tap means “Yes”, two taps mean “No”, and three taps mean “Maybe”. A total of 40 taps were heard across the five questions. Each question received at least one “Yes”, one “No”, and one “Maybe.” The following information is known. 1. Alia tapped a total of 6 times and received 9 taps to her question. She responded “Yes” to the questions asked by both Clive and Dilshan. 2. Dilshan and Ehsaan tapped a total of 11 and 9 times respectively. Dilshan responded “No” to Badal. 3. Badal, Dilshan, and Ehsaan received equal number of taps to their respective questions. 4. No one responded “Yes” more than twice. 5. No one’s answer to Alia’s question matched the answer that Alia gave to that person’s question. This was also true for Ehsaan. 6. Clive tapped more times in total than Badal.

How many taps did Clive receive for his question?

Entered answer:

Correct Answer

7

Correct Answer

Explanation →

Q22:

2025 Slot 1

Logical Reasoning > Math Puzzles

Hard

Alia, Badal, Clive, Dilshan, and Ehsaan played a game in which each asks a unique question to all the others and they respond by tapping their feet, either once or twice or thrice. One tap means “Yes”, two taps mean “No”, and three taps mean “Maybe”. A total of 40 taps were heard across the five questions. Each question received at least one “Yes”, one “No”, and one “Maybe.” The following information is known. 1. Alia tapped a total of 6 times and received 9 taps to her question. She responded “Yes” to the questions asked by both Clive and Dilshan. 2. Dilshan and Ehsaan tapped a total of 11 and 9 times respectively. Dilshan responded “No” to Badal. 3. Badal, Dilshan, and Ehsaan received equal number of taps to their respective questions. 4. No one responded “Yes” more than twice. 5. No one’s answer to Alia’s question matched the answer that Alia gave to that person’s question. This was also true for Ehsaan. 6. Clive tapped more times in total than Badal.

Which two people tapped an equal number of times in total?

Clive and Ehsaan

Dilshan and Clive

Badal and Dilshan

Alia and Badal

Correct Answer

Option 4

Correct Answer

Explanation →

Q23:

2025 Slot 1

Logical Reasoning > Math Puzzles

Hard

Alia, Badal, Clive, Dilshan, and Ehsaan played a game in which each asks a unique question to all the others and they respond by tapping their feet, either once or twice or thrice. One tap means “Yes”, two taps mean “No”, and three taps mean “Maybe”. A total of 40 taps were heard across the five questions. Each question received at least one “Yes”, one “No”, and one “Maybe.” The following information is known. 1. Alia tapped a total of 6 times and received 9 taps to her question. She responded “Yes” to the questions asked by both Clive and Dilshan. 2. Dilshan and Ehsaan tapped a total of 11 and 9 times respectively. Dilshan responded “No” to Badal. 3. Badal, Dilshan, and Ehsaan received equal number of taps to their respective questions. 4. No one responded “Yes” more than twice. 5. No one’s answer to Alia’s question matched the answer that Alia gave to that person’s question. This was also true for Ehsaan. 6. Clive tapped more times in total than Badal.

What was Clive’s response to Ehsaan’s question?

Yes

Maybe

No

Cannot be determined

Correct Answer

Option 3

Correct Answer

Explanation →

Q24:

2025 Slot 1

Logical Reasoning > Math Puzzles

Hard

Alia, Badal, Clive, Dilshan, and Ehsaan played a game in which each asks a unique question to all the others and they respond by tapping their feet, either once or twice or thrice. One tap means “Yes”, two taps mean “No”, and three taps mean “Maybe”. A total of 40 taps were heard across the five questions. Each question received at least one “Yes”, one “No”, and one “Maybe.” The following information is known. 1. Alia tapped a total of 6 times and received 9 taps to her question. She responded “Yes” to the questions asked by both Clive and Dilshan. 2. Dilshan and Ehsaan tapped a total of 11 and 9 times respectively. Dilshan responded “No” to Badal. 3. Badal, Dilshan, and Ehsaan received equal number of taps to their respective questions. 4. No one responded “Yes” more than twice. 5. No one’s answer to Alia’s question matched the answer that Alia gave to that person’s question. This was also true for Ehsaan. 6. Clive tapped more times in total than Badal.

How many “Yes” responses were received across all the questions?

