## DILR – Data Interpretation – Set

The following set contains four questions related to Data Interpretation. Choose the best answer to each question.

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:

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.

Q 1. Considering all companies’ products, which product category had the highest revenue?

a) Doubtful

b) Blockbuster

c) Promising

d) No-hope

Q 2. Which of the following is the correct sequence of numbers of products Bravo had in No-hope, Doubtful, Promising and Blockbuster categories respectively?

a) 3,3,1,2

b) 1,3,1,3

c) 1,3,1,2

d) 2,3,1,2

Q 3. Which of the following statements is NOT correct?

a) The total revenue from No-hope products was less than the total revenue from Doubtful products

b) Bravo and Charlie had the same revenues from No-hope products

c) Alfa’s revenue from Blockbuster products was the same as Charlie’s revenue from Promising products

d) Bravo’s revenue from Blockbuster products was greater than Alfa’s revenue from Doubtful products

Q 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?

a) 30

b) 40

c) 24

d) 34

Solution:

First of all , let do numbering for all the boxes and also divide the product ingiven four category on the basis of their respective M.P and P.P score :

Now from the given information following table can be made for the product and the companie they belong to :

 Company Product Alfa 1,3,4,7/8 Bravo 2,6,10 Charlie 5, 7/8, 9, 11

1. The areas of all the products in the different categories are as given below:

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 will have highest revenue.

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

So The correct sequence is 1, 3, 1, 2

Answer: c) 1, 3, 1, 2

3. We can check and find that only statement made in option d) Bravo’s revenue from Blockbuster products was greater than Alfa’s revenue from Doubtful products is not true. As

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

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

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

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## DILR – Data Interpretation – Set

The following set contains four questions related to Data Interpretation. Choose the best answer to each question.

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:

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

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.

Q 1. What is the weight of the faculty quality parameter?

a) 3

b) 2

c) 4

d) 1

Q 2. How many colleges receive the accreditation of AAA?

Q 3. What is the highest overall score among the eight colleges?

Q 4. How many colleges have overall scores between 31 and 40, both inclusive?

a) 1

b) 0

c) 3

d) 2

Solution:

Let f, r, p and i be the weights of parameters F, R, P and I respectively.

From point I), 30f + 20r + 20p + 40i > 40f + 30r + 20p + 20i

Or 2i > f + r ————-1)

From point II), 40f + 30r + 20p + 20i > 40f + 20r + 20p + 30i

OR  r > i ———————-2)

From point III), 50f + 50r + 40p + 50i > 50f + 50r + 50p + 40i

OR i  > p ————–3)

So from eq 1) , 2) and eq 3)

r > i > p and 2i > f+r so i > f

Thus r = 0.4 , i = 0.3 , p = 0.2 and f = 0.1

Now following table can be made :

 F(0.1) R(0.4) P(0.2) I (0.3) Total A-one 5 20 10 12 47 Best Ed 4 12 4 6 26 Cosmopolitan 4 8 4 9 25 Dominance 2 8 8 9 27 Education Aid 5 20 8 15 48 Fancy 5 20 8 12 45 Global 3 0 4 6 13 High Q 3 8 4 12 27

Now all questions can be answered.

1. d) 0.1

2. 3

3. 48

4. b) 0

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## DILR – Logical Reasoning – Set

The following set contains four questions related to Logical Reasoning. Choose the best answer to each question.

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.

Q 1. 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?

a) 38

b) 32

c) 36

d) 34

Q 2. 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

Q 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

Q 4. Which of the following statements MUST be FALSE?

a) The numbers of Gold and Platinum tickets bought by Young visitors were equal

b) The numbers of Middle-aged and Young visitors buying Gold tickets were equal

c) The numbers of Old and Middle-aged visitors buying Economy tickets were equal

d) The numbers of Old and Middle-aged visitors buying Platinum tickets were equal

Solution: Let the number of old visitors = x so number of middle aged and young visitors will be 2x and 4x respectively. So x+2x+4x=140 or x=20

Let total number of platinum ticket sold = p (even)

Now on the basis of information given following table can be made:

 Old Middle-aged young Total Platinum p/2 p Gold a 43 – p/2 – a 42 – p/2 85 – p Economy a 17 – a 38 55 Total 20 40 80 140

1. Given , the number of Old visitors buying Platinum tickets was equal to the number of Middle-aged visitors buying Platinum tickets, So

 Old Middle-aged young Total Platinum p/4 p/4 p/2 p Gold a 43 – p/2 – a 42 – p/2 85 – p Economy a 17 – a 38 55 Total 20 40 80 140

Now old = 40 so 2a + p/4 = 20

Or a + p/8 = 10

As p/8 must be an integer so p must be a multiple of 8. Thus option a) 38, c) 36 and d)34 get eliminated.

