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# CAT 2018 LRDI Question Paper with Solution [SLOT 2]

#### [SLOT 2]

Instruction

Each of the 23 boxes in the picture below represents a product manufactured by one of the following three companies: Alfa, Bravo and Charlie. The area of a box is proportional to the revenue from the corresponding product, while its centre represents the Product popularity and Market potential scores of the product (out of 20). The shadings of some of the boxes have got erased.

The companies classified their products into four categories based on a combination of scores (out of 20) on the two parameters – Product popularity and Market potential as given below:

 Promising Blockbuster Doubtful No-hope Product popularity score >10 >10 ≤10 ≤10 Market potential score >10 ≤10 >10 ≤10

The following facts are known:

1. Alfa and Bravo had the same number of products in the Blockbuster category.

2. Charlie had more products than Bravo but fewer products than Alfa in the No-hope category.

3. Each company had an equal number of products in the Promising category.

4. Charlie did not have any product in the Doubtful category, while Alfa had one product more than Bravo in this category.

5. Bravo had a higher revenue than Alfa from products in the Doubtful category.

6. Charlie had a higher revenue than Bravo from products in the Blockbuster category.

7. Bravo and Charlie had the same revenue from products in the No-hope category.

Question 1:
Considering all companies' products, which product category had the highest revenue?
1. Doubtful
2. Promising
3. No-hope
4. Blockbuster
Question 2:
Which of the following is the correct sequence of numbers of products Bravo had in No-hope, Doubtful, Promising and Blockbuster categories respectively?
1. 1,3,1,3
2. 1,3,1,2
3. 2,3,1,2
4. 3,3,1,2
Question 3:
Which of the following statements is NOT correct?
1. Bravo's revenue from Blockbuster products was greater than Alfa's revenue from Doubtful products
2. The total revenue from No-hope products was less than the total revenue from Doubtful products
3. Bravo and Charlie had the same revenues from No-hope products
4. Alfa's revenue from Blockbuster products was the same as Charlie's revenue from Promising products
Question 4:
If the smallest box on the grid is equivalent to revenue of Rs.1 crore, then what approximately was the total revenue of Bravo in Rs. crore?
1. 40
2. 24
3. 30
4. 34

From the given information we can find which product belong to which company. In the given figure the products (number) would belong to the following companies

So also the entire graph can be divided into four equal parts with the bottom left part having products in the No hope category, the bottom right part with products in the Blockbuster category, the top left part with products in the Doubtful category and the top right part with products in the promising category.

Question 1:

The areas of all the products in the different categories are

No-hope – 4 + 4 + 3 + 2 + 1 + 1 = 15

Blockbuster – 2 + 4 + 3 + 6 + 6 +6 + 9 = 36

Doubtful – 2 + 1+ 6 + 6 + 1 + 9 + 4 = 29

Promising – 2 + 9 + 3 = 14

As the areas is proportional to the revenue the corresponding product, products under Blockbuster category had the highest revenue.

Ans : Blockbuster

Question 2:

The number of products of Bravo in the different categories are

No-hope (bottom left) – 1

Doubtful (top left) – 3

Promising (top right) – 1

Blockbuster (bottom right) – 2

The correct sequence is 1, 3, 1, 2

Ans : 1, 3, 1, 2

Question 3:

Revenue of Bravo from No-hope products – 4

Revenue of Charlie from No-hope products – 4.

The statements is true.

Alfa's revenue from Blockbuster products

Charlie revenue from Promising products – 9

The statement is true

Total revenue from No-hope products – 15

Total revenue from Doubtful products – 29

The statement is true

Bravo's revenue from Blockbuster products – 6 + 4 = 10

Alfa's revenue from Doubtful products – 6 + 4 + 1 + 1= 12

The statement is not true

Ans : Bravo's revenue from Blockbuster products was

greater than Alfa's revenue from Doubtful products

Question 4:

The total revenue of Bravo is 4 (No. hope) + 10 (Blockbuster) + 17 (Doubtful) + 3 (Promising) = 34

crore. Ans : 34 .