Entered answer:

Correct Answer

6

Correct Answer

Explanation →

Q25:

CAT 2023 Slot 3

Logical Reasoning > Math Puzzles

Hard

There are only three female students- Amala, Koli and Rini and only three male students Biman, Mathew and Shyamal in a course. The course has two evaluation components, a project and a test. The aggregate score in the course is a weighted average of the two components, with the weights being positive and adding to 1. $$\newline$$ The projects are done in groups of two, with each group consisting of a female and a male student. Both the group members obtain the same score in the project. $$\newline$$ The following additional facts are known about the scores in the project and the test. $$\newline$$ 1. The minimum, maximum and the average of both project and test scores were identical, 40, 80 and 60, respectively. $$\newline$$ 2. The test scores of the students were all multiples of 10; four of them were distinct and the remaining two were equal to the average test scores. $$\newline$$ 3. Amala's score in the project was double that of Koli in the same, but Koli scored 20 more than Amala in the test. Yet Amala had the highest aggregate score. $$\newline$$ 4. Shyamal scored the second highest in the test. He scored two more than Koli, but two less than Amala in the aggregate. $$\newline$$ 5. Biman scored the second lowest in the test and the lowest in the aggregate. $$\newline$$ 6. Mathew scored more than Rini in the project, but less than her in the test.

What was Rini's score in the project?

Entered answer:

Correct Answer

60

Correct Answer

Explanation →

Q26:

CAT 2023 Slot 3

Logical Reasoning > Math Puzzles

Hard

There are only three female students- Amala, Koli and Rini and only three male students Biman, Mathew and Shyamal in a course. The course has two evaluation components, a project and a test. The aggregate score in the course is a weighted average of the two components, with the weights being positive and adding to 1. $$\newline$$ The projects are done in groups of two, with each group consisting of a female and a male student. Both the group members obtain the same score in the project. $$\newline$$ The following additional facts are known about the scores in the project and the test. $$\newline$$ 1. The minimum, maximum and the average of both project and test scores were identical, 40, 80 and 60, respectively. $$\newline$$ 2. The test scores of the students were all multiples of 10; four of them were distinct and the remaining two were equal to the average test scores. $$\newline$$ 3. Amala's score in the project was double that of Koli in the same, but Koli scored 20 more than Amala in the test. Yet Amala had the highest aggregate score. $$\newline$$ 4. Shyamal scored the second highest in the test. He scored two more than Koli, but two less than Amala in the aggregate. $$\newline$$ 5. Biman scored the second lowest in the test and the lowest in the aggregate. $$\newline$$ 6. Mathew scored more than Rini in the project, but less than her in the test.

What was the weight of the test component?

$0.50$

$0.60$

$0.40$

$0.75$

Correct Answer

Option 2

Correct Answer

Explanation →

Q27:

CAT 2023 Slot 3

Logical Reasoning > Math Puzzles

Hard

There are only three female students- Amala, Koli and Rini and only three male students Biman, Mathew and Shyamal in a course. The course has two evaluation components, a project and a test. The aggregate score in the course is a weighted average of the two components, with the weights being positive and adding to 1. $$\newline$$ The projects are done in groups of two, with each group consisting of a female and a male student. Both the group members obtain the same score in the project. $$\newline$$ The following additional facts are known about the scores in the project and the test. $$\newline$$ 1. The minimum, maximum and the average of both project and test scores were identical, 40, 80 and 60, respectively. $$\newline$$ 2. The test scores of the students were all multiples of 10; four of them were distinct and the remaining two were equal to the average test scores. $$\newline$$ 3. Amala's score in the project was double that of Koli in the same, but Koli scored 20 more than Amala in the test. Yet Amala had the highest aggregate score. $$\newline$$ 4. Shyamal scored the second highest in the test. He scored two more than Koli, but two less than Amala in the aggregate. $$\newline$$ 5. Biman scored the second lowest in the test and the lowest in the aggregate. $$\newline$$ 6. Mathew scored more than Rini in the project, but less than her in the test.

What was the maximum aggregate score obtained by the students?

