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CAT 2023 Slot 2 DILR · Set 1 of 4Logical ReasoningEasy DifficultyQ1–Q5 · 4 MCQ + 1 TITA

CAT 2023 Slot 2 DILR Set 1: Arrangements (5 Questions) with Solutions

The Arrangements set from the official CAT 2023 Slot 2 DILR paper: the caselet, all 5 questions, the official answer key and a step-by-step solution for each. 100% free, no sign-up.

The Set: Read the Caselet First

CAT 2023 Slot 2 DILR · Questions 1–5
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

In the exam this set competed with 3 others for 40 minutes. Budget about 10 minutes if you attempt it.

Q1. Arrangements

MCQ · +3 / −1
For which firm(s) can the amounts raised by them be concluded with certainty in each year?
  1. A) Only Drjbna
  2. B) Only Czechy
  3. C) Only Czechy and Drjbna
  4. D) Only Bzygoo and Czechy and Drjbna
Correct Answer
C) Only Czechy and Drjbna
Step-by-step solution
📌 Core Concept
Each firm's yearly series starts and ends at 1, rises and then falls strictly, and moves by 1 or 2 each year. A firm's amounts are certain only if exactly one series fits its years and total.
🔢 Step-by-Step Solution
1
Drjbna (2011 to 2015, total 10) has the series 1, x, y, z, 1 with x + y + z = 8, where x and z are 2 or 3. If x = 2, then y = 3 forces z = 3, which repeats an amount, so y = 4 and z = 2. If x = 3, then y must be at least 4 and z at most 1, which is impossible. So Drjbna is 1, 2, 4, 2, 1 and is certain.
2
Czechy (starts 2013, total 9) fits 1, 2, 3, 2, 1, which sums to 9. The other short series total 5 (1, 3, 1) or 7 (1, 2, 3, 1 and 1, 3, 2, 1), and 1, 2, 4, 2, 1 totals 10. So Czechy is certain.
3
Bzygoo (2012 to 2015) has the series 1, a, b, 1. Both 1, 2, 3, 1 and 1, 3, 2, 1 obey every rule, so Bzygoo is not certain.
4
Alfloo (eight years, total 21) can be 1, 2, 3, 4, 5, 3, 2, 1 or 1, 2, 3, 5, 4, 3, 2, 1. Both sum to 21, so Alfloo is not certain.
5
Elavalaki (starts 2010, total 13) can be 1, 3, 5, 3, 1 or 1, 2, 4, 3, 2, 1. Both sum to 13, so Elavalaki is not certain.
Only Czechy and Drjbna are fully determined.
Why Not the Others
A leaves out Czechy, which is also certain.
B leaves out Drjbna, which is also certain.
D wrongly includes Bzygoo, which has two valid series.
Correct Answer: C

Q2. Arrangements

MCQ · +3 / −1
What best can be concluded about the total amount of money raised in 2015?
  1. A) It is either Rs. 8 crores or Rs. 9 crores.
  2. B) It is exactly Rs. 8 crores.
  3. C) It is either Rs. 7 crores or Rs. 8 crores or Rs. 9 crores.
  4. D) It is either Rs. 7 crores or Rs. 8 crores.
Correct Answer
D) It is either Rs. 7 crores or Rs. 8 crores.
Step-by-step solution
📌 Core Concept
Fix the 2015 amount of each firm. Czechy and Drjbna are fully determined, and Bzygoo and Alfloo are pinned down for 2015. Only Elavalaki's closing year is open.
🔢 Step-by-Step Solution
1
Drjbna is 1, 2, 4, 2, 1 from 2011, so it raises 1 in 2015. Bzygoo closes in 2015, so it raises 1. Czechy is 1, 2, 3, 2, 1 from 2013, so it raises 3 in 2015.
2
Alfloo's 2015 is its seventh amount, followed by 1 in 2016. It must be 2 or 3. If it were 3, the series would have to peak by the sixth year at 4 or 5. Then the first five years would sum to at least 1 + 2 + 3 + 4 + 5 = 15, and with 4 + 3 + 1 for the last three the total would be at least 23, which is more than 21. So Alfloo raises 2 in 2015.
3
Elavalaki (starts 2010, total 13) can be 1, 3, 5, 3, 1, which closes in 2014 and raises 0 in 2015. It can also be 1, 2, 4, 3, 2, 1 or 1, 2, 3, 4, 2, 1, which close in 2015 and raise 1.
4
The 2015 total is 2 + 1 + 3 + 1 = 7 plus Elavalaki's amount. That gives 7 (it has closed) or 8 (it raises 1).
Why Not the Others
A and B require Alfloo to raise 3 or Elavalaki's amount to be fixed, and neither is forced.
C includes 9, which would need Alfloo at 3 or Elavalaki above 1, and both are impossible.
Correct Answer: D