Instruction

There are only four brands of entry level smartphones called Azra, Bysi, Cxqi, and Dipq in a country.

Details about their market share, unit selling price, and profitability (defined as the profit as a percentage of the revenue) for the year 2016 are given in the table below:

In 2017, sales volume of entry level smartphones grew by 40% as compared to that in 2016. Cxqi offered a 40% discount on its unit selling price in 2017, which resulted in a 15% increase in its market share. Each of the other three brands lost 5% market share. However, the profitability of Cxqi came down to half of its value in 2016. The unit selling prices of the other three brands and their profitability values remained the same in 2017 as they were in 2016.

Question 5:
The brand that had the highest revenue in 2016 is:
1. Dipq
2. Bysi
3. Cxqi
4. Azra
Question 6:
The brand that had the highest profit in 2016 is:
1. Azra
2. Bysi
3. Cxqi
4. Dipq
Question 7:
The brand that had the highest profit in 2017 is:
1. Dipq
2. Bysi
3. Cxqi
4. Azra
Question 8:
The complete list of brands whose profits went up in 2017 from 2016 is:
1. Azra, Bysi, Cxqi
2. Bysi, Cxqi, Dipq
3. Cxqi, Azra, Dipq
4. Azra, Bysi, Dipq

Question 1:

Let the total market size be 100 units. The sales of Azra, Bysi, Cxqi and dipq would be 40, 25, 15 and 20 units respectively.

The revenue would be as follows

Azra = 40 x 15,000 = 6.0 lac

Bysi = 25 x 20,000 = 5.0 lac

Cxgi = 15 x 30,000 = 4.5 lac

Dipq = 20 x 25,000 = 5.0 lac

The brand with the highest revenue is Azra.

Ans : Azra

Question 2:

The profits for the different brands, assuming revenue as in the previous question would be

Azra $- 6.0$ lac $\times \frac { 10 } { 100 } = 60,000$

Bysi $- 5.0$ lac $\times \frac { 30 } { 100 } = 1,50,000$

Cxgi $- 4.5$ lac $\times \frac { 40 } { 100 } = 1,80,000$

Dipq $- 5.0$ lac $\times \frac { 30 } { 100 } = 1,50,000$

The profit is the highest for Cxqi

Ans : Cxqi

Question 3:

The new market share, selling prices and profitability for the different brands are

Now the total sales is 140 units.(Increase of 40%) The profits are as follows

Azra $- 49 \times 15,000 \times \frac { 10 } { 100 } = 73,500$

Bysi $- 28 \times 20,000 \times \frac { 30 } { 100 } = 1,68,000$

Cxgi $- 42 \times 18,000 \times \frac { 20 } { 100 } = 1,51,200$

Dipq $- 21 \times 25,000 \times \frac { 30 } { 100 } = 1,57,500$

The profit is the highest for Bysi

Ans : Bysi

Question 4:

The profits increased for Azra (60,000 – 73,500) for

Bysi (1,50,000 – 1, 68,000) and Dipq (1,50,000 –

1,57,500)

Ans : Azra, Bysi, Dipq

Instruction

Seven candidates, Akil, Balaram, Chitra, Divya, Erina, Fatima, and Ganeshan, were invited to interview for a position. Candidates were required to reach the venue before 8 am. Immediately upon arrival, they were sent to one of three interview rooms: 101, 102, and 103. The following venue log shows the arrival times for these candidates. Some of the names have not been recorded in the log and have been marked as ‘?’.

 Time 7:10 am 7:15 am 7:25 am 7:30 am 7:40 am 7:45 am Person Akil, ? ? ? Chitra Fatima ?

Additionally here are some statements from the candidates:

Balaram: I was the third person to enter Room 101.

Chitra: I was the last person to enter the room I was allotted to.

Erina: I was the only person in the room I was allotted to.

Fatima: Three people including Akil were already in the room that I was allotted to when I entered it.

Ganeshan: I was one among the two candidates allotted to Room 102.

