CAT 2020 Slot 2 DILR Paper with Solutions

Set 1CAT 2020 · Slot 2 · DILR Q1–Q44 questionsTables & Missing Data

Department sales in four cities

A chain of departmental stores has outlets in Delhi, Mumbai, Bengaluru and Kolkata. The sales are categorized by its three departments - ‘Apparel’, ‘Electronics’, and ‘Home Décor’. An Accountant has been asked to prepare a summary of the 2018 and 2019 sales amounts for an internal report. He has collated partial information and prepared the following table.

Data for this set (chart, table or figure)

The following additional information is known.

1. The sales amounts in the Apparel departments were the same for Delhi and Kolkata in 2018.

2. The sales amounts in the Apparel departments were the same for Mumbai and Bengaluru in 2018. This sales amount matched the sales amount in the Apparel department for Delhi in 2019.

3. The sales amounts in the Home Décor departments were the same for Mumbai and Kolkata in 2018.

4. The sum of the sales amounts of four Electronics departments increased by the same amount as the sum of the sales amounts of four Apparel departments from 2018 to 2019.

5. The total sales amounts of the four Home Décor departments increased by Rs 70 Crores from 2018 to 2019.

6. The sales amounts in the Home Décor departments of Delhi and Bengaluru each increased by Rs 20 Crores from 2018 to 2019.

7. The sales amounts in the Apparel departments of Delhi and Bengaluru each increased by the same amount in 2019 from 2018. The sales amounts in the Apparel departments of Mumbai and Kolkata also each increased by the same amount in 2019 from 2018.

8. The sales amounts in the Apparel departments of Delhi, Kolkata and Bengaluru in 2019 followed an Arithmetic Progression.

Set solution: how to crack this set

Electronics rose from 330 to 370 (+40), so Apparel also rose by 40 in total.

Apparel 2018: Delhi $=$ Kolkata $= a$ , Mumbai $=$ Bengaluru $= b =$ Delhi 2019. Delhi and Bengaluru rise by $x$ , Mumbai and Kolkata by $y$ , with $2x + 2y = 40$ .

$b = a + x$ ; Kolkata 2019: $a + y = 54$ . AP (Delhi, Kolkata, Bengaluru 2019): $b + (b + x) = 108$ .

Solving: $x = 8$ , $y = 12$ , $a = 42$ , $b = 50$ .

Home Décor: 2019 total 306, so 2018 total 236. Delhi 80, Bengaluru 60, and Mumbai $=$ Kolkata $= \dfrac{236 - 140}{2} = 48$ .

Dept	Delhi	Mumbai	Bengaluru	Kolkata
Apparel	42 → 50	50 → 62	50 → 58	42 → 54
Electronics	78 → 98	82 → 102	90 → 70	80 → 100
Home Décor	80 → 100	48 → 72	60 → 80	48 → 54

Q1CAT 2020 · Slot 2 · DILR Q1MCQ

In Home Décor departments of which cities were the sales amounts the highest in 2018 and 2019, respectively?

Q2CAT 2020 · Slot 2 · DILR Q2MCQ

What was the increase in sales amount, in Crore Rupees, in the Apparel department of Mumbai from 2018 to 2019?

Q3CAT 2020 · Slot 2 · DILR Q3MCQ

Among all the 12 departments (i.e., the 3 departments in each of the 4 cities), what was the maximum percentage increase in sales amount from 2018 to 2019?

Q4CAT 2020 · Slot 2 · DILR Q4MCQ

What was the total sales amount, in Crore Rupees, in 2019 for the chain of departmental stores?

Set 2CAT 2020 · Slot 2 · DILR Q5–Q106 questionsTables & Missing Data

Election votes and security deposits

In an election several candidates contested for a constituency. In any constituency, the winning candidate was the one who polled the highest number of votes, the first runner up was the one who polled the second highest number of votes, the second runner up was the one who polled the third highest number of votes, and so on. There were no ties (in terms of number of votes polled by the candidates) in any of the constituencies in this election. In an electoral system, a security deposit is the sum of money that a candidate is required to pay to the election commission before he or she is permitted to contest. Only the defeated candidates (i.e., one who is not the winning candidate) who fail to secure more than one sixth of the valid votes polled in the constituency, lose their security deposits.

The following table provides some incomplete information about votes polled in four constituencies: A, B, C and D, in this election .

The following additional facts are known:

1. The first runner up polled 10,000 more votes than the second runner up in constituency A.

2. None of the candidates who contested in constituency C lost their security deposit. The difference in votes polled by any pair of candidates in this constituency was at least 10,000.

3. The winning candidate in constituency D polled 5% of valid votes more than that of the first runner up. All the candidates who lost their security deposits while contesting for this constituency, put together, polled 35% of the valid votes.

Set solution: how to crack this set

A candidate loses the deposit with at most $\dfrac{1}{6}$ of the valid votes.