Only possible option is b) 32

2. Given, the number of Old visitors buying Platinum tickets was equal to the number of Middle-aged visitors buying Economy tickets So

 Old Middle-aged young Total Platinum x p/2 p Gold a 42 – p/2 Economy a x 38 55 Total 20 40 80 140

So

2a + x = 20—–1) and

a+x + 38 =55——-2)

By solving above equations a = 3

So the number of Old visitors buying Gold tickets = 3

3. The number of Old visitors buying Gold tickets was strictly greater than the number of Young visitors buying Gold tickets, so 42 – p/2 < a

Or a + p/2 > 42

So minimum value of a + p/2 = 43

Number of Middle-aged visitors buying Gold tickets = 43 – (p/2 +a) = 0

4. Since Old – Economy + Middle age – economy = 17 which is odd so 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.

Answer: c) The numbers of Old and Middle-aged visitors buying Economy tickets were equal

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## DILR – Logical Reasoning – Set

The following set contains four questions related to Data Interpretation. Choose the best answer to each question.

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 ‘?’.

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

Q 1. What best can be said about the room to which Divya was allotted?

a) Definitely Room 102

b) Definitely Room 101

c) Either Room 101 or Room 102

d) Definitely Room 103

Q 2. Who else was in Room 102 when Ganeshan entered?

a) No one

b) Chitra

c) Akil

d) Divya

Q 3. When did Erina reach the venue?

a) 7:10 am

b) 7:15 am

c) 7:45 am

d) 7:25 am

Q 4. If Ganeshan entered the venue before Divya, when did Balaram enter the venue?

a) 7:15 am

b) 7:25 am

c) 7:45 am

d) 7:10 am

Solution:

From Chitra’s statement it is clear that Chitra and Fatima can not be in the same room. And also there will be 4 people in Fatima’s room and at least two people in Chitra’s room.

As there are only 7 people and 3 rooms . So the only possible case is that there must be exactly 1, 2 and 4 people in each room in any order.

Now from Balram’s statement it is clear that there were more than 2 people in room number 101. So number of people in room 101 = 4

As Ganeshan was in room number 102 so he/she must be there with Chitra as chitra was last one to enter his room. And E would be the last one to come.

These information can be tabulated as bellow

 Time (am) 7:10 7:15 7:25 7:30 7:40 7:45 Candidate Akil, G/D G/D/B B/G Chitra Fatima Erina

And

 Room no. 101 102 103 Candidate Akil, , Divya (D) Balram (B), Fatima Ganeshan , Chitra Erina

Now all questions can be answered

1. b) Definitely Room 101

2. a) no one

3. c) 7 : 45 am

4. b) 7 :25 am

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## DILR – Logical Reasoning – Set

The following set contains four questions related to Data Interpretation. Choose the best answer to each question.

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.

Q 1. How many units of currency A did the outlet buy on that day?

Q 2. How many units of currency C did the outlet sell on that day?

a) 6000

b) 19000

c) 22000

d) 3000

Q 3. What was the base exchange rate of currency B with respect to currency L on that day?

Q 4. What was the buying exchange rate of currency C with respect to currency L on that day?

a) 90

b) 10

c) 20

d) 95

Solution:

Given,

The base exchange rates (BER) of currencies A, B and C with respect to L is in the ratio 100 : 120 : 1. Also The buying exchange rates (BR) of each of A, B, and C with respect to L will be in the ratio  = 95 : 114: 0.95 and corresponding selling rates (SR) will be 110, 132 and 1.1 respectively as it is 10% more than base exchange rates.