Question 9:
What best can be said about the room to which Divya was allotted?
1. Definitely Room 102
2. Definitely Room 103
3. Definitely Room 101
4. Either Room 101 or Room 102
Question 10:
Who else was in Room 102 when Ganeshan entered?
1. No one
2. Divya
3. Chitra
4. Akil
Question 11:
When did Erina reach the venue?
1. 7:25 am
2. 7:45 am
3. 7:10 am
4. 7:15 am
Question 12:
If Ganeshan entered the venue before Divya, when did Balaram enter the venue?
1. 7:45 am
2. 7:25 am
3. 7:15 am
4. 7:10 am

From the given information,

Balaram is the third person to enter room 101.

Erina was allotted either room 102 or 103.

Three persons entered the room before Fatima. It means Fatima and Akil entered into room 101.

Ganeshan entered room 102 with only one other person. Thus, only Erina entered room 103.

Chitra was the last person to enter the room. Thus, Chitra entered room 102 with Ganeshan.

Divya, who was the second person to enter room 101 From the above information we get the arrangement as follows.

Question 1:

Divya entered room 101.

Ans : Definitely room 101

Question 2:

No one entered into the room 102 before Ganeshan.

Ans : No one

Question 3:

Erina entered room at 07:45am as in room 101- Divya and Balaram entered before Fatima and Ganeshan entered the room before Chitra, thus Divya, Balaram and Ganeshan entered room before Chitra and Fatima in any order.

Ans : 7:45 am

Question 4:

From the information, Ganeshan entered room at 7:10 am, Divya entered room at 7:15 am and Balaram

entered room at 7:25 am.

Ans : 7:25 am

Instruction

The base exchange rate of a currency X with respect to a currency Y is the number of units of currency Y which is equivalent in value to one unit of currency X. Currency exchange outlets buy currency at buying exchange rates that are lower than base exchange rates, and sell currency at selling exchange rates that are higher than base exchange rates.

A currency exchange outlet uses the local currency L to buy and sell three international currencies A, B, and C, but does not exchange one international currency directly with another. The base exchange rates of A, B and C with respect to L are in the ratio 100:120:1. The buying exchange rates of each of A, B, and C with respect to L are 5% below the corresponding base exchange rates, and their selling exchange rates are 10% above their corresponding base exchange rates.

The following facts are known about the outlet on a particular day:

1. The amount of L used by the outlet to buy C equals the amount of L it received by selling C.

2. The amounts of L used by the outlet to buy A and B are in the ratio 5:3.

3. The amounts of L the outlet received from the sales of A and B are in the ratio 5:9.

4. The outlet received 88000 units of L by selling A during the day.

5. The outlet started the day with some amount of L, 2500 units of A, 4800 units of B, and 48000 units of C.

6. The outlet ended the day with some amount of L, 3300 units of A, 4800 units of B, and 51000 units of C.

Question 13:
How many units of currency A did the outlet buy on that day?
Question 14:
How many units of currency C did the outlet sell on that day?
1. 19000
2. 3000
3. 6000
4. 22000
Question 15:
What was the base exchange rate of currency B with respect to currency L on that day?
Question 16:
What was the buying exchange rate of currency C with respect to currency L on that day?
1. 0.95
2. 1.10
3. 1.90
4. 2.20

The base exchange rates of currencies A, B and C with  respect to L is in the ratio 100 : 120 : 1.

The given information can be tabulated as follows

The outlet received 88,000 units of L by selling A and the ratio of amounts of L used to by A and B are in the ratio 5 : 3 and from the sales of A and B are in the ratio 5 : 9.

This set is best solved by looking at the choices for the question which asked for the base exchange rate of currency C. From that we have only two possible value for the base exchange rates for A, B and C 100,120 and 1 or 200, 240 and 2.

Assuming L to be100 for A.

Units sold of $\mathrm { A } = \frac { 88,000 } { 110 } = 800$

As the net addition is 800, the units of A bought is 1600 Amount of L used in buying 1600 units is 1600 x 0.95

x 100 = 152000 As the amount used to buy A and B are in the ratio 5 : 3, the amount used to buy B is $\frac { 152000 } { 5 } \times 3 = 91,200$

Number of units of B bought = $\frac { 91,200 } { 114 } = 800$

As the net addition of B is zero, number of units of B sold = 800.

