CAT 2023 Slot 2 · DILR · Question 9

CAT 2023 Slot 2 previous year question on Caselet DI, with the answer and a step-by-step solution.

Caselet DIData InterpretationMultiple choiceMedium

Set 2: Funds Raised by Five Firms of Odsville — this question belongs to a set. Read the full set with all 5 questions →

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

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?

A
12
B
9
C
11
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.

CAT 2023 Slot 2 · DILR · Question 9

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