CAT 2025 DILR Slot 1 Question Paper With Detailed PDF Solutions

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CAT 2025 DILR Slot 1 Paper With Answers & Explanation

Directions for questions 1 to 5: At InnovateX, six employees, Asha, Bunty, Chintu, Dolly, Eklavya, and Falguni, were split into two groups of three each: Elite led by Manager Kuku, and Novice led by Manager Lalu.

At the end of each quarter, Kuku and Lalu handed out ratings to all members in their respective groups. In each group, each employee received a distinct integer rating from 1 to 3.
The score for an employee at the end of a quarter is defined as their cumulative rating from the beginning of the year. At the end of each quarter the employee in Novice with the highest score was promoted to Elite, and the employee in Elite with the minimum score was demoted to Novice. If there was a tie in scores, the employee with a higher rating in the latest quarter was ranked higher.
1. Asha, Bunty, and Chintu were in Elite at the beginning of Quarter 1. All of them were in Novice at the beginning of Quarter 4.
2. Dolly and Falguni were the only employees who got the same rating across all the quarters.
3. The following is known about ratings given by Lalu:
• Bunty received a rating of 1 in Quarter 2.
• Asha and Dolly received ratings of 1 and 2, respectively, in Quarter 3.

Q. 1 What was Eklavya’s score at the end of Quarter 2?

Correct Answer

4

Explanation

Step 1:
From Condition (1), Asha, Bunty, and Chintu were in the Elite at the beginning of Quarter 1. Therefore, Dolly, Eklavya, and Falguni were in the Novice at the beginning of Quarter 1. All three—Asha, Bunty, and Chintu—were in the Novice at the beginning of Quarter 4. Hence, all three—Dolly, Eklavya, and Falguni—were in the Elite at the beginning of Quarter 4.
From Condition (3), based on the ratings given by Lalu, Bunty was demoted to the Novice in Quarter 2. Therefore, his rating in Quarter 1 was 1. Also, Asha and Dolly received ratings of 1 and 2, respectively, in Quarter 3.
From Condition (2), the ratings of Dolly and Falguni were 2 and 3, respectively, in all three quarters. Hence, Falguni was promoted to the Elite in Quarter 2.
Since Asha was demoted to the Novice in Quarter 3, her cumulative score in Quarter 2 was less than or equal to Chintu’s. Therefore, Asha’s and Chintu’s ratings in Quarter 1 were 2 and 3, in any order. Also, their ratings in Quarter 2 were 1 and 2, respectively.
Hence, the information can be shown in the table below.

Step 2: The cumulative scores of Dolly and Eklavya in Quarter 2 were 4 each, but Eklavya’s rating in Quarter 2 was higher than Dolly’s. Therefore, Eklavya was promoted to the Elite in Quarter 3.
Since Chintu was demoted to the Novice in Quarter 4, his cumulative score in Quarter 3 was less than or equal to that of Eklavya. Therefore, the ratings of Chintu and Eklavya in Quarter 3 were 1 and 2, respectively.
Hence, the final information is shown in the table below.


Eklavya’s score at the end of Quarter 2 was 4.

Q. 2 How many employees changed groups more than once up to the beginning of Quarter 4?

Correct Answer

0

Explanation

Step 1:
From Condition (1), Asha, Bunty, and Chintu were in the Elite at the beginning of Quarter 1. Therefore, Dolly, Eklavya, and Falguni were in the Novice at the beginning of Quarter 1. All three—Asha, Bunty, and Chintu—were in the Novice at the beginning of Quarter 4. Hence, all three—Dolly, Eklavya, and Falguni—were in the Elite at the beginning of Quarter 4.
From Condition (3), based on the ratings given by Lalu, Bunty was demoted to the Novice in Quarter 2. Therefore, his rating in Quarter 1 was 1. Also, Asha and Dolly received ratings of 1 and 2, respectively, in Quarter 3.
From Condition (2), the ratings of Dolly and Falguni were 2 and 3, respectively, in all three quarters. Hence, Falguni was promoted to the Elite in Quarter 2.
Since Asha was demoted to the Novice in Quarter 3, her cumulative score in Quarter 2 was less than or equal to Chintu’s. Therefore, Asha’s and Chintu’s ratings in Quarter 1 were 2 and 3, in any order. Also, their ratings in Quarter 2 were 1 and 2, respectively.
Hence, the information can be shown in the table below.