The amount received = 800 x 132 = 105600

The amount received form selling A = 88,000

As 88,000 : 105600 is not in the ratio 5 : 9 as given in the data the base exchange rate for A is not 100 and has to be 200.

Units sold for $\mathrm { A } = \frac { 88000 } { 220 } = 400$

As net addition is 800, the units of A bought is 1200.

Amount of L used in buying 1200 units of A = 1200 x 0.95 x 2000 = 228000.

As the amount used to buy A and B are in the ratio 5 :3, quantity of L used to buy B is $\frac { 228000 } { 5 } \times 3 = 136800$

Number of units of $\mathrm { B }$ bought $= \frac { 136800 } { 228 } = 600$

As the net addition in B is zero, the number of units of B sold = 600.

The amount received from selling B = 600 x 264= 158400

The amount received from selling A = 88,000

The required ratio $\frac { 88,000 } { 158400 } = \frac { 5 } { 9 }$

Question 1:

Number of units of currency A bought 400 + 800 = 1200

Question 2:

As the net addition in the number of units of C is 3,000 and the buying and selling rates are in the ratio 0.95 and 1.1, assuming x units are sold 0.95 (x + 3000) = 1.1 (x)

0.15x = 2850

X= 19000

Question 3:

The base exchange rate of currency B with respect to L is 240.

Question 4:

The buying exchange rate of currency C with respect to L on that day was 1.90.

Instruction

Fun Sports (FS) provides training in three sports – Gilli-danda (G), Kho-Kho (K), and Ludo (L). Currently it has an enrollment of 39 students each of whom is enrolled in at least one of the three sports. The following details are known:

1. The number of students enrolled only in L is double the number of students enrolled in all the three sports.

2. There are a total of 17 students enrolled in G.

3. The number of students enrolled only in G is one less than the number of students enrolled only in L.

4. The number of students enrolled only in K is equal to the number of students who are enrolled in both K and L.

5. The maximum student enrollment is in L.

6. Ten students enrolled in G are also enrolled in at least one more sport.

Question 17:
What is the minimum number of students enrolled in both G and L but not in K?
Question 18:
If the numbers of students enrolled in K and L are in the ratio 19:22, then what is the number of students enrolled in L?
1. 18
2. 19
3. 17
4. 22
Question 19:
Due to academic pressure, students who were enrolled in all three sports were asked to withdraw from one of the three sports. After the withdrawal, the number of students enrolled in G was six less than the number of students enrolled in L, while the number of students enrolled in K went down by one. After the withdrawal, how many students were enrolled in both G and K?
Question 20:
Due to academic pressure, students who were enrolled in all three sports were asked to withdraw from one of the three sports. After the withdrawal, the number of students enrolled in G was six less than the number of students enrolled in L, while the number of students enrolled in K went down by one. After the withdrawal, how many students were enrolled in both G and L?
1. 6
2. 7
3. 5
4. 8

The given data can be represented as follows.

f + g + d =10 (given)

g + e = b (given)

Since f + g + d = 10, g = 7 = 2g – 1

Therefore, 2g = 8  f = 4

Thus, g = 4, c = 8, a = 7 and f + d = 6

b + e = 39 – (G + c) = 14

therefore g + 2e = 14 Hence, e = 5 and b = 9

Since, L is maximum we get the following cases.

Case (i)

G = 17 K = 20 L = 21 d = 2 f = 4

Case (ii)

G = 17 K = 19 L = 22 d = 1 f = 5

Case (iii)

G = 17 K = 18 L = 23 d = 0 f = 6

Question 1:

G and L but not K = f = 4. Ans : 4

Question 2:

The given condition is possible in case (ii). Hence, the number of students enrolled in L = 22. Ans : 22

question 3:

From g = 4, one person moves to f, one person to d and two persons to e. Then the value of G and K = d + g = 2. Ans : 2

Question 4:

From the above G and L = f = 6. Ans : 6

Instruction

An agency entrusted to accredit colleges looks at four parameters: faculty quality (F), reputation (R), placement quality (P), and infrastructure (I). The four parameters are used to arrive at an overall score, which the agency uses to give an accreditation to the colleges. In each parameter, there are five possible letter grades given, each carrying certain points: A (50 points), B (40 points), C (30 points), D (20 points), and F (0 points). The overall score for a college is the weighted sum of the points scored in the four parameters. The weights of the parameters are 0.1, 0.2, 0.3 and 0.4 in some order, but the order is not disclosed. Accreditation is awarded based on the following scheme:

 Range Accreditation Overall score ≥ 45 AAA 35 ≤ Overall score < 45 BAA 25 ≤ Overall score < 35 BBA 15 ≤ Overall score < 25 BBB Overall score < 15 Junk

Eight colleges apply for accreditation, and receive the following grades in the four parameters (F, R, P, and I):

 F R P I A-one A A A B Best Ed B C D D Cosmopolitan B D D C Dominance D D B C Education Aid A A B A Fancy A A B B Global C F D D High Q C D D B

It is further known that in terms of overall scores:

1. High Q is better than Best Ed;

2. Best Ed is better than Cosmopolitan; and

3. Education Aid is better than A-one.

Question 21:
What is the weight of the faculty quality parameter?
1. 0.3
2. 0.2
3. 0.4
4. 0.1
Question 22:
How many colleges receive the accreditation of AAA?
Question 23:
What is the highest overall score among the eight colleges?
Question 24:
How many colleges have overall scores between 31 and 40, both inclusive?
1. 1
2. 3
3. 0
4. 2

Let a, b, c and d be the weights of parameters F, R, P and I respectively.

Given,

(i) 30a + 20b + 20c + 40d > 40a + 30b + 20c + 20d

(ii) 40a + 30b + 20c + 20d > 40a + 20b + 20c + 30d

(iii) 50a + 50b + 40c + 50d > 50a + 50b + 50c + 40d

From (i), 2d > a + b

From (ii), b > d

From (iii), d > c

$\Rightarrow$ b > d > c

a, b, c and d are 0.1, 0.2, 0.3 and 0.4 in any order.

d cannot be 0.1 or 0.2. (∵ 2d cannot be greater than a + b)

d can be 0.3 or 0.4, but given b > d.

$\Rightarrow$  b = 0.4, d = 0.3

2(0.3) > 0.4 + a

a < 0.2

a = 0.1, c = 0.2

Question 1

Weight of faculty parameter is 0.1.

Ans : 0.1

Question 2

Ans : 3

Question 3

Height overall score among the eight colleges is 48.

Ans : 48

Question 4

No college has score between 31 and 40 (both inclusive).

Ans : 0

Instruction

According to a coding scheme the sentence

Peacock is designated as the national bird of India

is coded as

5688999 35 1135556678 56 458 13666689 1334 79 13366

This coding scheme has the following rules:

1. The scheme is case-insensitive (does not distinguish between upper case and lower case letters).

2. Each letter has a unique code which is a single digit from among 1,2,3, …, 9.

3. The digit 9 codes two letters, and every other digit codes three letters.

4. The code for a word is constructed by arranging the digits corresponding to its letters in a non-decreasing sequence.

Answer these questions on the basis of this information.

Question 25:
What best can be concluded about the code for the letter L?
1. 1
2. 1 or 8
3. 6
4. 8
Question 26:
What best can be concluded about the code for the letter B?
1. 1 or 3 or 4
2. 3
3. 1
4. 3 or 4
Question 27:
For how many digits can the complete list of letters associated with that digit be identified?
1. 3
2. 0
3. 1
4. 2
Question 28:
Which set of letters CANNOT be coded with the same digit?
1. S,U,V
2. I,B,M
3. X,Y,Z
4. S,E,Z

Given 'peacock is designated as the national bird of India' is coded as ' 5688999 35 1135556678 56 458 13666689 1334 79 13366'

9 is the code for o and c from the words peacock and of.

F is coded as 7 from the word of.

I is coded as either 3 or 6 from the word India, but from the word 'is' and 'designated' code for 'I' is 3.

S is coded as 5 from the word is.

A is coded as 6 from the word 'as'.

