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Q1:

2025 Slot 3

Arrangements

Hard

Seven children, Aarav, Bina, Chirag, Diya, Eshan, Farhan, and Gaurav, are sitting in a circle facing inside (not necessarily in the same order) and playing a game of 'Passing the Buck'.

The game is played over 10 rounds. In each round, the child holding the Buck must pass it directly to a child sitting in one of the following positions:

  • Immediately to the left;
  • Immediate to the right;
  • Second to the left; or
  • Second to the right.

The game starts with Bina passing the Buck and ends with Chirag receiving the Buck. The table below provides some information about the pass types and the child receiving the Buck. Some information is missing and labelled as '?'.

Who is sitting immediately to the right of Bina?

Answer options
Option 3
Correct Answer
Explanation for 2025 Slot 3 DILR question 1

Q2:

2025 Slot 3

Arrangements

Hard

Seven children, Aarav, Bina, Chirag, Diya, Eshan, Farhan, and Gaurav, are sitting in a circle facing inside (not necessarily in the same order) and playing a game of 'Passing the Buck'.

The game is played over 10 rounds. In each round, the child holding the Buck must pass it directly to a child sitting in one of the following positions:

  • Immediately to the left;
  • Immediate to the right;
  • Second to the left; or
  • Second to the right.

The game starts with Bina passing the Buck and ends with Chirag receiving the Buck. The table below provides some information about the pass types and the child receiving the Buck. Some information is missing and labelled as '?'.

Who is sitting third to the left of Eshan?

Answer options
Option 1
Correct Answer
Explanation for 2025 Slot 3 DILR question 2

Q3:

2025 Slot 3

Arrangements

Hard

Seven children, Aarav, Bina, Chirag, Diya, Eshan, Farhan, and Gaurav, are sitting in a circle facing inside (not necessarily in the same order) and playing a game of 'Passing the Buck'.

The game is played over 10 rounds. In each round, the child holding the Buck must pass it directly to a child sitting in one of the following positions:

  • Immediately to the left;
  • Immediate to the right;
  • Second to the left; or
  • Second to the right.

The game starts with Bina passing the Buck and ends with Chirag receiving the Buck. The table below provides some information about the pass types and the child receiving the Buck. Some information is missing and labelled as '?'.

For which of the following pass types can the total number of occurrences be uniquely determined?

Answer options
Option 4
Correct Answer
Explanation for 2025 Slot 3 DILR question 3

Q4:

2025 Slot 3

Arrangements

Hard

Seven children, Aarav, Bina, Chirag, Diya, Eshan, Farhan, and Gaurav, are sitting in a circle facing inside (not necessarily in the same order) and playing a game of 'Passing the Buck'.

The game is played over 10 rounds. In each round, the child holding the Buck must pass it directly to a child sitting in one of the following positions:

  • Immediately to the left;
  • Immediate to the right;
  • Second to the left; or
  • Second to the right.

The game starts with Bina passing the Buck and ends with Chirag receiving the Buck. The table below provides some information about the pass types and the child receiving the Buck. Some information is missing and labelled as '?'.

For which of the following children is it possible to determine how many times they received the Buck?

Answer options
Option 2
Correct Answer
Explanation for 2025 Slot 3 DILR question 4

Q5:

2025 Slot 2

Arrangements

Hard

Ananya Raga, Bhaskar Tala, Charu Veena, and Devendra Sur are four musicians. Each of them started and completed their training as students under each of three Gurus - Pandit Meghnath, Ustad Samiran, and Acharya Raghunath between 2013 and 2024, including both the years. Each Guru trains any student for consecutive years only, for a span of 2, 3, or 4 years, with each Guru having a different span. During some of these years, a student may not have trained under these Gurus; however, they never trained under multiple Gurus in the same year.

In none of these years, any of these Gurus trained more than two of these students at the same time. When two students train under the same Guru at the same time, they are referred to as Gurubhai, irrespective of their gender.

The following additional facts are known.