$68$

$80$

$66$

$62$

Correct Answer

Option 1

Correct Answer

Explanation →

Q28:

CAT 2023 Slot 3

Logical Reasoning > Math Puzzles

Hard

There are only three female students- Amala, Koli and Rini and only three male students Biman, Mathew and Shyamal in a course. The course has two evaluation components, a project and a test. The aggregate score in the course is a weighted average of the two components, with the weights being positive and adding to 1. $$\newline$$ The projects are done in groups of two, with each group consisting of a female and a male student. Both the group members obtain the same score in the project. $$\newline$$ The following additional facts are known about the scores in the project and the test. $$\newline$$ 1. The minimum, maximum and the average of both project and test scores were identical, 40, 80 and 60, respectively. $$\newline$$ 2. The test scores of the students were all multiples of 10; four of them were distinct and the remaining two were equal to the average test scores. $$\newline$$ 3. Amala's score in the project was double that of Koli in the same, but Koli scored 20 more than Amala in the test. Yet Amala had the highest aggregate score. $$\newline$$ 4. Shyamal scored the second highest in the test. He scored two more than Koli, but two less than Amala in the aggregate. $$\newline$$ 5. Biman scored the second lowest in the test and the lowest in the aggregate. $$\newline$$ 6. Mathew scored more than Rini in the project, but less than her in the test.

What was Mathew's score in the test?

Entered answer:

Correct Answer

40

Correct Answer

Explanation →

Q29:

CAT 2023 Slot 3

Logical Reasoning > Math Puzzles

Hard

There are only three female students- Amala, Koli and Rini and only three male students Biman, Mathew and Shyamal in a course. The course has two evaluation components, a project and a test. The aggregate score in the course is a weighted average of the two components, with the weights being positive and adding to 1. $$\newline$$ The projects are done in groups of two, with each group consisting of a female and a male student. Both the group members obtain the same score in the project. $$\newline$$ The following additional facts are known about the scores in the project and the test. $$\newline$$ 1. The minimum, maximum and the average of both project and test scores were identical, 40, 80 and 60, respectively. $$\newline$$ 2. The test scores of the students were all multiples of 10; four of them were distinct and the remaining two were equal to the average test scores. $$\newline$$ 3. Amala's score in the project was double that of Koli in the same, but Koli scored 20 more than Amala in the test. Yet Amala had the highest aggregate score. $$\newline$$ 4. Shyamal scored the second highest in the test. He scored two more than Koli, but two less than Amala in the aggregate. $$\newline$$ 5. Biman scored the second lowest in the test and the lowest in the aggregate. $$\newline$$ 6. Mathew scored more than Rini in the project, but less than her in the test.

Which of the following pairs of students were part of the same project team? $$\newline$$ i) Amala and Biman $\newline$ ii) Koli and Mathew

Both (i) and (ii)

Only (ii)

Neither (i) nor (ii)

Only (i)

Correct Answer

Option 3

Correct Answer

Explanation →

Q30:

CAT 2021 Slot 3

Logical Reasoning > Math Puzzles

Hard

Each of the bottles mentioned in this question contains 50 ml of liquid. The liquid in any bottle can be 100% pure content (P) or can have certain amount of impurity (I). Visually it is not possible to distinguish between P and I. There is a testing device which detects impurity, as long as the percentage of impurity in the content tested is 10% or more. $$\newline$$ For example, suppose bottle 1 contains only P, and bottle 2 contains 80% P and 20% I. If content from bottle 1 is tested, it will be found out that it contains only P. If content of bottle 2is tested, the test will reveal that it contains some amount of I. If 10 ml of content from bottle 1is mixed with 20 ml content from bottle 2, the test will show that the mixture has impurity, and hence we can conclude that at least one of the two bottles has I. However, if 10 ml of content from bottle 1 is mixed with 5 ml of content from bottle 2. the test will not detect any impurity in the resultant mixture.

5 ml of content from bottle A is mixed with 5 ml of content from bottle B. The resultant mixture, when tested, detects the presence of I. If it is known that bottle A contains only P, what BEST can be concluded about the volume of I in bottle B?

10 ml or more

Less than 1 ml

1 ml

10 ml

Correct Answer

Option 1

Correct Answer

Explanation →

Q31:

CAT 2021 Slot 3

Logical Reasoning > Math Puzzles

Hard

Each of the bottles mentioned in this question contains 50 ml of liquid. The liquid in any bottle can be 100% pure content (P) or can have certain amount of impurity (I). Visually it is not possible to distinguish between P and I. There is a testing device which detects impurity, as long as the percentage of impurity in the content tested is 10% or more. $$\newline$$ For example, suppose bottle 1 contains only P, and bottle 2 contains 80% P and 20% I. If content from bottle 1 is tested, it will be found out that it contains only P. If content of bottle 2is tested, the test will reveal that it contains some amount of I. If 10 ml of content from bottle 1is mixed with 20 ml content from bottle 2, the test will show that the mixture has impurity, and hence we can conclude that at least one of the two bottles has I. However, if 10 ml of content from bottle 1 is mixed with 5 ml of content from bottle 2. the test will not detect any impurity in the resultant mixture.