Q3. Arrangements

TITA · +3 / 0
What is the largest possible total amount of money (in Rs. crores) that could have been raised in 20132013?
Correct Answer
17
Step-by-step solution
📌 Core Concept
The 2013 total is the sum of each firm's maximum possible 2013 amount. Those maxima can be chosen independently, because the firms' series do not constrain each other.
🔢 Step-by-Step Solution
1
Czechy starts in 2013, so it raises 1. Drjbna is 1, 2, 4, 2, 1 from 2011, so it raises 4 in 2013.
2
Bzygoo (2012 to 2015) is 1, 2, 3, 1 or 1, 3, 2, 1, so its 2013 amount is at most 3.
3
Elavalaki (starts 2010, total 13) can be 1, 3, 5, 3, 1, 1, 2, 4, 3, 2, 1 or 1, 2, 3, 4, 2, 1. Its 2013 amount is 3, 3 or 4, so the maximum is 4.
4
Alfloo's 2013 is its fifth amount. Reaching 6 in the fifth year needs at least 1 + 2 + 3 + 4 + 6 = 16, and the last three years need at least 4 + 2 + 1 = 7. That totals 23, which is more than 21, so 6 is impossible. A fifth amount of 5 works with 1, 2, 3, 4, 5, 3, 2, 1, which sums to 21. So the maximum is 5.
5
Largest 2013 total = 5 + 3 + 1 + 4 + 4 = 17.
Quick Check
The maxima come from Alfloo 1, 2, 3, 4, 5, 3, 2, 1, Bzygoo 1, 3, 2, 1 and Elavalaki 1, 2, 3, 4, 2, 1. These are all valid, and 5 + 3 + 1 + 4 + 4 = 17.
Correct Answer: 17

Q4. Arrangements

MCQ · +3 / −1
If Elavalaki raised Rs. 3 crores in 2013, then what is the smallest possible total amount of money (in Rs. crores) that could have been raised by all the companies in 2012?
  1. A) 11
  2. B) 9
  3. C) 12
  4. D) 10
Correct Answer
A) 11
Step-by-step solution
📌 Core Concept
The condition on Elavalaki's 2013 amount narrows its possible series. After that, the 2012 total is found by taking each firm's smallest possible 2012 amount.
🔢 Step-by-Step Solution
1
Elavalaki's possible series are 1, 3, 5, 3, 1, 1, 2, 4, 3, 2, 1 and 1, 2, 3, 4, 2, 1, starting in 2010. Their 2013 amounts are 3, 3 and 4. Raising 3 in 2013 leaves the first two series, so its 2012 amount is 5 or 4. The minimum is 4.
2
Czechy starts in 2013, so it raises 0 in 2012. Bzygoo starts in 2012, so it raises 1. Drjbna is 1, 2, 4, 2, 1 from 2011, so it raises 2 in 2012.
3
Alfloo's 2012 is its fourth amount. On the way up it is at least 4, because 1, then at least 2, then at least 3, then at least 4. After the peak it must exceed three further decreasing amounts ending at 1, so it is at least 5. The minimum is 4, achieved by 1, 2, 3, 4, 5, 3, 2, 1, which sums to 21.
4
Smallest 2012 total = 4 + 1 + 0 + 2 + 4 = 11.
Why Not the Others
9 and 10 would need Alfloo or Elavalaki below the minimum amounts worked out above.
12 is attainable, but it is not the smallest.
Correct Answer: A

Q5. Arrangements

MCQ · +3 / −1
If the total amount of money raised in 2014 is Rs. 12 crores, then which of the following is not possible?
  1. A) Alfloo raised the same amount of money as Bzygoo in 2014.
  2. B) Bzygoo raised more money than Elavalaki in 2014
  3. C) Alfloo raised the same amount of money as Drjbna in 2013.
  4. D) Bzygoo raised the same amount of money as Elavalaki in 2013
Correct Answer
D) Bzygoo raised the same amount of money as Elavalaki in 2013
Step-by-step solution
📌 Core Concept
A 2014 total of 12 fixes Bzygoo's and Elavalaki's series. Each option can then be tested against the series that remain.
🔢 Step-by-Step Solution
1
In 2014, Czechy raises 2 (1, 2, 3, 2, 1 from 2013) and Drjbna raises 2 (1, 2, 4, 2, 1 from 2011). That leaves 8 for Alfloo, Bzygoo and Elavalaki.
2
Alfloo's 2014 is its sixth amount, followed by 2 in 2015 and 1 in 2016. It is 3 or 4. If it were 4, the first five years would sum to 21 - 4 - 2 - 1 = 14, but a fifth amount above 4 forces at least 15, so it is impossible. Alfloo's 2014 amount is therefore 3, and its 2013 amount is 5 (1, 2, 3, 4, 5, 3, 2, 1) or 4 (1, 2, 3, 5, 4, 3, 2, 1).
3
Bzygoo plus Elavalaki must be 5 in 2014. Bzygoo is 3 or 2 and Elavalaki is 1 or 2, so Bzygoo is 3 and Elavalaki is 2. That means Bzygoo is 1, 2, 3, 1, with 2 in 2013. Elavalaki is 1, 2, 4, 3, 2, 1 or 1, 2, 3, 4, 2, 1, with 3 or 4 in 2013.
4
Test the options. A: Alfloo 3 equals Bzygoo 3, so it is possible. B: Bzygoo 3 is greater than Elavalaki 2, so it is possible. C: Alfloo's 2013 amount can be 4, which equals Drjbna's 4, so it is possible. D: Bzygoo raised 2 in 2013, but Elavalaki raised 3 or 4, so they cannot be equal.
Correct Answer: D
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CAT 2023 Slot 2 DILR at a Glance

Sets in this section4
Questions in this section20
Section time40 minutes
Convenor IIMIIM Lucknow

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