  1. Ustad Samiran never trained more than one of these students in the same year.
  2. Acharya Raghunath did not train any of these students during 2015-2018, as well as during 2021-24.
  3. Ananya and Devendra were never Gurubhai; neither were Bhaskar and Charu. All other pairs of musicians were Gurubhai for exactly 2 years.
  4. In 2013, Ananya and Bhaskar started their trainings under Pandit Meghnath and under Ustad Samiran, respectively.

In which of the following years were Ananya and Bhaskar Gurubhai?

Answer options
Option 1
Correct Answer
Explanation for 2025 Slot 2 DILR question 5

Q6:

2025 Slot 2

Arrangements

Hard

Ananya Raga, Bhaskar Tala, Charu Veena, and Devendra Sur are four musicians. Each of them started and completed their training as students under each of three Gurus - Pandit Meghnath, Ustad Samiran, and Acharya Raghunath between 2013 and 2024, including both the years. Each Guru trains any student for consecutive years only, for a span of 2, 3, or 4 years, with each Guru having a different span. During some of these years, a student may not have trained under these Gurus; however, they never trained under multiple Gurus in the same year.

In none of these years, any of these Gurus trained more than two of these students at the same time. When two students train under the same Guru at the same time, they are referred to as Gurubhai, irrespective of their gender.

The following additional facts are known.

  1. Ustad Samiran never trained more than one of these students in the same year.
  2. Acharya Raghunath did not train any of these students during 2015-2018, as well as during 2021-24.
  3. Ananya and Devendra were never Gurubhai; neither were Bhaskar and Charu. All other pairs of musicians were Gurubhai for exactly 2 years.
  4. In 2013, Ananya and Bhaskar started their trainings under Pandit Meghnath and under Ustad Samiran, respectively.

In which year did Charu begin her training under Pandit Meghnath?

Answer options
Option 1
Correct Answer
Explanation for 2025 Slot 2 DILR question 6

Q7:

2025 Slot 2

Arrangements

Hard

Ananya Raga, Bhaskar Tala, Charu Veena, and Devendra Sur are four musicians. Each of them started and completed their training as students under each of three Gurus - Pandit Meghnath, Ustad Samiran, and Acharya Raghunath between 2013 and 2024, including both the years. Each Guru trains any student for consecutive years only, for a span of 2, 3, or 4 years, with each Guru having a different span. During some of these years, a student may not have trained under these Gurus; however, they never trained under multiple Gurus in the same year.

In none of these years, any of these Gurus trained more than two of these students at the same time. When two students train under the same Guru at the same time, they are referred to as Gurubhai, irrespective of their gender.

The following additional facts are known.

  1. Ustad Samiran never trained more than one of these students in the same year.
  2. Acharya Raghunath did not train any of these students during 2015-2018, as well as during 2021-24.
  3. Ananya and Devendra were never Gurubhai; neither were Bhaskar and Charu. All other pairs of musicians were Gurubhai for exactly 2 years.
  4. In 2013, Ananya and Bhaskar started their trainings under Pandit Meghnath and under Ustad Samiran, respectively.

In which of the following years were Bhaskar and Devendra Gurubhai?

Answer options
Option 3
Correct Answer
Explanation for 2025 Slot 2 DILR question 7

Q8:

2025 Slot 2

Arrangements

Hard

Ananya Raga, Bhaskar Tala, Charu Veena, and Devendra Sur are four musicians. Each of them started and completed their training as students under each of three Gurus - Pandit Meghnath, Ustad Samiran, and Acharya Raghunath between 2013 and 2024, including both the years. Each Guru trains any student for consecutive years only, for a span of 2, 3, or 4 years, with each Guru having a different span. During some of these years, a student may not have trained under these Gurus; however, they never trained under multiple Gurus in the same year.

In none of these years, any of these Gurus trained more than two of these students at the same time. When two students train under the same Guru at the same time, they are referred to as Gurubhai, irrespective of their gender.

The following additional facts are known.

