CAT 2023 Slot 2 · DILR · Set 2: Funds Raised by Five Firms of Odsville

The full set and all 5 questions (Q6–Q10) from CAT 2023 Slot 2, with answers and solutions.

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 6 · Caselet DI

For which firm(s) can the amounts raised by them be concluded with certainty in each year?
  1. A
    Only Bzygoo and Czechy and Drjbna
  2. B
    Only Czechy and Drjbna
  3. C
    Only Drjbna
  4. D
    Only Czechy
Pick an option, then check.
Answer & solution

Answer: Option B

Solving the set

Step 1 – Rules for each firm's yearly amounts: start and end at 1, rise (by 1 or 2 each year) to a single peak, then fall (by 1 or 2 each year), never the same in two consecutive years.

Step 2 – List all sequences that fit each firm's years and total:

Firm

Years

Total

Possible yearly amounts (Rs. crores)

Alfloo

2009–2016

21

1, 2, 3, 4, 5, 3, 2, 1 or 1, 2, 3, 5, 4, 3, 2, 1

Bzygoo

2012–2015

?

1, 2, 3, 1 or 1, 3, 2, 1

Czechy

2013–?

9

1, 2, 3, 2, 1 (2013–2017) only

Drjbna

2011–2015

10

1, 2, 4, 2, 1 only

Elavalaki

2010–?

13

1, 3, 5, 3, 1 (to 2014) or 1, 2, 3, 4, 2, 1 or 1, 2, 4, 3, 2, 1 (to 2015)

For example, Drjbna has 5 years totalling 10: 1, a, b, c, 1 with a, b, c adding to 8; only 2, 4, 2 obeys the steps. Czechy totals 9: 1, 2, 3, 2, 1 is the only option (shorter runs total too little, longer ones too much). Bzygoo's total is not given, so both 4-year patterns are possible.

Step 3 – Amounts by year (Elavalaki's three cases separated by /):

Firm

2012

2013

2014

2015

Alfloo

4 or 5

5 or 4

3

2

Bzygoo

1

2 or 3

3 or 2

1

Czechy

—

1

2

3

Drjbna

2

4

2

1

Elavalaki

5 / 3 / 4

3 / 4 / 3

1 / 2 / 2

— / 1 / 1

This question

From Step 2, only Czechy and Drjbna have a unique sequence. Bzygoo has two, Alfloo two and Elavalaki three.

Hence, the answer is option 2.

Question 7 · Caselet DI

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 or Rs. 9 crores.
  2. B
    It is exactly Rs. 8 crores.
  3. C
    It is either Rs. 7 crores or Rs. 8 crores.
  4. D
    It is either Rs. 8 crores or Rs. 9 crores.
Pick an option, then check.
Answer & solution

Answer: Option C

Solving the set

Step 1 – Rules for each firm's yearly amounts: start and end at 1, rise (by 1 or 2 each year) to a single peak, then fall (by 1 or 2 each year), never the same in two consecutive years.

Step 2 – List all sequences that fit each firm's years and total:

Firm

Years

Total

Possible yearly amounts (Rs. crores)

Alfloo

2009–2016

21

1, 2, 3, 4, 5, 3, 2, 1 or 1, 2, 3, 5, 4, 3, 2, 1

Bzygoo

2012–2015

?

1, 2, 3, 1 or 1, 3, 2, 1

Czechy

2013–?

9

1, 2, 3, 2, 1 (2013–2017) only

Drjbna

2011–2015

10

1, 2, 4, 2, 1 only

Elavalaki

2010–?

13

1, 3, 5, 3, 1 (to 2014) or 1, 2, 3, 4, 2, 1 or 1, 2, 4, 3, 2, 1 (to 2015)

For example, Drjbna has 5 years totalling 10: 1, a, b, c, 1 with a, b, c adding to 8; only 2, 4, 2 obeys the steps. Czechy totals 9: 1, 2, 3, 2, 1 is the only option (shorter runs total too little, longer ones too much). Bzygoo's total is not given, so both 4-year patterns are possible.

Step 3 – Amounts by year (Elavalaki's three cases separated by /):

Firm

2012

2013

2014

2015

Alfloo

4 or 5

5 or 4

3

2

Bzygoo

1

2 or 3

3 or 2

1

Czechy

—

1

2

3

Drjbna

2

4

2

1

Elavalaki

5 / 3 / 4

3 / 4 / 3

1 / 2 / 2

— / 1 / 1

This question

From the 2015 column: Alfloo 2 + Bzygoo 1 + Czechy 3 + Drjbna 1 = 7, plus Elavalaki 0 (if it closed in 2014) or 1. So the total is 7 or 8.

Hence, the answer is option 3.

Question 8 · Caselet DI

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

Answer: 17

Solving the set

Step 1 – Rules for each firm's yearly amounts: start and end at 1, rise (by 1 or 2 each year) to a single peak, then fall (by 1 or 2 each year), never the same in two consecutive years.

Step 2 – List all sequences that fit each firm's years and total:

Firm

Years

Total

Possible yearly amounts (Rs. crores)

Alfloo

2009–2016

21

1, 2, 3, 4, 5, 3, 2, 1 or 1, 2, 3, 5, 4, 3, 2, 1

Bzygoo

2012–2015

?

1, 2, 3, 1 or 1, 3, 2, 1

Czechy

2013–?

9

1, 2, 3, 2, 1 (2013–2017) only

Drjbna

2011–2015

10

1, 2, 4, 2, 1 only

Elavalaki

2010–?