There are four bottles. Each bottle is known to contain only P or only I. They will be considered to be “collectively ready for despatch” if all of them contain only P. In minimum how many tests, is it possible to ascertain whether these four bottles are “collectively ready for despatch”?.

Entered answer:

Correct Answer

1

Correct Answer

Explanation →

Q32:

CAT 2021 Slot 3

Logical Reasoning > Math Puzzles

Hard

Each of the bottles mentioned in this question contains 50 ml of liquid. The liquid in any bottle can be 100% pure content (P) or can have certain amount of impurity (I). Visually it is not possible to distinguish between P and I. There is a testing device which detects impurity, as long as the percentage of impurity in the content tested is 10% or more. $$\newline$$ For example, suppose bottle 1 contains only P, and bottle 2 contains 80% P and 20% I. If content from bottle 1 is tested, it will be found out that it contains only P. If content of bottle 2is tested, the test will reveal that it contains some amount of I. If 10 ml of content from bottle 1is mixed with 20 ml content from bottle 2, the test will show that the mixture has impurity, and hence we can conclude that at least one of the two bottles has I. However, if 10 ml of content from bottle 1 is mixed with 5 ml of content from bottle 2. the test will not detect any impurity in the resultant mixture.

There are four bottles. It is known that three of these bottles contain only P, while the remaining one contains 80% P and 20% I. What is the minimum number of tests required to definitely identify the bottle containing some amount of I?

Entered answer:

Correct Answer

2

Correct Answer

Explanation →

Q33:

CAT 2021 Slot 3

Logical Reasoning > Math Puzzles

Hard

Each of the bottles mentioned in this question contains 50 ml of liquid. The liquid in any bottle can be 100% pure content (P) or can have certain amount of impurity (I). Visually it is not possible to distinguish between P and I. There is a testing device which detects impurity, as long as the percentage of impurity in the content tested is 10% or more. $$\newline$$ For example, suppose bottle 1 contains only P, and bottle 2 contains 80% P and 20% I. If content from bottle 1 is tested, it will be found out that it contains only P. If content of bottle 2is tested, the test will reveal that it contains some amount of I. If 10 ml of content from bottle 1is mixed with 20 ml content from bottle 2, the test will show that the mixture has impurity, and hence we can conclude that at least one of the two bottles has I. However, if 10 ml of content from bottle 1 is mixed with 5 ml of content from bottle 2. the test will not detect any impurity in the resultant mixture.

There are four bottles. It is known that either one or two of these bottles contain(s)only P, while the remaining ones contain 85% P and 15% I. What is the minimum number of tests required to ascertain the exact number of bottles containing only P?

2

1

3

4

Correct Answer

Option 2

Correct Answer

Explanation →

Q34:

CAT 2019 Slot 1

Logical Reasoning > Math Puzzles

Medium

A new game show on TV has 100 boxes numbered 1, 2,..., 100 in a row, each containing a mystery prize. The prizes are items of different types, a, b, c, ..., in decreasing order of value. The most expensive item is of type a, a diamond ring, and there is exactly one of these. You are told that the number of items at least doubles as you move to the next type. For example, there would be at least twice as many items of type b as of type a, at least twice as many items of type c as of type b and so on. There is no particular order in which the prizes are placed in the boxes.

What is the minimum possible number of different types of prizes?

Entered answer:

Correct Answer

2

Correct Answer

Explanation →

Q35:

CAT 2019 Slot 1

Logical Reasoning > Math Puzzles

Medium

A new game show on TV has 100 boxes numbered 1, 2,..., 100 in a row, each containing a mystery prize. The prizes are items of different types, a, b, c, ..., in decreasing order of value. The most expensive item is of type a, a diamond ring, and there is exactly one of these. You are told that the number of items at least doubles as you move to the next type. For example, there would be at least twice as many items of type b as of type a, at least twice as many items of type c as of type b and so on. There is no particular order in which the prizes are placed in the boxes.