  1. Ustad Samiran never trained more than one of these students in the same year.
  2. Acharya Raghunath did not train any of these students during 2015-2018, as well as during 2021-24.
  3. Ananya and Devendra were never Gurubhai; neither were Bhaskar and Charu. All other pairs of musicians were Gurubhai for exactly 2 years.
  4. In 2013, Ananya and Bhaskar started their trainings under Pandit Meghnath and under Ustad Samiran, respectively.

Which of the following statements is TRUE?

Answer options
Option 4
Correct Answer
Explanation for 2025 Slot 2 DILR question 8

Q9:

2025 Slot 2

Arrangements

Hard

Ananya Raga, Bhaskar Tala, Charu Veena, and Devendra Sur are four musicians. Each of them started and completed their training as students under each of three Gurus - Pandit Meghnath, Ustad Samiran, and Acharya Raghunath between 2013 and 2024, including both the years. Each Guru trains any student for consecutive years only, for a span of 2, 3, or 4 years, with each Guru having a different span. During some of these years, a student may not have trained under these Gurus; however, they never trained under multiple Gurus in the same year.

In none of these years, any of these Gurus trained more than two of these students at the same time. When two students train under the same Guru at the same time, they are referred to as Gurubhai, irrespective of their gender.

The following additional facts are known.

  1. Ustad Samiran never trained more than one of these students in the same year.
  2. Acharya Raghunath did not train any of these students during 2015-2018, as well as during 2021-24.
  3. Ananya and Devendra were never Gurubhai; neither were Bhaskar and Charu. All other pairs of musicians were Gurubhai for exactly 2 years.
  4. In 2013, Ananya and Bhaskar started their trainings under Pandit Meghnath and under Ustad Samiran, respectively.

In how many of the years between 2013-24, were only two of these four musicians training under these three Gurus?

Q10:

2025 Slot 1

Arrangements

Medium

A round table has seven chairs around it. The chairs are numbered 1 through 7 in a clockwise direction. Four friends, Aslam, Bashir, Chhavi, and Davies, sit on four of the chairs. In the starting position, Aslam and Chhavi are sitting next to each other, while for Bashir as well as Davies, there are empty chairs on either side of the chairs that are sitting on.

The friends take turns moving either clockwise or counterclockwise from their chair. The friend who has to move in a turn occupies the first empty chair in whichever direction (s)he chooses to move. Aslam moves first (Turn 1), followed by Bashir, Chhavi, and Davies (Turns 2, 3, and 4, respectively). Then Aslam moves again followed by Bashir, and Chhavi (Turns 5, 6, and 7, respectively).

The following information is known.

  1. The four friends occupy adjacent chairs only at the end of Turn 2 and Turn 6.
  2. Davies occupies Chair 2 after Turn 1 and Chair 4 after Turn 5, and Chhavi occupies Chair 7 after Turn 2.

What is the number of the chair initially occupied by Bashir?

Q11:

2025 Slot 1

Arrangements

Medium

A round table has seven chairs around it. The chairs are numbered 1 through 7 in a clockwise direction. Four friends, Aslam, Bashir, Chhavi, and Davies, sit on four of the chairs. In the starting position, Aslam and Chhavi are sitting next to each other, while for Bashir as well as Davies, there are empty chairs on either side of the chairs that are sitting on.

The friends take turns moving either clockwise or counterclockwise from their chair. The friend who has to move in a turn occupies the first empty chair in whichever direction (s)he chooses to move. Aslam moves first (Turn 1), followed by Bashir, Chhavi, and Davies (Turns 2, 3, and 4, respectively). Then Aslam moves again followed by Bashir, and Chhavi (Turns 5, 6, and 7, respectively).

The following information is known.

  1. The four friends occupy adjacent chairs only at the end of Turn 2 and Turn 6.
  2. Davies occupies Chair 2 after Turn 1 and Chair 4 after Turn 5, and Chhavi occupies Chair 7 after Turn 2.

Who sits on the chair numbered 4 at the end of Turn 3?

