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This mock test of CAT LRDI MCQ - 4 for CAT helps you for every CAT entrance exam.
This contains 32 Multiple Choice Questions for CAT CAT LRDI MCQ - 4 (mcq) to study with solutions a complete question bank.
The solved questions answers in this CAT LRDI MCQ - 4 quiz give you a good mix of easy questions and tough questions. CAT
students definitely take this CAT LRDI MCQ - 4 exercise for a better result in the exam. You can find other CAT LRDI MCQ - 4 extra questions,
long questions & short questions for CAT on EduRev as well by searching above.

QUESTION: 1

Group Question

Answer the following question based on the information given below.

In the placement season of a leading management institute, all the available placements were offered to the prospective candidates in such a way that all the candidates got at least one job. The placements were from the following industries: Infrastructure, Services and Consultancy. None of the candidates got more than one job from the same industry.

There were 15 candidates who got placed in exactly one industry, while the number of candidates who got placed in all the three industries was not more than 5. The number of candidates who got placed in at least two industries, one of which is Services, was more than those who got placed in Infrastructure as well as Consultancy. The number of candidates who did not get placed in Services was the same as those who did not get placed in Consultancy, but was different from those who did not get placed in Infrastructure.

The number of candidates who got placed in Services as well as Consultancy was one more than those who got placed in Infrastructure as well as Services, but was one less than those who got placed in Infrastructure as well as Consultancy. The number of candidates who got placed only in Infrastructure was the same as those who got placed in Services as well as Consultancy, but not in Infrastructure.

It was further known that the number of prospective candidates that this institute had was less than 40.

Q. What was the maximum possible number of placements that were offered to the candidates in this institute?

Solution:

Let the number of candidates who got placed in only Infrastructure be x. Then, the number of candidates who got placed in Services as well as Consultancy, but not in Infrastructure is also x.

Let y be the number of candidates who got placed in all the three industries, then we have y < 5 ... (i)

Let z be the number of candidates who got placed in only Consultancy. Then, we have the following graphical representation:

Now, the number of candidates who got placed in Services as well as Consultancy was one more than those who got placed in Infrastructure as well as Services, but was one less than those who got placed in Infrastructure as well as Consultancy. Since the number of candidates who got placed in Services as well as Consultancy (but not Infrastructure) is jc, hence the number of candidates who got placed in Infrastructure as well as Services (but not Consultancy) is (x - 1) and the number of candidates who got placed in Infrastructure and Consultancy (but not services) would be (x + 1).

Let p be the number of candidates who got placed in only Services. Since the number of candidates who did not get placed in Services is the same as those who did not get placed in Consultancy, we have:

x + (x - 1) +p = x + (x + 1) + z; implying that p = z + 2 Hence, the final distribution would be as shown below:

Now, since the total number of candidates in this institute was less than 40, we have;

4x + y + 2z + 2 < 40

Implying that 4x + y + 2z < 3 8 ... (ii)

Further, since the number of candidates who got placement from exactly one industry was 15, we have:

x + 2z + 2 = 15, implying x + 2z = 13 ... (iii)

From (ii) and (iii), we get, 3x + y < 25 ... (iv)

Now, since y cannot be negative, we have x < 8 ...(v)

The number of candidates who got placed in at least two industries, one of which is Services, is more than those who got placed in Infrastructure as well as Consultancy. Hence, we have,

2x+y—>x+y+_{9} implying x > 2

Thus, we have, 2 < x < 8 and further from (iii) x can take only odd values, hence x = 3 or 5 or 7

Case 1: If x = 3, then z = 5 Case 2: If x = 5, then z = 4 Case 3: Ifx = 7, thenz = 3

However, the number of candidates who did not get placed in Services was different from those who did not get placed in Infrastructure; i.e. 2x + z + 1 ^ x + 2z + 2 i.e. x^z + 1

Thus, Case 2 gets eliminated.

Hence, now we have two possibilities:

Since we are supposed to maximize the number of placements, this would be possible in Case 2, where the total number of candidates is 36 + y. Now since the maximum number of candidates in this institute is less than 40, we have 36 +y = 39, implying thaty = 3. Note that in Case 1, even though we get the total number of candidates as 24 +y = 39, implying thaty =15. However, since the maximum possible value ofy can be 5, the total number of placements can be (3 + 5 + 7) + 2(2 + 4 + 3) + 3(5) = 48.