Step 2: The cumulative scores of Dolly and Eklavya in Quarter 2 were 4 each, but Eklavya’s rating in Quarter 2 was higher than Dolly’s. Therefore, Eklavya was promoted to the Elite in Quarter 3.
Since Chintu was demoted to the Novice in Quarter 4, his cumulative score in Quarter 3 was less than or equal to that of Eklavya. Therefore, the ratings of Chintu and Eklavya in Quarter 3 were 1 and 2, respectively.
Hence, the final information is shown in the table below.


No employee changed groups more than once up to the beginning of Quarter 4.

Q. 3 What was Bunty’s score at the end of Quarter 3?

Correct Answer

5

Explanation

Step 1:
From Condition (1), Asha, Bunty, and Chintu were in the Elite at the beginning of Quarter 1. Therefore, Dolly, Eklavya, and Falguni were in the Novice at the beginning of Quarter 1. All three—Asha, Bunty, and Chintu—were in the Novice at the beginning of Quarter 4. Hence, all three—Dolly, Eklavya, and Falguni—were in the Elite at the beginning of Quarter 4.
From Condition (3), based on the ratings given by Lalu, Bunty was demoted to the Novice in Quarter 2. Therefore, his rating in Quarter 1 was 1. Also, Asha and Dolly received ratings of 1 and 2, respectively, in Quarter 3.
From Condition (2), the ratings of Dolly and Falguni were 2 and 3, respectively, in all three quarters. Hence, Falguni was promoted to the Elite in Quarter 2.
Since Asha was demoted to the Novice in Quarter 3, her cumulative score in Quarter 2 was less than or equal to Chintu’s. Therefore, Asha’s and Chintu’s ratings in Quarter 1 were 2 and 3, in any order. Also, their ratings in Quarter 2 were 1 and 2, respectively.
Hence, the information can be shown in the table below.

Step 2: The cumulative scores of Dolly and Eklavya in Quarter 2 were 4 each, but Eklavya’s rating in Quarter 2 was higher than Dolly’s. Therefore, Eklavya was promoted to the Elite in Quarter 3.
Since Chintu was demoted to the Novice in Quarter 4, his cumulative score in Quarter 3 was less than or equal to that of Eklavya. Therefore, the ratings of Chintu and Eklavya in Quarter 3 were 1 and 2, respectively.
Hence, the final information is shown in the table below.


Bunty’s score at the end of Quarter 3 was 5.

Q. 4 For how many employees can the scores at the end of Quarter 3 be determined with certainty?

Correct Answer

4

Explanation

Step 1:
From Condition (1), Asha, Bunty, and Chintu were in the Elite at the beginning of Quarter 1. Therefore, Dolly, Eklavya, and Falguni were in the Novice at the beginning of Quarter 1. All three—Asha, Bunty, and Chintu—were in the Novice at the beginning of Quarter 4. Hence, all three—Dolly, Eklavya, and Falguni—were in the Elite at the beginning of Quarter 4.
From Condition (3), based on the ratings given by Lalu, Bunty was demoted to the Novice in Quarter 2. Therefore, his rating in Quarter 1 was 1. Also, Asha and Dolly received ratings of 1 and 2, respectively, in Quarter 3.
From Condition (2), the ratings of Dolly and Falguni were 2 and 3, respectively, in all three quarters. Hence, Falguni was promoted to the Elite in Quarter 2.
Since Asha was demoted to the Novice in Quarter 3, her cumulative score in Quarter 2 was less than or equal to Chintu’s. Therefore, Asha’s and Chintu’s ratings in Quarter 1 were 2 and 3, in any order. Also, their ratings in Quarter 2 were 1 and 2, respectively.
Hence, the information can be shown in the table below.

Step 2: The cumulative scores of Dolly and Eklavya in Quarter 2 were 4 each, but Eklavya’s rating in Quarter 2 was higher than Dolly’s. Therefore, Eklavya was promoted to the Elite in Quarter 3.
Since Chintu was demoted to the Novice in Quarter 4, his cumulative score in Quarter 3 was less than or equal to that of Eklavya. Therefore, the ratings of Chintu and Eklavya in Quarter 3 were 1 and 2, respectively.
Hence, the final information is shown in the table below.