Answer options
Option 4
Correct Answer
Explanation for 2025 Slot 1 DILR question 11

Q12:

2025 Slot 1

Arrangements

Medium

A round table has seven chairs around it. The chairs are numbered 1 through 7 in a clockwise direction. Four friends, Aslam, Bashir, Chhavi, and Davies, sit on four of the chairs. In the starting position, Aslam and Chhavi are sitting next to each other, while for Bashir as well as Davies, there are empty chairs on either side of the chairs that are sitting on.

The friends take turns moving either clockwise or counterclockwise from their chair. The friend who has to move in a turn occupies the first empty chair in whichever direction (s)he chooses to move. Aslam moves first (Turn 1), followed by Bashir, Chhavi, and Davies (Turns 2, 3, and 4, respectively). Then Aslam moves again followed by Bashir, and Chhavi (Turns 5, 6, and 7, respectively).

The following information is known.

  1. The four friends occupy adjacent chairs only at the end of Turn 2 and Turn 6.
  2. Davies occupies Chair 2 after Turn 1 and Chair 4 after Turn 5, and Chhavi occupies Chair 7 after Turn 2.

Which of the chairs are occupied at the end of Turn 6?

Answer options
Option 1
Correct Answer
Explanation for 2025 Slot 1 DILR question 12

Q13:

2025 Slot 1

Arrangements

Medium

A round table has seven chairs around it. The chairs are numbered 1 through 7 in a clockwise direction. Four friends, Aslam, Bashir, Chhavi, and Davies, sit on four of the chairs. In the starting position, Aslam and Chhavi are sitting next to each other, while for Bashir as well as Davies, there are empty chairs on either side of the chairs that are sitting on.

The friends take turns moving either clockwise or counterclockwise from their chair. The friend who has to move in a turn occupies the first empty chair in whichever direction (s)he chooses to move. Aslam moves first (Turn 1), followed by Bashir, Chhavi, and Davies (Turns 2, 3, and 4, respectively). Then Aslam moves again followed by Bashir, and Chhavi (Turns 5, 6, and 7, respectively).

The following information is known.

  1. The four friends occupy adjacent chairs only at the end of Turn 2 and Turn 6.
  2. Davies occupies Chair 2 after Turn 1 and Chair 4 after Turn 5, and Chhavi occupies Chair 7 after Turn 2.

Which of the following BEST describes the friends sitting on chairs adjacent to the one occupied by Bashir at the end of Turn 7?

Answer options
Option 4
Correct Answer
Explanation for 2025 Slot 1 DILR question 13

Q14:

CAT 2024 Slot 2

Arrangements

Hard

The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are placed in ten slots of the following grid based on the conditions below.

  1. Numbers in any row appear in an increasing order from left to right.
  2. Numbers in any column appear in a decreasing order from top to bottom.
  3. 1 is placed either in the same row or in the same column as 10.
  4. Neither 2 nor 3 is placed in the same row or in the same column as 10.
  5. Neither 7 nor 8 is placed in the same row or in the same column as 9.
  6. 4 and 6 are placed in the same row.

What is the row number which has the least sum of numbers placed in that row?

Q15:

CAT 2024 Slot 2

Arrangements

Hard

The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are placed in ten slots of the following grid based on the conditions below.

  1. Numbers in any row appear in an increasing order from left to right.
  2. Numbers in any column appear in a decreasing order from top to bottom.
  3. 1 is placed either in the same row or in the same column as 10.
  4. Neither 2 nor 3 is placed in the same row or in the same column as 10.
  5. Neither 7 nor 8 is placed in the same row or in the same column as 9.
  6. 4 and 6 are placed in the same row.

Which of the following statements MUST be true?

I. 10 is placed in a slot in Row 1.
II. 1 is placed in a slot in Row 4.

Answer options
Option 2
Correct Answer
Explanation for CAT 2024 Slot 2 DILR question 15

Q16:

CAT 2024 Slot 2

Arrangements

Hard

The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are placed in ten slots of the following grid based on the conditions below.