What is the maximum possible number of different types of prizes?

Entered answer:

Correct Answer

6

Correct Answer

Explanation →

Q36:

CAT 2019 Slot 1

Logical Reasoning > Math Puzzles

Medium

A new game show on TV has 100 boxes numbered 1, 2,..., 100 in a row, each containing a mystery prize. The prizes are items of different types, a, b, c, ..., in decreasing order of value. The most expensive item is of type a, a diamond ring, and there is exactly one of these. You are told that the number of items at least doubles as you move to the next type. For example, there would be at least twice as many items of type b as of type a, at least twice as many items of type c as of type b and so on. There is no particular order in which the prizes are placed in the boxes.

Which of the following is not possible?

There are exactly 60 items of type d.

There are exactly 30 items of type b

There are exactly 45 items of typе с

There are exactly 75 items of type e

Correct Answer

Option 3

Correct Answer

Explanation →

Q37:

CAT 2019 Slot 1

Logical Reasoning > Math Puzzles

Medium

A new game show on TV has 100 boxes numbered 1, 2,..., 100 in a row, each containing a mystery prize. The prizes are items of different types, a, b, c, ..., in decreasing order of value. The most expensive item is of type a, a diamond ring, and there is exactly one of these. You are told that the number of items at least doubles as you move to the next type. For example, there would be at least twice as many items of type b as of type a, at least twice as many items of type c as of type b and so on. There is no particular order in which the prizes are placed in the boxes.

You ask for the type of item in box 45. Instead of being given a direct answer, you are told that there are 31 items of the same type as box 45 in boxes 1 to 44 and 43 items of the same type as box 45 in boxes 46 to 100. $$\newline$$ What is the maximum possible number of different types of items?

6

4

3

5

Correct Answer

Option 4

Correct Answer

Explanation →

Q38:

CAT 2018 Slot 2

Logical Reasoning > Math Puzzles

Medium

Each visitor to an amusement park needs to buy a ticket. Tickets can be Platinum, Gold, or Economy. Visitors are classified as Old, Middle-aged, or Young. The following facts are known about visitors and ticket sales on a particular day: $$\newline$$ 1. $140$ tickets were sold. $$\newline$$ 2. The number of Middle-aged visitors was twice the number of Old visitors, while the number of Young visitors was twice the number of Middle-aged visitors. $$\newline$$ 3. Young visitors bought $38$ of the $55$ Economy tickets that were sold, and they bought half the total number of Platinum tickets that were sold. $$\newline$$ 4. The number of Gold tickets bought by Old visitors was equal to the number of Economy tickets bought by Old visitors.

If the number of Old visitors buying Platinum tickets was equal to the number of Middle-aged visitors buying Platinum tickets, then which among the following could be the total number of Platinum tickets sold?

34

38

36

32

Correct Answer

Option 4

Correct Answer

Explanation →

Q39:

CAT 2018 Slot 2

Logical Reasoning > Math Puzzles

Medium

Each visitor to an amusement park needs to buy a ticket. Tickets can be Platinum, Gold, or Economy. Visitors are classified as Old, Middle-aged, or Young. The following facts are known about visitors and ticket sales on a particular day: $$\newline$$ 1. $140$ tickets were sold. $$\newline$$ 2. The number of Middle-aged visitors was twice the number of Old visitors, while the number of Young visitors was twice the number of Middle-aged visitors. $$\newline$$ 3. Young visitors bought $38$ of the $55$ Economy tickets that were sold, and they bought half the total number of Platinum tickets that were sold. $$\newline$$ 4. The number of Gold tickets bought by Old visitors was equal to the number of Economy tickets bought by Old visitors.

If the number of Old visitors buying Platinum tickets was equal to the number of Middle-aged visitors buying Economy tickets, then the number of Old visitors buying Gold tickets was

Entered answer:

Correct Answer

3

Correct Answer

Explanation →

Q40:

CAT 2018 Slot 2

Logical Reasoning > Math Puzzles

Medium

Each visitor to an amusement park needs to buy a ticket. Tickets can be Platinum, Gold, or Economy. Visitors are classified as Old, Middle-aged, or Young. The following facts are known about visitors and ticket sales on a particular day: $$\newline$$ 1. $140$ tickets were sold. $$\newline$$ 2. The number of Middle-aged visitors was twice the number of Old visitors, while the number of Young visitors was twice the number of Middle-aged visitors. $$\newline$$ 3. Young visitors bought $38$ of the $55$ Economy tickets that were sold, and they bought half the total number of Platinum tickets that were sold. $$\newline$$ 4. The number of Gold tickets bought by Old visitors was equal to the number of Economy tickets bought by Old visitors.