The scores of four employees—Bunty, Dolly, Eklavya, and Falguni—at the end of Quarter 3 can be determined with certainty.

Q. 5 Which of the following statements is/are NECESSARILY true?
I. Asha received a rating of 2 in Quarter 1.
II. Asha received a rating of 1 in Quarter 2.

Correct Answer

4

Explanation

Step 1:
From Condition (1), Asha, Bunty, and Chintu were in the Elite at the beginning of Quarter 1. Therefore, Dolly, Eklavya, and Falguni were in the Novice at the beginning of Quarter 1. All three—Asha, Bunty, and Chintu—were in the Novice at the beginning of Quarter 4. Hence, all three—Dolly, Eklavya, and Falguni—were in the Elite at the beginning of Quarter 4.
From Condition (3), based on the ratings given by Lalu, Bunty was demoted to the Novice in Quarter 2. Therefore, his rating in Quarter 1 was 1. Also, Asha and Dolly received ratings of 1 and 2, respectively, in Quarter 3.
From Condition (2), the ratings of Dolly and Falguni were 2 and 3, respectively, in all three quarters. Hence, Falguni was promoted to the Elite in Quarter 2.
Since Asha was demoted to the Novice in Quarter 3, her cumulative score in Quarter 2 was less than or equal to Chintu’s. Therefore, Asha’s and Chintu’s ratings in Quarter 1 were 2 and 3, in any order. Also, their ratings in Quarter 2 were 1 and 2, respectively.
Hence, the information can be shown in the table below.

Step 2: The cumulative scores of Dolly and Eklavya in Quarter 2 were 4 each, but Eklavya’s rating in Quarter 2 was higher than Dolly’s. Therefore, Eklavya was promoted to the Elite in Quarter 3.
Since Chintu was demoted to the Novice in Quarter 4, his cumulative score in Quarter 3 was less than or equal to that of Eklavya. Therefore, the ratings of Chintu and Eklavya in Quarter 3 were 1 and 2, respectively.
Hence, the final information is shown in the table below.


Only Statement II is necessarily true.

Directons for questions 6 to 9: 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.

Q. 6 How many taps did Clive receive for his question?

Correct Answer

7

Explanation

Step 1:
One tap means “Yes”, two taps mean “No”, and three taps mean “Maybe”.
Each question received at least one “Yes”, one “No”, and one “Maybe’’. So each person received more than 6 taps.
From conditions (1) and (4), Alia tapped 2 Yes and 2 No.
From condition (6), Badal and Clive tapped = 40 – (6 + 11 + 9) = 14 times and Clive tapped more times in total than Badal.
Also, from condition (4), Badal tapped 6 times and Clive tapped 8 times.
From condition (3), Let the number of taps received by Badal or Dilshan or Ehsaan be x.
Then, the number of taps received by Clive = 40 – 9 – 3x = 31 – 3x.
But 31 – 3x > 6 or x < 8.33 i.e., x = 7 or 8
For x = 7, the number of taps received by Clive will be 31 – 21 = 10, which is not possible. Since Badal tapped Yes or No for Clive.
For x = 8, then the number of tabs received by Clive will be 31 – 24 = 7, which is possible.
The information can be shown in the table below.

Step 2:
From condition (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.
The final information can be shown in the table below.


Clive received 7 taps for his question.

Q. 7 Which two people tapped an equal number of times in total?

Correct Answer

1

Explanation

Step 1:
One tap means “Yes”, two taps mean “No”, and three taps mean “Maybe”.
Each question received at least one “Yes”, one “No”, and one “Maybe’’. So each person received more than 6 taps.
From conditions (1) and (4), Alia tapped 2 Yes and 2 No.
From condition (6), Badal and Clive tapped = 40 – (6 + 11 + 9) = 14 times and Clive tapped more times in total than Badal.
Also, from condition (4), Badal tapped 6 times and Clive tapped 8 times.
From condition (3), Let the number of taps received by Badal or Dilshan or Ehsaan be x.
Then, the number of taps received by Clive = 40 – 9 – 3x = 31 – 3x.
But 31 – 3x > 6 or x < 8.33 i.e., x = 7 or 8
For x = 7, the number of taps received by Clive will be 31 – 21 = 10, which is not possible. Since Badal tapped Yes or No for Clive.
For x = 8, then the number of tabs received by Clive will be 31 – 24 = 7, which is possible.
The information can be shown in the table below.