  1. Numbers in any row appear in an increasing order from left to right.
  2. Numbers in any column appear in a decreasing order from top to bottom.
  3. 1 is placed either in the same row or in the same column as 10.
  4. Neither 2 nor 3 is placed in the same row or in the same column as 10.
  5. Neither 7 nor 8 is placed in the same row or in the same column as 9.
  6. 4 and 6 are placed in the same row.

Which of the following statements MUST be true?

I. 22 is placed in a slot in Column 22.

II. 33 is placed in a slot in Column 33.

Answer options
Option 1
Correct Answer
Explanation for CAT 2024 Slot 2 DILR question 16

Q17:

CAT 2024 Slot 2

Arrangements

Hard

The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are placed in ten slots of the following grid based on the conditions below.

  1. Numbers in any row appear in an increasing order from left to right.
  2. Numbers in any column appear in a decreasing order from top to bottom.
  3. 1 is placed either in the same row or in the same column as 10.
  4. Neither 2 nor 3 is placed in the same row or in the same column as 10.
  5. Neither 7 nor 8 is placed in the same row or in the same column as 9.
  6. 4 and 6 are placed in the same row.

For how many slots in the grid, placement of numbers CANNOT be determined with certainty?

Q18:

CAT 2024 Slot 2

Arrangements

Hard

The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 are placed in ten slots of the following grid based on the conditions below.

  1. Numbers in any row appear in an increasing order from left to right.
  2. Numbers in any column appear in a decreasing order from top to bottom.
  3. 1 is placed either in the same row or in the same column as 10.
  4. Neither 2 nor 3 is placed in the same row or in the same column as 10.
  5. Neither 7 nor 8 is placed in the same row or in the same column as 9.
  6. 4 and 6 are placed in the same row.

What is the sum of the numbers placed in Column 4?

Q19:

CAT 2024 Slot 2

Arrangements

Medium

Eight gymnastics players numbered 1 through 8 underwent a training camp where they were coached by three coaches - Xena, Yuki, and Zara. Each coach trained at least two players. Yuki trained only even numbered players, while Zara trained only odd numbered players. After the camp, the coaches evaluated the players and gave integer ratings to the respective players trained by them on a scale of 1 to 7, with 1 being the lowest rating and 7 the highest.

The following additional information is known.

  1. Xena trained more players than Yuki.
  2. Player-1 and Player-4 were trained by the same coach, while the coaches who trained Player-2, Player-3 and Player-5 were all different.
  3. Player-5 and Player-7 were trained by the same coach and got the same rating. All other players got a unique rating.
  4. The average of the ratings of all the players was 4.
  5. Player-2 got the highest rating.
  6. The average of the ratings of the players trained by Yuki was twice that of the players trained by Xena and two more than that of the players trained by Zara.
  7. Player-4's rating was double of Player-8's and less than Player-5's.

What best can be concluded about the number of players coached by Zara?

Answer options
Option 1
Correct Answer
Explanation for CAT 2024 Slot 2 DILR question 19

Q20:

CAT 2024 Slot 2

Arrangements

Medium

Eight gymnastics players numbered 1 through 8 underwent a training camp where they were coached by three coaches - Xena, Yuki, and Zara. Each coach trained at least two players. Yuki trained only even numbered players, while Zara trained only odd numbered players. After the camp, the coaches evaluated the players and gave integer ratings to the respective players trained by them on a scale of 1 to 7, with 1 being the lowest rating and 7 the highest.

The following additional information is known.

  1. Xena trained more players than Yuki.
  2. Player-1 and Player-4 were trained by the same coach, while the coaches who trained Player-2, Player-3 and Player-5 were all different.
  3. Player-5 and Player-7 were trained by the same coach and got the same rating. All other players got a unique rating.
  4. The average of the ratings of all the players was 4.
  5. Player-2 got the highest rating.
  6. The average of the ratings of the players trained by Yuki was twice that of the players trained by Xena and two more than that of the players trained by Zara.
  7. Player-4's rating was double of Player-8's and less than Player-5's.