N is coded as 6 from the word national.

Thus D is coded as 1 from the word India.

E is coded as 5 from the word designated.

T is coded as 8 from the word 'the' and 'National'.

Thus H is coded as 4 from the word 'the'. G is coded as 7. L is coded as 1 from the word 'National'.

P and K are coded as 8 from the word 'peacock'. B and R are coded as 3 and 4 many order from the word 'bird'.

We get the codes as follows

.

B and R is coded as 3 or 4.

Question 1

L is coded as '1'. Ans : 1

Question 2

Either 3 or 4 is the code for B. Ans : 3 or 4

Question 3

The code for 8 and 9 is identified. Ans : 2

Question 4

S, U, V cannot be coded with same digit.

Ans : S, U, V

Instruction

Each visitor to an amusement park needs to buy a ticket. Tickets can be Platinum, Gold, or Economy. Visitors are classified as Old, Middle-aged, or Young. The following facts are known about visitors and ticket sales on a particular day:

1. 140 tickets were sold.

2. The number of Middle-aged visitors was twice the number of Old visitors, while the number of Young visitors was twice the number of Middle-aged visitors.

3. Young visitors bought 38 of the 55 Economy tickets that were sold, and they bought half the total number of Platinum tickets that were sold.

4. The number of Gold tickets bought by Old visitors was equal to the number of Economy tickets bought by Old visitors.

Question 29:
If the number of Old visitors buying Platinum tickets was equal to the number of Middle-aged visitors buying Platinum tickets, then which among the following could be the total number of Platinum tickets sold?
1. 34
2. 38
3. 32
4. 36
Question 30:
If the number of Old visitors buying Platinum tickets was equal to the number of Middle-aged visitors buying Economy tickets, then the number of Old visitors buying Gold tickets was
Question 31:
If the number of Old visitors buying Gold tickets was strictly greater than the number of Young visitors buying Gold tickets, then the number of Middle-aged visitors buying Gold tickets was
Question 32:
Which of the following statements MUST be FALSE?
1. The numbers of Old and Middle-aged visitors buying Economy tickets were equal
2. The numbers of Old and Middle-aged visitors buying Platinum tickets were equal
3. The numbers of Middle-aged and Young visitors buying Gold tickets were equal
4. The numbers of Gold and Platinum tickets bought by Young visitors were equal

Number of young visitors = 2 x number of middle age visitors

Number of middle age visitors = 2 x number of old visitors

Total number of tickets sold = total number of visitors = 140

Hence, the number of young visitors = 80, the number of middle age visitors = 40 and the number of old visitors = 20

The given data can be tabulated as follows.

Question 1

Since half of the platinum tickets were purchased by young visitors, the remaining half were purchased by old and middle age visitors. Since these two are equal, half of total number of platinum tickets should be an even number. Among the given values, this is possible only for 32 and 36.

In case of 36, Old- Platinum = 9. In that case 2a = 11. But this is not possible. Hence, the total number of platinum tickets sold can only be 32.

Ans : 32

Question 2

Let Old – platinum = Middle aged – Economy = x

We get x + 2a = 20 and a + x + 38 = 55

By solving these two equations we get x = 3.

Ans : 3

Question 3

If the number of Old visitors buying Gold tickets was strictly greater than the number of Young visitors buying Gold tickets, then the number of Middle-aged visitors buying Gold tickets was

The maximum possible value of Young - gold = x – 1

Then young – platinum = 80 – (38 + x – 1) = 43 – x

Hence, Old – platinum + Middle age – Platinum = 43 – x

Total old + Middle age = 60

(Old – platinum + Middle age – platinum) + (Old – gold + Middle age – gold ) + (Old – economy + Middle age – economy) = 60

Hence, Old – gold + Middle age – gold = x

Thus, Middle age – gold = 0

Ans : Zero

Question 4

Since Old – Economy + Middle age – economy = 17, these two can never be equal. Hence, the statement that “The numbers of Old and Middle-aged visitors buying Economy tickets were equal” is false.

Ans : “The numbers of Old and Middle-aged visitors buying Economy tickets were equal”

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