Step 2:
From condition (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.
The final information can be shown in the table below.


Alia and Badal tapped an equal number of times in total.

Q. 8 What was Clive’s response to Ehsaan’s question?

Correct Answer

1

Explanation

Step 1:
One tap means “Yes”, two taps mean “No”, and three taps mean “Maybe”.
Each question received at least one “Yes”, one “No”, and one “Maybe’’. So each person received more than 6 taps.
From conditions (1) and (4), Alia tapped 2 Yes and 2 No.
From condition (6), Badal and Clive tapped = 40 – (6 + 11 + 9) = 14 times and Clive tapped more times in total than Badal.
Also, from condition (4), Badal tapped 6 times and Clive tapped 8 times.
From condition (3), Let the number of taps received by Badal or Dilshan or Ehsaan be x.
Then, the number of taps received by Clive = 40 – 9 – 3x = 31 – 3x.
But 31 – 3x > 6 or x < 8.33 i.e., x = 7 or 8
For x = 7, the number of taps received by Clive will be 31 – 21 = 10, which is not possible. Since Badal tapped Yes or No for Clive.
For x = 8, then the number of tabs received by Clive will be 31 – 24 = 7, which is possible.
The information can be shown in the table below.

Step 2:
From condition (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.
The final information can be shown in the table below.


Clive’s response to Ehsaan’s question was ‘No’.

Q. 9 How many “Yes” responses were received across all the questions?

Correct Answer

6

Explanation

Step 1:
One tap means “Yes”, two taps mean “No”, and three taps mean “Maybe”.
Each question received at least one “Yes”, one “No”, and one “Maybe’’. So each person received more than 6 taps.
From conditions (1) and (4), Alia tapped 2 Yes and 2 No.
From condition (6), Badal and Clive tapped = 40 – (6 + 11 + 9) = 14 times and Clive tapped more times in total than Badal.
Also, from condition (4), Badal tapped 6 times and Clive tapped 8 times.
From condition (3), Let the number of taps received by Badal or Dilshan or Ehsaan be x.
Then, the number of taps received by Clive = 40 – 9 – 3x = 31 – 3x.
But 31 – 3x > 6 or x < 8.33 i.e., x = 7 or 8
For x = 7, the number of taps received by Clive will be 31 – 21 = 10, which is not possible. Since Badal tapped Yes or No for Clive.
For x = 8, then the number of tabs received by Clive will be 31 – 24 = 7, which is possible.
The information can be shown in the table below.

Step 2:
From condition (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.
The final information can be shown in the table below.


Six ‘’Yes” responses were received across all the questions.

Directions for questions 10 to 13: 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.

Q. 10 What is the number of the chair initially occupied by Bashir?

Correct Answer

4

Explanation

Step 1:
In the initial position, Aslam and Chhavi are sitting next to each other, while both Bashir and Davies have empty chairs on either side of them. Since the arrangement is circular, the initial order of Aslam and Chhavi does not matter.

From condition (1), the four friends occupy adjacent chairs only at the end of Turns 2 and 6. If Aslam moves counterclockwise, then they will not occupy adjacent chairs at the end of Turn 2. Therefore, Aslam must move clockwise, and in Turn 1, Bashir moves counterclockwise.
From condition (2), Davies occupies Chair 2 after Turn 1, and Chhavi occupies Chair 7 after Turn 2.

Step 2:
In Turn 3, Chhavi moves in counterclockwise and occupies chair No. 6.

From condition (2), Davies occupies Chair 4 after Turn 5.
So in Turn 4, Davies moves clockwise and occupies Chair 4.


The number of the chair initially occupied by Bashir is 4.

Q. 11 Who sits on the chair numbered 4 at the end of Turn 3?

Correct Answer

4

Explanation

Step 1:
In the initial position, Aslam and Chhavi are sitting next to each other, while both Bashir and Davies have empty chairs on either side of them. Since the arrangement is circular, the initial order of Aslam and Chhavi does not matter.