What was the rating of Player-7?

Q21:

CAT 2024 Slot 2

Arrangements

Medium

Eight gymnastics players numbered 1 through 8 underwent a training camp where they were coached by three coaches - Xena, Yuki, and Zara. Each coach trained at least two players. Yuki trained only even numbered players, while Zara trained only odd numbered players. After the camp, the coaches evaluated the players and gave integer ratings to the respective players trained by them on a scale of 1 to 7, with 1 being the lowest rating and 7 the highest.

The following additional information is known.

  1. Xena trained more players than Yuki.
  2. Player-1 and Player-4 were trained by the same coach, while the coaches who trained Player-2, Player-3 and Player-5 were all different.
  3. Player-5 and Player-7 were trained by the same coach and got the same rating. All other players got a unique rating.
  4. The average of the ratings of all the players was 4.
  5. Player-2 got the highest rating.
  6. The average of the ratings of the players trained by Yuki was twice that of the players trained by Xena and two more than that of the players trained by Zara.
  7. Player-4's rating was double of Player-8's and less than Player-5's.

What was the rating of Player-6?

Q22:

CAT 2024 Slot 2

Arrangements

Medium

Eight gymnastics players numbered 1 through 8 underwent a training camp where they were coached by three coaches - Xena, Yuki, and Zara. Each coach trained at least two players. Yuki trained only even numbered players, while Zara trained only odd numbered players. After the camp, the coaches evaluated the players and gave integer ratings to the respective players trained by them on a scale of 1 to 7, with 1 being the lowest rating and 7 the highest.

The following additional information is known.

  1. Xena trained more players than Yuki.
  2. Player-1 and Player-4 were trained by the same coach, while the coaches who trained Player-2, Player-3 and Player-5 were all different.
  3. Player-5 and Player-7 were trained by the same coach and got the same rating. All other players got a unique rating.
  4. The average of the ratings of all the players was 4.
  5. Player-2 got the highest rating.
  6. The average of the ratings of the players trained by Yuki was twice that of the players trained by Xena and two more than that of the players trained by Zara.
  7. Player-4's rating was double of Player-8's and less than Player-5's.

For how many players the ratings can be determined with certainty?

Q23:

CAT 2024 Slot 2

Arrangements

Medium

Eight gymnastics players numbered 1 through 8 underwent a training camp where they were coached by three coaches - Xena, Yuki, and Zara. Each coach trained at least two players. Yuki trained only even numbered players, while Zara trained only odd numbered players. After the camp, the coaches evaluated the players and gave integer ratings to the respective players trained by them on a scale of 1 to 7, with 1 being the lowest rating and 7 the highest.

The following additional information is known.

  1. Xena trained more players than Yuki.
  2. Player-1 and Player-4 were trained by the same coach, while the coaches who trained Player-2, Player-3 and Player-5 were all different.
  3. Player-5 and Player-7 were trained by the same coach and got the same rating. All other players got a unique rating.
  4. The average of the ratings of all the players was 4.
  5. Player-2 got the highest rating.
  6. The average of the ratings of the players trained by Yuki was twice that of the players trained by Xena and two more than that of the players trained by Zara.
  7. Player-4's rating was double of Player-8's and less than Player-5's.

Who all were the players trained by Xena?

Answer options
Option 3
Correct Answer
Explanation for CAT 2024 Slot 2 DILR question 23

Q24:

CAT 2023 Slot 3

Arrangements

Medium

An air conditioner (AC) company has four dealers, D1, D2, D3 and D4 in a city. It is evaluating sales performances of these dealers. The company sells two variants of AC's Window and Split. Both these variants can be either Inverter type or Non-inverter type. It is known that of the total number of ACs sold in the city, 25% were of Window variant, while the rest were of Split variant. Among the Inverter ACs sold, 20% were of Window variant.