The given information can be tabulated as follows:

 A B C BER 100x 120x x BR 95x 114x 0.95x SR 110x 132x 1.1x Net Addition 800 0 3000

From point 4) The outlet received 88,000 units of L by selling A.

From point 2) & 3)  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.

Let the base exchange rates for A, B and C 100x,120x and x .

Units sold of A = 88,000/110x = 800/x.

As the net addition is 800, the units of A bought is 800 + 800/x

Amount of L used in buying 800 + 800/x units is (800 +800/x)×0.95 × 100x = 76000(x+1) .

Now As the amount used to buy A and B are in the ratio 5 : 3,

The amount used to buy B is 76000(x+1) /5 X 3 = 45,600(x+1)

Number of units of B bought = 45,600(x+1)/114x = 400(x+1)/x

As the net addition of B is zero, number of units of B sold = 400(x+1)/x

The amount received form selling A = 88,000

As given 88,000 : 52800(x+1) = 5 : 9

880/528(x+1) = 5/9

(x+1) = 880*9/558*5 = 3

x = 2

1. The units of A bought is 800 + 800/x = 800+ 800/2 = 1200

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

3. The base exchange rate of currency B with respect to L is 120x = 120*2 = 240

4. The buying exchange rate of currency C with respect to L on that day was 0.95x = 1.9

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## DILR – Logical Reasoning – Set

The following set contains four questions related to Data Interpretation. Choose the best answer to each question.

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.

Q 1. What best can be concluded about the code for the letter L?

a) 6

b) 8

c) 1 or 8

d) 1

Q 2. What best can be concluded about the code for the letter B?

a) 1 or 3 or 4

b) 3 or 4

c) 3

d) 1

Q 3. For how many digits can the complete list of letters associated with that digit be identified?

a) 1

b) 3

c) 2

d) 0

Q 4. Which set of letters CANNOT be coded with the same digit?

a) S,U,V

b) X,Y,Z

c) I,B,M

d) S,E,Z

Solution:

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

So from first and 2nd last word of sentence that is from the coding of peacock and of  we can say  9 is the code for o and c .  It means F is coded as 7 from the word of.

Now from 2nd word (is ) and the 3rd last word (bird) we can say the code for ‘I’ is 3. So S is coded as 5 from the word is and A is coded as 6 from the word ‘as’.

Now N is coded as 6 from the word national. Thus the only alphabet left in the word India ‘D ‘ is coded as 1. T is coded as 8 from the word ‘the’ and ‘National’ similarly E is coded as 5 from the word designated. Thus H is coded as 4 from the word ‘the’. Also 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’.

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’.

So following table can be made for the letters and their code digit

 Code Letter 1 D,L 2 3 I 4 H 5 S,E 6 A,N 7 F,G 8 T,P,K 9 O,C

Now all the questions can be answered.

1. d) 1

2. b) 3 or 4

3. c) 2 , for 8 and 9

4. a) S,U,V , as S and E are already coded with 5 and one digit can not be coded for more than 3 letters.

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## DILR – Logical Reasoning – Set

The following set contains four questions related to Data Interpretation. Choose the best answer to each question.

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.

Q 1. What is the minimum number of students enrolled in both G and L but not in K?

Q 2. 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?

a) 19

b) 22

c) 17

d) 18

Q 3. 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?

Q 4. 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?

a) 7

b) 5

c) 8

d) 6

Solution:

Let the number of students enrolled in all the three sports = g and

The number of students enrolled only in K = a

So from point 1) The number of students enrolled only in L = 2g

And from point 3) The number of students enrolled only in  G = 2g – 1

So on the  basis of information given, following Venn Diagram can be made,

From point 6) , b+c+g=10——1)

From point 2) (2g-1)+b+c+g=17——2)

From eq 1) & eq 2)

(2g-1)=7 or g=4

As total number of students = 39

So (2g-1)+b+c+g +(2g+a-g+a )=39
17+(2g+a-g+a )=39
17+4+2a=39
a = 9

So final Venn diagram will look like,

As number of students in L is maximum , so 8+6-b>9+b or b<2.5

So b can be either 0, 1 or 2 .

