CAT 2023 Slot 2 DILR Set 3 Q11–Q15

A DILR caselet from the Data Interpretation & Logical Reasoning (DILR) section of CAT 2023 Slot 2, with 5 questions (Quant-based Puzzles). Answers are CAT's official key.

The set

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.
Firm First year of existence Last year of
existence		 Total amount raised (Rs. crores)
Alfloo 2009 2016 21
Bzygoo 2012 2015
Czechy 2013 9
Drjbna 2011 2015 10
Elavalaki 2010 13

Question 11

For which firm(s) can the amounts raised by them be concluded with certainty in each year?
  1. A
    Only Czechy and Drjbna
  2. B
    Only Bzygoo and Czechy and Drjbna
  3. C
    Only Czechy
  4. D
    Only Drjbna

Answer: (A) Only Czechy and Drjbna Quant-based Puzzles MCQ

Solution

  1. Each firm's yearly amounts start and end at 1, rise then fall, with steps of 1 or 2 and no repeats in consecutive years.
  2. Drjbna, 5 years totalling 10: the middle three sum to 8 and must be 2, 4, 2, so it is fixed.
  3. Czechy, total 9 from 2013: only 1, 2, 3, 2, 1 works, so it is fixed.
  4. Bzygoo could be 1, 2, 3, 1 or 1, 3, 2, 1 (no total given), and Alfloo and Elavalaki have several options. So only Czechy and Drjbna are certain.

Question 12

What best can be concluded about the total amount of money raised in 2015?
  1. A
    It is either Rs. 7 crores or Rs. 8 crores.
  2. B
    It is either Rs. 7 crores or Rs. 8 crores or Rs. 9 crores.
  3. C
    It is exactly Rs. 8 crores.
  4. D
    It is either Rs. 8 crores or Rs. 9 crores.

Answer: (A) It is either Rs. 7 crores or Rs. 8 crores. Quant-based Puzzles MCQ

Solution

  1. Drjbna (5 years, total 10) must be 1, 2, 4, 2, 1. Czechy (from 2013, total 9) must be 1, 2, 3, 2, 1 (2013-2017). Bzygoo is 1, 2, 3, 1 or 1, 3, 2, 1.
  2. Alfloo (8 years, 21): its 7th year (2015) must be 2 and its 6th (2014) must be 3, which leaves 1, 2, 3, 4, 5, 3, 2, 1 or 1, 2, 3, 5, 4, 3, 2, 1.
  3. Elavalaki (from 2010, total 13): 1, 3, 5, 3, 1 (to 2014), or 1, 2, 3, 4, 2, 1 or 1, 2, 4, 3, 2, 1 (to 2015).
  4. 2015: Alfloo 2, Bzygoo 1, Czechy 3, Drjbna 1, Elavalaki 1 or 0 (if it closed in 2014).
  5. Total \(= 7 + (0\text{ or }1)\), i.e. 7 or 8 crores.

Question 13

What is the largest possible total amount of money (in Rs. crores) that could have been raised in 2013?

TITA: type in the answer. There are no options and no negative marking.

Answer: 17 Quant-based Puzzles TITA

Solution

  1. Drjbna (5 years, total 10) must be 1, 2, 4, 2, 1. Czechy (from 2013, total 9) must be 1, 2, 3, 2, 1 (2013-2017). Bzygoo is 1, 2, 3, 1 or 1, 3, 2, 1.
  2. Alfloo (8 years, 21): its 7th year (2015) must be 2 and its 6th (2014) must be 3, which leaves 1, 2, 3, 4, 5, 3, 2, 1 or 1, 2, 3, 5, 4, 3, 2, 1.
  3. Elavalaki (from 2010, total 13): 1, 3, 5, 3, 1 (to 2014), or 1, 2, 3, 4, 2, 1 or 1, 2, 4, 3, 2, 1 (to 2015).
  4. 2013 maxima: Alfloo 5 (5th year of 1, 2, 3, 4, 5, 3, 2, 1), Bzygoo 3 (1, 3, 2, 1), Czechy 1, Drjbna 4, Elavalaki 4 (1, 2, 3, 4, 2, 1).
  5. The firms are independent, so the largest total is \(5 + 3 + 1 + 4 + 4 = 17\).

Question 14

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
    12
  2. B
    11
  3. C
    10
  4. D
    9

Answer: (B) 11 Quant-based Puzzles MCQ

Solution

  1. Drjbna (5 years, total 10) must be 1, 2, 4, 2, 1. Czechy (from 2013, total 9) must be 1, 2, 3, 2, 1 (2013-2017). Bzygoo is 1, 2, 3, 1 or 1, 3, 2, 1.
  2. Alfloo (8 years, 21): its 7th year (2015) must be 2 and its 6th (2014) must be 3, which leaves 1, 2, 3, 4, 5, 3, 2, 1 or 1, 2, 3, 5, 4, 3, 2, 1.
  3. Elavalaki (from 2010, total 13): 1, 3, 5, 3, 1 (to 2014), or 1, 2, 3, 4, 2, 1 or 1, 2, 4, 3, 2, 1 (to 2015).
  4. Elavalaki 3 in 2013 means 1, 3, 5, 3, 1 or 1, 2, 4, 3, 2, 1, so its 2012 amount is 5 or 4 (minimum 4).
  5. 2012: Alfloo's 4th year is at least 4, Bzygoo 1, Czechy 0 (not yet founded), Drjbna 2.
  6. Smallest total \(= 4 + 1 + 0 + 2 + 4 = 11\).

Question 15

If the total amount of money raised in 2014 is Rs. 12 crores, then which of the following is not possible?
  1. A
    Bzygoo raised the same amount of money as Elavalaki in 2013.
  2. B
    Alfloo raised the same amount of money as Drjbna in 2013.
  3. C
    Alfloo raised the same amount of money as Bzygoo in 2014.
  4. D
    Bzygoo raised more money than Elavalaki in 2014.

Answer: (A) Bzygoo raised the same amount of money as Elavalaki in 2013. Quant-based Puzzles MCQ

Solution

  1. Drjbna (5 years, total 10) must be 1, 2, 4, 2, 1. Czechy (from 2013, total 9) must be 1, 2, 3, 2, 1 (2013-2017). Bzygoo is 1, 2, 3, 1 or 1, 3, 2, 1.
  2. Alfloo (8 years, 21): its 7th year (2015) must be 2 and its 6th (2014) must be 3, which leaves 1, 2, 3, 4, 5, 3, 2, 1 or 1, 2, 3, 5, 4, 3, 2, 1.
  3. Elavalaki (from 2010, total 13): 1, 3, 5, 3, 1 (to 2014), or 1, 2, 3, 4, 2, 1 or 1, 2, 4, 3, 2, 1 (to 2015).
  4. 2014: Alfloo 3, Czechy 2, Drjbna 2, so Bzygoo + Elavalaki \(= 5\). Bzygoo is 2 or 3 and Elavalaki is 1 or 2, so Bzygoo = 3 (1, 2, 3, 1) and Elavalaki = 2 (one of the two six-year patterns).
  5. Then in 2013 Bzygoo raised 2 while Elavalaki raised 4 or 3, so A is impossible. B works with 1, 2, 3, 5, 4, ... (Alfloo 4 = Drjbna 4); C (3 = 3) and D (3 > 2) hold.

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