The following information is also known:

  1. Every dealer sold at least two window ACs.
  2. D1 sold 13 inverter ACs, while D3 sold 5 Non-inverter ACs.
  3. A total of six Window Non-inverter ACs and 36 Split Inverter ACs were sold in the city.
  4. The number of Split ACs sold by D1 was twice the number of Window ACs sold by it.
  5. D3 and D4 sold an equal number of Window ACs and this number was one-third of the number of similar ACs sold by D2.
  6. D2 and D3 were the only ones who sold Window Non-inverter ACs. The number of these ACs sold by D2 was twice the number of these ACs sold by D3.
  7. D3 and D4 sold an equal number of Split Inverter ACs. This number was half the number of similar ACs sold by D2.

How many Split Inverter ACs did D2 sell?

Q25:

CAT 2023 Slot 3

Arrangements

Medium

An air conditioner (AC) company has four dealers, D1, D2, D3 and D4 in a city. It is evaluating sales performances of these dealers. The company sells two variants of AC's Window and Split. Both these variants can be either Inverter type or Non-inverter type. It is known that of the total number of ACs sold in the city, 25% were of Window variant, while the rest were of Split variant. Among the Inverter ACs sold, 20% were of Window variant.

The following information is also known:

  1. Every dealer sold at least two window ACs.
  2. D1 sold 13 inverter ACs, while D3 sold 5 Non-inverter ACs.
  3. A total of six Window Non-inverter ACs and 36 Split Inverter ACs were sold in the city.
  4. The number of Split ACs sold by D1 was twice the number of Window ACs sold by it.
  5. D3 and D4 sold an equal number of Window ACs and this number was one-third of the number of similar ACs sold by D2.
  6. D2 and D3 were the only ones who sold Window Non-inverter ACs. The number of these ACs sold by D2 was twice the number of these ACs sold by D3.
  7. D3 and D4 sold an equal number of Split Inverter ACs. This number was half the number of similar ACs sold by D2.

What percentage of ACs sold were of Non-Inverter type?

Q26:

CAT 2023 Slot 3

Arrangements

Medium

An air conditioner (AC) company has four dealers, D1, D2, D3 and D4 in a city. It is evaluating sales performances of these dealers. The company sells two variants of AC's Window and Split. Both these variants can be either Inverter type or Non-inverter type. It is known that of the total number of ACs sold in the city, 25% were of Window variant, while the rest were of Split variant. Among the Inverter ACs sold, 20% were of Window variant.

The following information is also known:

  1. Every dealer sold at least two window ACs.
  2. D1 sold 13 inverter ACs, while D3 sold 5 Non-inverter ACs.
  3. A total of six Window Non-inverter ACs and 36 Split Inverter ACs were sold in the city.
  4. The number of Split ACs sold by D1 was twice the number of Window ACs sold by it.
  5. D3 and D4 sold an equal number of Window ACs and this number was one-third of the number of similar ACs sold by D2.
  6. D2 and D3 were the only ones who sold Window Non-inverter ACs. The number of these ACs sold by D2 was twice the number of these ACs sold by D3.
  7. D3 and D4 sold an equal number of Split Inverter ACs. This number was half the number of similar ACs sold by D2.

What was the total number of ACs sold by D2 and D4?.

Q27:

CAT 2023 Slot 3

Arrangements

Medium

An air conditioner (AC) company has four dealers, D1, D2, D3 and D4 in a city. It is evaluating sales performances of these dealers. The company sells two variants of AC's Window and Split. Both these variants can be either Inverter type or Non-inverter type. It is known that of the total number of ACs sold in the city, 25% were of Window variant, while the rest were of Split variant. Among the Inverter ACs sold, 20% were of Window variant.