Hence, from Case 2, the maximum number of placements would be: (7 + 5 + 3) + 2(6 + 8 + 7) + 3(3) = 15 + 42 + 9 = 66

Hence, option 4.

QUESTION: 2

In the placement season of a leading management institute, all the available placements were offered to the prospective candidates in such a way that all the candidates got at least one job. The placements were from the following industries: Infrastructure, Services and Consultancy. None of the candidates got more than one job from the same industry.

There were 15 candidates who got placed in exactly one industry, while the number of candidates who got placed in all the three industries was not more than 5. The number of candidates who got placed in at least two industries, one of which is Services, was more than those who got placed in Infrastructure as well as Consultancy. The number of candidates who did not get placed in Services was the same as those who did not get placed in Consultancy, but was different from those who did not get placed in Infrastructure.

The number of candidates who got placed in Services as well as Consultancy was one more than those who got placed in Infrastructure as well as Services, but was one less than those who got placed in Infrastructure as well as Consultancy. The number of candidates who got placed only in Infrastructure was the same as those who got placed in Services as well as Consultancy, but not in Infrastructure.

It was further known that the number of prospective candidates that this institute had was less than 40.

Which of the following can be the number of candidates in this institute?

Solution:

In case 1, the range of number of candidates can be from 24 (24 + 0) to 29 (24 + 5)

In case 2, the number of candidates can be from 36 (36 + 0) to 39 (since the number of prospective candidates that the institute had was less than 40)

Hence, option 4.

QUESTION: 3

In the placement season of a leading management institute, all the available placements were offered to the prospective candidates in such a way that all the candidates got at least one job. The placements were from the following industries: Infrastructure, Services and Consultancy. None of the candidates got more than one job from the same industry.

There were 15 candidates who got placed in exactly one industry, while the number of candidates who got placed in all the three industries was not more than 5. The number of candidates who got placed in at least two industries, one of which is Services, was more than those who got placed in Infrastructure as well as Consultancy. The number of candidates who did not get placed in Services was the same as those who did not get placed in Consultancy, but was different from those who did not get placed in Infrastructure.

The number of candidates who got placed in Services as well as Consultancy was one more than those who got placed in Infrastructure as well as Services, but was one less than those who got placed in Infrastructure as well as Consultancy. The number of candidates who got placed only in Infrastructure was the same as those who got placed in Services as well as Consultancy, but not in Infrastructure.

It was further known that the number of prospective candidates that this institute had was less than 40.

If there were a maximum of 35 candidates in the institute then which of the following statements is/are definitely true?

Solution:

If there were a maximum of 35 candidates then only case 1 would be possible, and the range of students can be from 24-29.

Consider the candidates who had got placed in say: Infrastructure is 9+y and those who did not get placed in Infrastructure was 15. The maximum possible value of y is 5; hence the number of candidates who got placed in Infrastructure can be atmost 14. Hence redistribution is not possible.

Hence statement 1 is definitely true.

Statement 2 is evident as the number of candidates who got placed in two industries was 9.

Hence both the statements are true.

Hence, option 3.

QUESTION: 4

Group Question

Answer the following question based on the information given below.

The bar graph below shows the performance of company A.

Approximately, what is the percentage increase in the production of company A from 2011 to 2013?

Solution:

The production of company A in 2011 = 35000 and sales in 2013 = 60000

••• Percentage increase = (60 — 35) x 100/35 ~ 71

Hence, option 1.

QUESTION: 5

The bar graph below shows the performance of company A.

In which year is the ratio of sales to production the least if the ratio in 2010 was 0.63?

Solution:

The ratio of sales to production in 2011 = 0.57, in 2012 = 0.66 and in 2013 = 0.75

The ratio was least in 2011 = 0.57

Hence, option 1.

*Answer can only contain numeric values

QUESTION: 6

Group Question

Answer the following question based on the information given below.

The population of three countries are represented by the area of base and two circular sections of a cone of radius 13 km and height 63 km.

P_{2} and P3 are the populations of countries T_{1?} T_{2} and T_{3} respectively.

The following three pie charts show the percentage of males and females above 18 years of age and males and females below 18 years of age in the three countries.

By how many percent is the number of females below 18 years of age in T_{1} greater than the number of males above 18 years of age in T_{3}?

Solution:

Let the radius of cone be r.