If the number of Old visitors buying Gold tickets was strictly greater than the number of Young visitors buying Gold tickets, then the number of Middle-aged visitors buying Gold tickets was

Entered answer:

Correct Answer

0

Correct Answer

Explanation →

Q41:

CAT 2018 Slot 2

Logical Reasoning > Math Puzzles

Medium

Each visitor to an amusement park needs to buy a ticket. Tickets can be Platinum, Gold, or Economy. Visitors are classified as Old, Middle-aged, or Young. The following facts are known about visitors and ticket sales on a particular day: $$\newline$$ 1. $140$ tickets were sold. $$\newline$$ 2. The number of Middle-aged visitors was twice the number of Old visitors, while the number of Young visitors was twice the number of Middle-aged visitors. $$\newline$$ 3. Young visitors bought $38$ of the $55$ Economy tickets that were sold, and they bought half the total number of Platinum tickets that were sold. $$\newline$$ 4. The number of Gold tickets bought by Old visitors was equal to the number of Economy tickets bought by Old visitors.

Which of the following statements MUST be FALSE?

The numbers of Gold and Platinum tickets bought by Young visitors were equal

The numbers of Old and Middle-aged visitors buying Platinum tickets were equal

The numbers of Old and Middle-aged visitors buying Economy tickets were equal

The numbers of Middle-aged and Young visitors buying Gold tickets were equal

Correct Answer

Option 3

Correct Answer

Explanation →

Q42:

CAT 2018 Slot 1

Logical Reasoning > Math Puzzles

Medium

An ATM dispenses exactly Rs. $5000$ per withdrawal using $100$, $200$ and $500$ rupee notes. The ATM requires every customer to give her preference for one of the three denominations of notes. It then dispenses notes such that the number of notes of the customer’s preferred denomination exceeds the total number of notes of other denominations dispensed to her.

In how many different ways can the ATM serve a customer who gives $500$ rupee notes as her preference?

Entered answer:

Correct Answer

7

Correct Answer

Explanation →

Q43:

CAT 2018 Slot 1

Logical Reasoning > Math Puzzles

Medium

An ATM dispenses exactly Rs. $5000$ per withdrawal using $100$, $200$ and $500$ rupee notes. The ATM requires every customer to give her preference for one of the three denominations of notes. It then dispenses notes such that the number of notes of the customer’s preferred denomination exceeds the total number of notes of other denominations dispensed to her.

If the ATM could serve only $10$ customers with a stock of fifty $500$ rupee notes and a sufficient number of notes of other denominations, what is the maximum number of customers among these $10$ who could have given $500$ rupee notes as their preferences?

Entered answer:

Correct Answer

6

Correct Answer

Explanation →

Q44:

CAT 2018 Slot 1

Logical Reasoning > Math Puzzles

Medium

An ATM dispenses exactly Rs. $5000$ per withdrawal using $100$, $200$ and $500$ rupee notes. The ATM requires every customer to give her preference for one of the three denominations of notes. It then dispenses notes such that the number of notes of the customer’s preferred denomination exceeds the total number of notes of other denominations dispensed to her.

What is the maximum number of customers that the ATM can serve with a stock of fifty $500$ rupee notes and a sufficient number of notes of other denominations, if all the customers are to be served with at most $20$ notes per withdrawal?

12

10

13

16

Correct Answer

Option 1

Correct Answer

Explanation →

Q45:

CAT 2018 Slot 1

Logical Reasoning > Math Puzzles

Medium

An ATM dispenses exactly Rs. $5000$ per withdrawal using $100$, $200$ and $500$ rupee notes. The ATM requires every customer to give her preference for one of the three denominations of notes. It then dispenses notes such that the number of notes of the customer’s preferred denomination exceeds the total number of notes of other denominations dispensed to her.

What is the number of $500$ rupee notes required to serve $50$ customers with $500$ rupee notes as their preferences and another $50$ customers with $100$ rupee notes as their preferences, if the total number of notes to be dispensed is the smallest possible?

900

800

750

1400

Correct Answer

Option 1

Correct Answer

Explanation →