A: $\dfrac{1}{6}$ of 5,00,000 $\approx 83{,}333$ . Second runner-up has $95{,}000 - 10{,}000 = 85{,}000$ (keeps it). The other 7 share $5{,}00{,}000 - 2{,}75{,}000 - 95{,}000 - 85{,}000 = 45{,}000$ , all losing.

B: the winner has only 48,750, below $\dfrac{1}{6}$ of 3,25,000 ( $\approx 54{,}167$ ), so all 11 losers lose deposits (2,76,250 votes).

C: each loser has more than 1,00,005, so at least 1,00,006, and gaps are at least 10,000. Minimum for the four losers: $4 \times 100006 + 60000$ , leaving the winner at most 1,40,006; but the winner must exceed the top loser by 10,000, so at least 1,40,006. Winner $= 1{,}40{,}006$ , runner-up 1,30,006.

D: with $V = 1{,}75{,}000$ : winner $= 37{,}500 + 0.05V = 46{,}250$ ; top three $= 1{,}13{,}750$ ; the rest $= 61{,}250 = 35\%$ , and each is below $\dfrac{V}{6} \approx 29{,}167$ while the second runner-up (30,000) is above. It fits.

Q5CAT 2020 · Slot 2 · DILR Q5TITA

What is the percentage of votes polled in total by all the candidates who lost their security deposits while contesting for constituency A?

Q6CAT 2020 · Slot 2 · DILR Q6TITA

How many candidates who contested in constituency B lost their security deposit?

Q7CAT 2020 · Slot 2 · DILR Q7MCQ

What BEST can be concluded about the number of votes polled by the winning candidate in constituency C?

Q8CAT 2020 · Slot 2 · DILR Q8MCQ

What was the number of valid votes polled in constituency D?

Q9CAT 2020 · Slot 2 · DILR Q9MCQ

The winning margin of a constituency is defined as the difference of votes polled by the winner and that of the first runner up. Which of the following CANNOT be the list of constituencies, in increasing order of winning margin?

Q10CAT 2020 · Slot 2 · DILR Q10MCQ

For all the four constituencies taken together, what was the approximate number of votes polled by all the candidates who lost their security deposit expressed as a percentage of the total valid votes from these four constituencies?

Set 3CAT 2020 · Slot 2 · DILR Q11–Q144 questionsGrids & Matrices

Coloured beads in a 5×5 grid

Twenty five coloured beads are to be arranged in a grid comprising of five rows and five columns. Each cell in the grid must contain exactly one bead. Each bead is coloured either Red, Blue or Green. While arranging the beads along any of the five rows or along any of the five columns, the rules given below are to be followed:

1. Two adjacent beads along the same row or column are always of different colours.

2. There is at least one Green bead between any two Blue beads along the same row or column.

3. There is at least one Blue and at least one Green bead between any two Red beads along the same row or column.

Every unique, complete arrangement of twenty five beads is called a configuration.

Set solution: how to crack this set

In any row or column: neighbours differ, two Blues need a Green between them, and two Reds need both a Blue and a Green between them.

So two Reds in a line are at least 3 apart: a line of 5 holds at most 2 Reds, at positions 1 & 4, 1 & 5 or 2 & 5, never in the middle.

Example with 9 Reds:

R	B	G	R	B
G	R	B	G	R
B	G	R	B	G
R	B	G	R	B
G	R	B	G	R

Q11CAT 2020 · Slot 2 · DILR Q11TITA

The total number of possible configurations using beads of only two colours is:

Q12CAT 2020 · Slot 2 · DILR Q12TITA

What is the maximum possible number of Red beads that can appear in any configuration?

Q13CAT 2020 · Slot 2 · DILR Q13TITA

What is the minimum number of Blue beads in any configuration?

Q14CAT 2020 · Slot 2 · DILR Q14TITA

Two Red beads have been placed in ‘second row, third column’ and ‘third row, second column’. How many more Red beads can be placed so as to maximise the number of Red beads used in the configuration?

Set 4CAT 2020 · Slot 2 · DILR Q15–Q206 questionsScheduling & Timelines

Seminar slots for eight doctoral students

The Humanities department of a college is planning to organize eight seminars, one for each of the eight doctoral students - A, B, C, D, E, F, G and H. Four of them are from Economics, three from Sociology and one from Anthropology department. Each student is guided by one among P, Q, R, S and T. Two students are guided by each of P, R and T, while one student is guided by each of Q and S. Each student is guided by a guide belonging to their department. Each seminar is to be scheduled in one of four consecutive 30-minute slots starting at 9:00 am, 9:30 am, 10:00 am and 10:30 am on the same day. More than one seminars can be scheduled in a slot, provided the guide is free. Only three rooms are available and hence at the most three seminars can be scheduled in a slot. Students who are guided by the same guide must be scheduled in consecutive slots.

The following additional facts are also known.

1. Seminars by students from Economics are scheduled in each of the four slots.

2. A’s is the only seminar that is scheduled at 10:00 am. A is guided by R.

3. F is an Anthropology student whose seminar is scheduled at 10:30 am.

4. The seminar of a Sociology student is scheduled at 9:00 am.

5. B and G are both Sociology students, whose seminars are scheduled in the same slot. The seminar of an Economics student, who is guided by T, is also scheduled in the same slot.