From condition (1), the four friends occupy adjacent chairs only at the end of Turns 2 and 6. If Aslam moves counterclockwise, then they will not occupy adjacent chairs at the end of Turn 2. Therefore, Aslam must move clockwise, and in Turn 1, Bashir moves counterclockwise.
From condition (2), Davies occupies Chair 2 after Turn 1, and Chhavi occupies Chair 7 after Turn 2.

Step 2:
In Turn 3, Chhavi moves in counterclockwise and occupies chair No. 6.

From condition (2), Davies occupies Chair 4 after Turn 5.
So in Turn 4, Davies moves clockwise and occupies Chair 4.


No one sits on the chair numbered 4 at the end of Turn 3.

Q. 12 Which of the chairs are occupied at the end of Turn 6?

Correct Answer

1

Explanation

Step 1:
In the initial position, Aslam and Chhavi are sitting next to each other, while both Bashir and Davies have empty chairs on either side of them. Since the arrangement is circular, the initial order of Aslam and Chhavi does not matter.

From condition (1), the four friends occupy adjacent chairs only at the end of Turns 2 and 6. If Aslam moves counterclockwise, then they will not occupy adjacent chairs at the end of Turn 2. Therefore, Aslam must move clockwise, and in Turn 1, Bashir moves counterclockwise.
From condition (2), Davies occupies Chair 2 after Turn 1, and Chhavi occupies Chair 7 after Turn 2.

Step 2:
In Turn 3, Chhavi moves in counterclockwise and occupies chair No. 6.

From condition (2), Davies occupies Chair 4 after Turn 5.
So in Turn 4, Davies moves clockwise and occupies Chair 4.


Chairs numbered 4, 5, 6, and 7 are occupied at the end of Turn 6.

Q. 13 Which of the following BEST describes the friends sitting on chairs adjacent to the one occupied by Bashir at the end of Turn 7?

Correct Answer

3

Explanation

Step 1:
In the initial position, Aslam and Chhavi are sitting next to each other, while both Bashir and Davies have empty chairs on either side of them. Since the arrangement is circular, the initial order of Aslam and Chhavi does not matter.

From condition (1), the four friends occupy adjacent chairs only at the end of Turns 2 and 6. If Aslam moves counterclockwise, then they will not occupy adjacent chairs at the end of Turn 2. Therefore, Aslam must move clockwise, and in Turn 1, Bashir moves counterclockwise.
From condition (2), Davies occupies Chair 2 after Turn 1, and Chhavi occupies Chair 7 after Turn 2.

Step 2:
In Turn 3, Chhavi moves in counterclockwise and occupies chair No. 6.

From condition (2), Davies occupies Chair 4 after Turn 5.
So in Turn 4, Davies moves clockwise and occupies Chair 4.


At the end of Turn 7, only Davies is sitting on a chair adjacent to the one occupied by Bashir.

Directions for questions 14 to 17: Five countries engage in trade with each other. Each country levies import tariffs on the other countries. The import tariff levied by Country X on Country Y is calculated by multiplying the corresponding tariff percentage with the total imports of Country X from Country Y.

The radar chart below depicts different import tariff percentages charged by each of the five countries on the others.
For example, US (the blue line in the chart) charges 20%, 40%, 30%, and 30% import tariff percentages on imports from France, India, Japan, and UK, respectively. The bar chart depicts the import tariffs levied by each county on other countries. For example, US charged import tariff of 3 billion USD on UK.

Assume that imports from one country to another equals the exports from the latter to the former.
The trade surplus of Country X with Country Y is defined as follows.
Trade surplus = Exports from Country X to Country Y – Imports to Country X from Country Y.
A negative trade surplus is called trade deficit.

Q. 14 How much is Japan’s export to India worth?

Correct Answer

1

Explanation

From the radar graph, the table below shows the import tariffs (in %) imposed by each country on other countries.

From the bar graph, the table below shows the import tariffs (in Billion USD) imposed by each country on other countries.


India charged an import tariff of 3.5 billion USD on imports from Japan, which is 50% of the total imports.
Hence, Japan’s exports to India are worth 7.0 billion USD.