1. Minimum number of students enrolled in both G and L but not K = 6 –b

So it will be minimum ,when b is maximum which is 2. So

Minimum number of students enrolled in both G and L but not K = 6 -2 = 4

2. As per above question maximum and minimum possible number of student in L are 23 and 21 respectively . So required ratio will be 19 : 22 if there is 22 students in L.

3. From g = 4, one person moves to (6-b), one person to b and two persons to (a-g) . after the withdrawal

4. d) 6

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## DILR – Data Interpretation – Set

The following set contains four questions related to Data Interpretation. Choose the best answer to each question.

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.

Q 1. The brand that had the highest revenue in 2016 is:
a) Cxqi
b) Bysi
c) Dipq
d) Azra

Q 2. The brand that had the highest profit in 2016 is:
a) Dipq
b) Azra
c) Cxqi
d) Bysi

Q 3. The brand that had the highest profit in 2017 is:
a) Bysi
b) Azra
c) Dipq
d) Cxqi

Q 4. The complete list of brands whose profits went up in 2017 from 2016 is:
a) Azra, Bysi, Cxqi
b) Bysi, Cxqi, Dipq
c) Cxqi, Azra, Dipq
d) Azra, Bysi, Dipq

Solution:

For question number 1 and 2: Let the total market size in 2016 be 100x units. The sales of Azra, Bysi, Cxqi and dipq would be 40x,25x,15x and 20x units respectively.

So the revenue of Azra = 40x × 15,000 = 6,00,000x ,

profit = 10% of 6,00,000x = 60,000x

Revenue of Bysi = 25x ×20,000 = 5,00,000x

Profit = 30% of 500000x = 1,50,000x

Revenue of Cxgi = 15x × 30,000 = 4,50,000x

Profit = 40 % of 4,50,000x = 1,80,000x

Revenue of Dipq = 20x × 25,000 = 5,00,000x

Profit = 30 % of 5,00,000x = 1,50,000x

1. the for the year brand with the highest revenue is Azra.

2. maximum profit is 1,80,000 for Cxgi.

For question number 3 and 4: In 2017 Sales volume increased by 40% as compare to sales volume in 2016 so new sales volume = 140x and similarly market share of Cxgi went up by 15% point and others get down by 5 percentage point. The information can be tabulated as given bellow (Profit and revenue can be calculated as previous question )

Total Sales volume = 140x

 Brand Market Share (%) Selling price Profitability Revenue Profit Azra 35 15,000 10 7,35,000x 73,500x Bysi 20 20,000 30 5,60,000x 1,68,000x Cxgi 30 18,000 20 7,56,000x 1,51,200x Dipq 15 25,000 30 5,25,000x 1,57,500x

3. the profit is the highest for Bysi .

4. The profits increased for Azra (60,000 to 73,500) for Bysi (1,50,000 to 1, 68,000) and Dipq (1,50,000 to 1,57,500)

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## DILR – Logical Reasoning – Set

The following set contains four questions related to Logical Reasoning. Choose the best answer to each question.

Fuel contamination levels at each of 20 petrol pumps P1, P2, …, P20 were recorded as either high, medium, or low.

1. Contamination levels at three pumps among P1 – P5 were recorded as high.
2. P6 was the only pump among P1 – P10 where the contamination level was recorded as low.
3. P7 and P8 were the only two consecutively numbered pumps where the same levels of contamination were recorded.
4. High contamination levels were not recorded at any of the pumps P16 – P20.
5. The number of pumps where high contamination levels were recorded was twice the number of pumps where low contamination levels were recorded.

1) Which of the following MUST be true?

a) The contamination level at P20 was recorded as medium.

b) The contamination level at P10 was recorded as high.

c) The contamination level at P12 was recorded as high.

d) The contamination level at P13 was recorded as low.

2) What best can be said about the number of pumps at which the contamination levels were recorded as medium?

a) At least 8

b) More than 4

c) Exactly 8

d) At most 9

3) If the contamination level at P11 was recorded as low, then which of the following MUST be true?

a) The contamination level at P14 was recorded as medium.

b) The contamination level at P18 was recorded as low.

c) The contamination level at P15 was recorded as medium.

d) The contamination level at P12 was recorded as high.