The following information is also known:

  1. Every dealer sold at least two window ACs.
  2. D1 sold 13 inverter ACs, while D3 sold 5 Non-inverter ACs.
  3. A total of six Window Non-inverter ACs and 36 Split Inverter ACs were sold in the city.
  4. The number of Split ACs sold by D1 was twice the number of Window ACs sold by it.
  5. D3 and D4 sold an equal number of Window ACs and this number was one-third of the number of similar ACs sold by D2.
  6. D2 and D3 were the only ones who sold Window Non-inverter ACs. The number of these ACs sold by D2 was twice the number of these ACs sold by D3.
  7. D3 and D4 sold an equal number of Split Inverter ACs. This number was half the number of similar ACs sold by D2.

Which of the following statements is necessarily false?

A) D1 and D3 together sold more ACs as compared to D2 and D4 together.

B) D4 sold more Split ACs as compared to D3.

C) D2 sold the highest number of ACs.

D) D1 and D3 sold an equal number of Split ACs.

Q28:

CAT 2023 Slot 3

Arrangements

Medium

An air conditioner (AC) company has four dealers, D1, D2, D3 and D4 in a city. It is evaluating sales performances of these dealers. The company sells two variants of AC's Window and Split. Both these variants can be either Inverter type or Non-inverter type. It is known that of the total number of ACs sold in the city, 25% were of Window variant, while the rest were of Split variant. Among the Inverter ACs sold, 20% were of Window variant.

The following information is also known:

  1. Every dealer sold at least two window ACs.
  2. D1 sold 13 inverter ACs, while D3 sold 5 Non-inverter ACs.
  3. A total of six Window Non-inverter ACs and 36 Split Inverter ACs were sold in the city.
  4. The number of Split ACs sold by D1 was twice the number of Window ACs sold by it.
  5. D3 and D4 sold an equal number of Window ACs and this number was one-third of the number of similar ACs sold by D2.
  6. D2 and D3 were the only ones who sold Window Non-inverter ACs. The number of these ACs sold by D2 was twice the number of these ACs sold by D3.
  7. D3 and D4 sold an equal number of Split Inverter ACs. This number was half the number of similar ACs sold by D2.

If D3 and D4 sold an equal number of ACs, then what was the number of Non-Inverter ACs sold by D2?

Answer options
Option 1
Correct Answer
Explanation for CAT 2023 Slot 3 DILR question 28

Q29:

CAT 2023 Slot 2

Arrangements

Easy

Odsville has five firms – Alfloo, Bzygoo, Czechy, Drjbna and Elavalaki. Each of these firms was founded in some year and also closed down a few years later.

Each firm raised Rs. 1 crore in its first and last year of existence. The amount each firm raised every year increased until it reached a maximum, and then decreased until the firm closed down. No firm raised the same amount of money in two consecutive years. Each annual increase and decrease was either by Rs. 1 crore or by Rs. 2 crores.

The table below provides partial information about the five firms.

FirmFirst year of existenceLast year of existenceTotal amount raised (Rs. crores)
Alfloo2009201621
Bzygoo20122015
Czechy20139
Drjbna2011201510
Elavalaki201013

For which firm(s) can the amounts raised by them be concluded with certainty in each year?

Answer options
Option 3
Correct Answer
Explanation for CAT 2023 Slot 2 DILR question 29

Q30:

CAT 2023 Slot 2

Arrangements

Easy

Odsville has five firms – Alfloo, Bzygoo, Czechy, Drjbna and Elavalaki. Each of these firms was founded in some year and also closed down a few years later.

Each firm raised Rs. 1 crore in its first and last year of existence. The amount each firm raised every year increased until it reached a maximum, and then decreased until the firm closed down. No firm raised the same amount of money in two consecutive years. Each annual increase and decrease was either by Rs. 1 crore or by Rs. 2 crores.

The table below provides partial information about the five firms.

FirmFirst year of existenceLast year of existenceTotal amount raised (Rs. crores)
Alfloo2009201621
Bzygoo20122015
Czechy20139
Drjbna2011201510
Elavalaki201013

What best can be concluded about the total amount of money raised in 2015?

Answer options
Option 4
Correct Answer
Explanation for CAT 2023 Slot 2 DILR question 30