13

1, 3, 5, 3, 1 (to 2014) or 1, 2, 3, 4, 2, 1 or 1, 2, 4, 3, 2, 1 (to 2015)

For example, Drjbna has 5 years totalling 10: 1, a, b, c, 1 with a, b, c adding to 8; only 2, 4, 2 obeys the steps. Czechy totals 9: 1, 2, 3, 2, 1 is the only option (shorter runs total too little, longer ones too much). Bzygoo's total is not given, so both 4-year patterns are possible.

Step 3 – Amounts by year (Elavalaki's three cases separated by /):

Firm

2012

2013

2014

2015

Alfloo

4 or 5

5 or 4

3

2

Bzygoo

1

2 or 3

3 or 2

1

Czechy

—

1

2

3

Drjbna

2

4

2

1

Elavalaki

5 / 3 / 4

3 / 4 / 3

1 / 2 / 2

— / 1 / 1

This question

From the 2013 column, take the largest value for each firm: Alfloo 5, Bzygoo 3, Czechy 1, Drjbna 4, Elavalaki 4. Total = 17.

Hence, the answer is 17.

Question 9 · Caselet DI

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
    9
  3. C
    11
  4. D
    10
Pick an option, then check.
Answer & solution

Answer: Option C

Solving the set

Step 1 – Rules for each firm's yearly amounts: start and end at 1, rise (by 1 or 2 each year) to a single peak, then fall (by 1 or 2 each year), never the same in two consecutive years.

Step 2 – List all sequences that fit each firm's years and total:

Firm

Years

Total

Possible yearly amounts (Rs. crores)

Alfloo

2009–2016

21

1, 2, 3, 4, 5, 3, 2, 1 or 1, 2, 3, 5, 4, 3, 2, 1

Bzygoo

2012–2015

?

1, 2, 3, 1 or 1, 3, 2, 1

Czechy

2013–?

9

1, 2, 3, 2, 1 (2013–2017) only

Drjbna

2011–2015

10

1, 2, 4, 2, 1 only

Elavalaki

2010–?

13

1, 3, 5, 3, 1 (to 2014) or 1, 2, 3, 4, 2, 1 or 1, 2, 4, 3, 2, 1 (to 2015)

For example, Drjbna has 5 years totalling 10: 1, a, b, c, 1 with a, b, c adding to 8; only 2, 4, 2 obeys the steps. Czechy totals 9: 1, 2, 3, 2, 1 is the only option (shorter runs total too little, longer ones too much). Bzygoo's total is not given, so both 4-year patterns are possible.

Step 3 – Amounts by year (Elavalaki's three cases separated by /):

Firm

2012

2013

2014

2015

Alfloo

4 or 5

5 or 4

3

2

Bzygoo

1

2 or 3

3 or 2

1

Czechy

—

1

2

3

Drjbna

2

4

2

1

Elavalaki

5 / 3 / 4

3 / 4 / 3

1 / 2 / 2

— / 1 / 1

This question

Elavalaki = 3 in 2013 leaves its first case (2012 = 5) or third case (2012 = 4). For the smallest 2012 total take Alfloo 4, Bzygoo 1, Drjbna 2 and Elavalaki 4 (Czechy starts in 2013): 4 + 1 + 2 + 4 = 11.

Hence, the answer is option 3.

Question 10 · Caselet DI

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.
Pick an option, then check.
Answer & solution

Answer: Option A

Solving the set

Step 1 – Rules for each firm's yearly amounts: start and end at 1, rise (by 1 or 2 each year) to a single peak, then fall (by 1 or 2 each year), never the same in two consecutive years.

Step 2 – List all sequences that fit each firm's years and total:

Firm

Years

Total

Possible yearly amounts (Rs. crores)

Alfloo

2009–2016

21

1, 2, 3, 4, 5, 3, 2, 1 or 1, 2, 3, 5, 4, 3, 2, 1

Bzygoo

2012–2015

?

1, 2, 3, 1 or 1, 3, 2, 1

Czechy

2013–?

9

1, 2, 3, 2, 1 (2013–2017) only

Drjbna

2011–2015

10

1, 2, 4, 2, 1 only

Elavalaki

2010–?

13

1, 3, 5, 3, 1 (to 2014) or 1, 2, 3, 4, 2, 1 or 1, 2, 4, 3, 2, 1 (to 2015)

For example, Drjbna has 5 years totalling 10: 1, a, b, c, 1 with a, b, c adding to 8; only 2, 4, 2 obeys the steps. Czechy totals 9: 1, 2, 3, 2, 1 is the only option (shorter runs total too little, longer ones too much). Bzygoo's total is not given, so both 4-year patterns are possible.

Step 3 – Amounts by year (Elavalaki's three cases separated by /):

Firm

2012

2013

2014

2015

Alfloo

4 or 5

5 or 4

3

2

Bzygoo

1

2 or 3

3 or 2

1

Czechy

—

1

2

3

Drjbna

2

4

2

1

Elavalaki

5 / 3 / 4

3 / 4 / 3

1 / 2 / 2

— / 1 / 1

This question

2014: Alfloo 3, Czechy 2, Drjbna 2 are fixed, so Bzygoo + Elavalaki = 12 − 7 = 5 ⇒ Bzygoo 3 and Elavalaki 2. Then in 2013 Bzygoo = 2 and Elavalaki = 4 or 3.

• Bzygoo = Elavalaki in 2013: 2 vs 3 or 4 – not possible.

• Alfloo = Drjbna in 2013: Alfloo 4 (second case) = Drjbna 4 – possible.

• Alfloo = Bzygoo in 2014: 3 = 3 – true.

• Bzygoo > Elavalaki in 2014: 3 > 2 – true.

Hence, the answer is option 1.

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