Q. 15 Which among the following is the highest?

Correct Answer

4

Explanation

From the radar graph, the table below shows the import tariffs (in %) imposed by each country on other countries.

From the bar graph, the table below shows the import tariffs (in Billion USD) imposed by each country on other countries.


Option (1): Exports by Japan to UK = 6 × 1/0.4
= 15 Billion USD
Option (2): Exports by France to Japan = 3 × 1/ 0.3 = 10 Billion USD
Option (3): Imports by France from India = 6.5 × 1/ 0.4 = 16.25 Billion USD
Option (4): Imports by US from France = 6 × 1/0.2 = 30 Billion USD
Hence, option (4) is the correct answer.

Q. 16 What is the trade surplus/trade deficit of India with UK?

Correct Answer

1

Explanation

From the radar graph, the table below shows the import tariffs (in %) imposed by each country on other countries.

From the bar graph, the table below shows the import tariffs (in Billion USD) imposed by each country on other countries.


Import by India from UK = 5 × 1/0.2 = 25 Billion USD
Export from India to UK = 3 × 1/0.3 = 10 Billion USD
Hence, trade deficit of India with UK = 25 – 10 = 15 Billion USD

Q. 17 Among France and UK, who has/have trade surplus(es) with US?

Correct Answer

4

Explanation

From the radar graph, the table below shows the import tariffs (in %) imposed by each country on other countries.

From the bar graph, the table below shows the import tariffs (in Billion USD) imposed by each country on other countries.


Import by France from US = 5.5 × 1/0.3 = 18.33 Billion USD
Export by France to US = 6 × 1/0.2 = 30 Billion USD
So trade surplus of France with US = 30 – 18.33 = 11.66 Billion USD
Import by UK from US = 2.5 × 1/0.2 = 12.5 Billion USD
Export from UK to US = 3 × 1/0.3 = 10 Billion USD So trade deficit of UK with US = 12.5 – 10 = 2.5 Billion USD
Hence, only France has trade surplus with US.

Directions for questions 18 to 22: 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.

Q. 18 What was the occupancy factor for segment D – E?

Correct Answer

3

Explanation

Step 1:
From condition (2), Exactly 40 tickets were booked from B to C and 30 tickets were booked from B to E.
From condition (5), No tickets were booked from A to B, from B to D and from D to E.
From condition (4), The number of tickets booked from A to C = The number of tickets booked from A to E > 30 From condition (3), Among the seats reserved on segment D – E, exactly four-sevenths were from stations before C i.e., from A and B.
The factors of both 7 and 10 are 70 and 140.
70 is not possible, since A to E + B to E > 60 So A to E + B to E = 140 × 4/7 = 80 and C to E = 140 – 80 = 60
Step 2:
From conditions (1) and (6), Segment C – D had an occupancy = 0.95 × 200 = 190 and segment B – C had an occupancy = 200.
AC + AD + AE + BC + BD + BE = 200
⇒ 50 + AD + 50 + 40 + 0 + 30 = 200
⇒ AD = 30
AD + AE + BD + BE + CD + CE = 190
⇒ 30 + 50 + 0 + 30 + CD + 60 = 190
⇒ CD = 20
Hence, the final information can be shown in the table below.


The occupancy for segment D – E was = A to E + B to E + C to E + D to E
= 50 + 30 + 60 + 0 = 140
Hence, the occupancy factor for segment D – E was = 140/200 × 100 = 70%.

Q. 19 How many tickets were booked from Station A to Station E?

Correct Answer

50

Explanation

Step 1:
From condition (2), Exactly 40 tickets were booked from B to C and 30 tickets were booked from B to E.
From condition (5), No tickets were booked from A to B, from B to D and from D to E.
From condition (4), The number of tickets booked from A to C = The number of tickets booked from A to E > 30 From condition (3), Among the seats reserved on segment D – E, exactly four-sevenths were from stations before C i.e., from A and B.
The factors of both 7 and 10 are 70 and 140.
70 is not possible, since A to E + B to E > 60 So A to E + B to E = 140 × 4/7 = 80 and C to E = 140 – 80 = 60
Step 2:
From conditions (1) and (6), Segment C – D had an occupancy = 0.95 × 200 = 190 and segment B – C had an occupancy = 200.
AC + AD + AE + BC + BD + BE = 200
⇒ 50 + AD + 50 + 40 + 0 + 30 = 200
⇒ AD = 30
AD + AE + BD + BE + CD + CE = 190
⇒ 30 + 50 + 0 + 30 + CD + 60 = 190
⇒ CD = 20
Hence, the final information can be shown in the table below.