4) If contamination level at P15 was recorded as medium, then which of the following MUST be FALSE?

a) Contamination level at P14 was recorded to be higher than that at P15.

b) Contamination levels at P13 and P17 were recorded as the same.

c) Contamination levels at P11 and P16 were recorded as the same.

d) Contamination levels at P10 and P14 were recorded as the same.

Solution:

From point 2) we can say that P6 was the only pump among P1 – P10 where the contamination level was recorded as low and in other pipe it can be either medium or high .

From point 3) only P7 and P8 were the only two consecutively numbered pumps where the same levels of contamination were recorded

And From point 1) Contamination levels at three pumps among P1 – P5 were recorded as high it means P1 , P3 and P5 have high Contamination level and P2 and P4 will have medium Contamination level. Thus we get two possible cases for P1 to P10 .

Case a )

 P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 H M H M H L H H M H

Case b)

 P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 H M H M H L M M H M

From point 5)

H = 2L

Thus H + L = 3L must be multiple of 3.

Case 1) From point 4)  High contamination levels were not recorded at any of the pumps P16 – P20.

So maximum possible number of pipe with High contamination levels = 8 (P1,P3,P5,P7,P8 ,P10 , P12 and P14)

In this case number of pipes with Low contamination levels = 8/2 = 4

So medium (M) = 8

The possible arrangement will be

 P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P20 H M H M H L H H M H M H M H M/L L/M M/L L/M M/L L/M

Or

 P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P20 H M H M H L H H M H L M H M H M L M L M

Case 2) if Low contamination levels pipes were minimum , which can be 3,then number of pipes with high contamination level = 6

Number of pipes with medium contamination level = 11 which is not possible .

So only case 1) is possible

Now all the questions can be answered.

1) b) The contamination level at P10 was recorded as high

2) c) Exactly 8

3) a) The contamination level at P14 was recorded as medium

4) c) Contamination levels at P11 and P16 were recorded as the same.

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## DILR – Logical Reasoning – Set

The following set contains four questions related to Logical Reasoning. Choose the best answer to each question.

Twenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees:

1. The numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee.
2. The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees.
3. 60% of the politicians are in the administration committee, and 20% are in the teaching committee.

1) Based on the given information, which of the following statements MUST be FALSE?

a) The size of the research committee is less than the size of the teaching committee

b) In the teaching committee the number of educationalists is equal to the number of politicians

c) The size of the research committee is less than the size of the administration committee

d) In the administration committee the number of bureaucrats is equal to the number of educationalists

2) What is the number of bureaucrats in the administration committee?

3) What is the number of educationalists in the research committee?

4) Which of the following CANNOT be determined uniquely based on the given information?

a) The size of the teaching committee

b) The size of the research committee

c) The total number of educationalists in the three committees

d) The total number of bureaucrats in the three committees

Solution:

Let the number of bureaucrats in the research committee = x and total number of politicians = y

From point 1) Then number of bureaucrats in the teaching and administration committees will be x and 4x/3 respectively.

From point 3) number of the politicians in the administration committee teaching committee will be 0.6y and 0.2y respectively.

Now let Number of educationalist in research , teaching and administration department are a, b and z   such that a > b and a = (b+z)/2 thus z > a > b and a+b+z = 3a

From the given information following table can be made :

 Research Teaching Administration Total Bureaucrats x x 4x/3 10x/3 Politicians 0.2y 0.2y 0.6y y Educationalist a > b b z 3a

Now as all the values in the table must be integers so minimum value of x = 3 and y = 5 also

10x/3 + y + 3a = 24

So the only possible value for a, x and y are 3, 3 and 5 . Thus the table with required number of people in each committees will be

 Research Teaching Administration Total Bureaucrats 3 3 4 10 Politicians 1 1 3 5 Educationalist 3 2 4 9 Total 7 6 11

Or

 Research Teaching Administration Total Bureaucrats 3 3 4 10 Politicians 1 1 3 5 Educationalist 3 1 5 9 Total 7 5 12 24

Now all the question can be answered :

1) a) The size of the research committee is less than the size of the teaching committee

2) 4

3) 3

4) a) The size of the teaching committee

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