6. P, who is guiding both B and C, has students scheduled in the first two slots.

7. A and G are scheduled in two consecutive slots.

Set solution: how to crack this set

P guides B (Sociology) and C, so P is a Sociology guide and C is Sociology too. Sociology: B, C, G. F (Anthropology) and G each have a single-student guide (Q or S). Economics: A, D, E, H, guided by R (A and one more) and T (two).

G is next to A's 10:00 slot. 10:30 already has F, so B, G, F and a T student would be 4. Hence B, G and an Economics T student are at 9:30.

P's students fill the first two slots: C at 9:00 (the 9:00 Sociology seminar).

T's students are consecutive: the other one is at 9:00 (10:00 has only A). R's other student is at 10:30 (9:30 is full).

Slot	Seminars
9:00	C (P), Econ (T)
9:30	B (P), G (Q/S), Econ (T)
10:00	A (R)
10:30	F (Q/S), Econ (R)

D, E, H fill the three Economics places.

Q15CAT 2020 · Slot 2 · DILR Q15MCQ

Which one of the following statements is true?

Q16CAT 2020 · Slot 2 · DILR Q16MCQ

Who all are NOT guiding any Economics students?

Q17CAT 2020 · Slot 2 · DILR Q17MCQ

Which of the following statements is necessarily true?

Q18CAT 2020 · Slot 2 · DILR Q18MCQ

If D is scheduled in a slot later than Q's, then which of the following two statement(s) is(are) true?

(i) E and H are guided by T.

(ii) G is guided by Q.

Q19CAT 2020 · Slot 2 · DILR Q19MCQ

If E and Q are both scheduled in the same slot, then which of the following statements BEST describes the relationship between D, H, and T?

Q20CAT 2020 · Slot 2 · DILR Q20MCQ

If D is scheduled in the slot immediately before Q’s, then which of the following is NOT necessarily true?

Set 5CAT 2020 · Slot 2 · DILR Q21–Q244 questionsArrangements

Compact cars and SUVs in a parking row

A shopping mall has a large basement parking lot with parking slots painted in it along a single row. These slots are quite narrow; a compact car can fit in a single slot but an SUV requires two slots. When a car arrives, the parking attendant guides the car to the first available slot from the beginning of the row into which the car can fit.

For our purpose, cars are numbered according to the order in which they arrive at the lot. For example, the first car to arrive is given a number 1, the second a number 2, and so on. This numbering does not indicate whether a car is a compact or an SUV. The configuration of a parking lot is a sequence of the car numbers in each slot. Each single vacant slot is represented by letter V.

For instance, suppose cars numbered 1 through 5 arrive and park, where cars 1, 3 and 5 are compact cars and 2 and 4 are SUVs. At this point, the parking lot would be described by the sequence 1, 2, 3, 4, 5. If cars 2 and 5 now vacate their slots, the parking lot would now be described as 1, V, V, 3, 4. If a compact car (numbered 6) arrives subsequently followed by an SUV (numbered 7), the parking lot would be described by the sequence 1, 6, V, 3, 4, 7.

Answer the following questions INDEPENDENTLY of each other.

Set solution: how to crack this set

Each car takes the first gap from the start that fits it (1 slot for a compact, 2 for an SUV).

Q21CAT 2020 · Slot 2 · DILR Q21MCQ

Initially cars numbered 1, 2, 3, and 4 arrive among which 1 and 4 are SUVs while 2 and 3 are compact cars. Car 1 then leaves, followed by the arrivals of car 5 (a compact car) and car 6 (an SUV). Car 4 then leaves. Then car 7 (an SUV) and car 8 (a compact car) arrive. At this moment, which among the following numbered car is parked next to car 3?

Q22CAT 2020 · Slot 2 · DILR Q22MCQ

Suppose eight cars have arrived, of which two have left. Also suppose that car 4 is a compact and car 7 is an SUV. Which of the following is a POSSIBLE current configuration of the parking lot?

Q23CAT 2020 · Slot 2 · DILR Q23MCQ

Suppose the sequence at some point of time is 4, 5, 6, V, 3. Which of the following is NOT necessarily true?

Q24CAT 2020 · Slot 2 · DILR Q24MCQ

Suppose that car 4 is not the first car to leave and that the sequence at a time between the arrival of the car 7 and car 8 is V, 7, 3, 6, 5. Then which of the following statements MUST be false?

CAT 2020 Slot 2 DILR paper with solutions

Department sales in four cities

Solution

Solution

Solution

Solution

Election votes and security deposits

Solution

Solution

Solution

Solution

Solution

Solution

Coloured beads in a 5×5 grid

Solution

Solution

Solution

Solution

Seminar slots for eight doctoral students

Solution

Solution

Solution

Solution

Solution

Solution

Compact cars and SUVs in a parking row

Solution

Solution

Solution

Solution