The number of tickets booked from Station A to Station E was 50.

Q. 20 How many tickets were booked from Station C?

Correct Answer

80

Explanation

Step 1:
From condition (2), Exactly 40 tickets were booked from B to C and 30 tickets were booked from B to E.
From condition (5), No tickets were booked from A to B, from B to D and from D to E.
From condition (4), The number of tickets booked from A to C = The number of tickets booked from A to E > 30 From condition (3), Among the seats reserved on segment D – E, exactly four-sevenths were from stations before C i.e., from A and B.
The factors of both 7 and 10 are 70 and 140.
70 is not possible, since A to E + B to E > 60 So A to E + B to E = 140 × 4/7 = 80 and C to E = 140 – 80 = 60
Step 2:
From conditions (1) and (6), Segment C – D had an occupancy = 0.95 × 200 = 190 and segment B – C had an occupancy = 200.
AC + AD + AE + BC + BD + BE = 200
⇒ 50 + AD + 50 + 40 + 0 + 30 = 200
⇒ AD = 30
AD + AE + BD + BE + CD + CE = 190
⇒ 30 + 50 + 0 + 30 + CD + 60 = 190
⇒ CD = 20
Hence, the final information can be shown in the table below.


The number of tickets booked from Station C was = 20 + 60 = 80.

Q. 21 What is the difference between the number of tickets booked to Station C and the number of tickets booked to Station D?

Correct Answer

40

Explanation

Step 1:
From condition (2), Exactly 40 tickets were booked from B to C and 30 tickets were booked from B to E.
From condition (5), No tickets were booked from A to B, from B to D and from D to E.
From condition (4), The number of tickets booked from A to C = The number of tickets booked from A to E > 30 From condition (3), Among the seats reserved on segment D – E, exactly four-sevenths were from stations before C i.e., from A and B.
The factors of both 7 and 10 are 70 and 140.
70 is not possible, since A to E + B to E > 60 So A to E + B to E = 140 × 4/7 = 80 and C to E = 140 – 80 = 60
Step 2:
From conditions (1) and (6), Segment C – D had an occupancy = 0.95 × 200 = 190 and segment B – C had an occupancy = 200.
AC + AD + AE + BC + BD + BE = 200
⇒ 50 + AD + 50 + 40 + 0 + 30 = 200
⇒ AD = 30
AD + AE + BD + BE + CD + CE = 190
⇒ 30 + 50 + 0 + 30 + CD + 60 = 190
⇒ CD = 20
Hence, the final information can be shown in the table below.


Required difference = (50 + 40) – (30 + 20) = 40.

Q. 22 How many tickets were booked to travel in exactly one segment?

Correct Answer

60

Explanation

Step 1:
From condition (2), Exactly 40 tickets were booked from B to C and 30 tickets were booked from B to E.
From condition (5), No tickets were booked from A to B, from B to D and from D to E.
From condition (4), The number of tickets booked from A to C = The number of tickets booked from A to E > 30 From condition (3), Among the seats reserved on segment D – E, exactly four-sevenths were from stations before C i.e., from A and B.
The factors of both 7 and 10 are 70 and 140.
70 is not possible, since A to E + B to E > 60 So A to E + B to E = 140 × 4/7 = 80 and C to E = 140 – 80 = 60
Step 2:
From conditions (1) and (6), Segment C – D had an occupancy = 0.95 × 200 = 190 and segment B – C had an occupancy = 200.
AC + AD + AE + BC + BD + BE = 200
⇒ 50 + AD + 50 + 40 + 0 + 30 = 200
⇒ AD = 30
AD + AE + BD + BE + CD + CE = 190
⇒ 30 + 50 + 0 + 30 + CD + 60 = 190
⇒ CD = 20
Hence, the final information can be shown in the table below.


The number of tickets booked to travel in exactly one segment = B to C + C to D = 40 + 20 = 60.