Then by similarity of triangles, the radii of the circle representing T_{2 }and T_{3} are 2r/3 and r/3 respectively.

∴ Areas of circles representing T_{1}, T_{2} and T_{3} are

Number of females below 18 years of age in T1

Number of males above 18 years of age in T_{3
}

∴ Required percentage Difference

Answer: 800

*Answer can only contain numeric values

QUESTION: 7

The population of three countries are represented by the area of base and two circular sections of a cone of radius 13 km and height 63 km.

P_{2} and P3 are the populations of countries T_{1?} T_{2} and T_{3} respectively.

The following three pie charts show the percentage of males and females above 18 years of age and males and females below 18 years of age in the three countries.

If 50% of females below 18 years of age from T2 migrate to T3, by how many percent will the female population of T3 increase? (Round off your answer to the nearest integer.)

Solution:

50% of female population below 18 years from T_{2}

Now, angle represting female population of T_{3} = 120° + 60° = 180°

∴ Female population of T_{3} increases by

Answer: 67

QUESTION: 8

Group Question

Answer the following question based on the information given below.

A consulting firm carried out a perception mapping exercise for 15 companies and plotted the results as shown below. The perception mapping was done on the basis of two parameters : the trust of products (made by each company) among the customers and the popularity of the company among customers. The consulting firm plotted popularity on the X-axis and trust on the Y-axis. Each company received a rating from -10 to +10 for both the parameters. A rating of+10 was considered to be the highest while that of-10 was considered to be the lowest.

Each company was given the result and the consulting firm bagged the contract to improve the ratings for these companies. To improve the ratings on each parameter, the consulting firm charged each company as per the tariff structure shown in the table below. It improved the performance of the company based on marketing needs and product manufacturing. To improve the trust ratings, the consulting firm suggested a mechanism to improve the product while it suggested marketing ideas to improve the popularity ratings of the company. The tariff worked on the mechanism of pills wherein each pill would improve a certain parameter for the company as shown below. For example, a White Pill would cost the company Rs. 9 Lakhs and it would improve the popularity rating of the company by 1 point but would decrease the trust rating of the company by 0.5 points.

Based on historical data, the consulting firm identified the maximum success rate for each firm as shown by the graph below. Thus, even though a particular Pill could theoretically improve a rating up to a certain level, the actual improvement would be constrained by the success rate shown in the graph below. For instance, if Company A took a White Pill then, at the most, the consulting firm could have improved the popularity rating by 0.8 points (80% of 1) but the trust rating would still go down by 0.5 points. Also, the amount charged would still be the same though for all the companies for that pill.

Answer the questions below based on the data given above.

What is the maximum percentage increase in the popularity rating of 3 Company E if it takes 2 White Pills and 1 Blue Pill?

Solution:

The popularity rating of Company E is currently at -6 points.

If Company E takes 2 Whilte Pills and 1 Blue Pill, its popularity rating can improve by (2 x 1) + 0.5 = 2.5 points.

However, the success rate for Company E is 90%

Therefore, the actual maximum increase in the popularity rating = 0.9 x 2.5 = 2.25 points.

Therefore, the new popularity rating = -6 + 2.25 = -3.75 Therefore, the maximum percentage increase in the popularity rating =

[(-6)-(-3.75)]/(-6)}xl00 = (2.25/6) x 100 = 37.5%

Hence, option 1.

QUESTION: 9

A consulting firm carried out a perception mapping exercise for 15 companies and plotted the results as shown below. The perception mapping was done on the basis of two parameters : the trust of products (made by each company) among the customers and the popularity of the company among customers. The consulting firm plotted popularity on the X-axis and trust on the Y-axis. Each company received a rating from -10 to +10 for both the parameters. A rating of+10 was considered to be the highest while that of-10 was considered to be the lowest.

Each company was given the result and the consulting firm bagged the contract to improve the ratings for these companies. To improve the ratings on each parameter, the consulting firm charged each company as per the tariff structure shown in the table below. It improved the performance of the company based on marketing needs and product manufacturing. To improve the trust ratings, the consulting firm suggested a mechanism to improve the product while it suggested marketing ideas to improve the popularity ratings of the company. The tariff worked on the mechanism of pills wherein each pill would improve a certain parameter for the company as shown below. For example, a White Pill would cost the company Rs. 9 Lakhs and it would improve the popularity rating of the company by 1 point but would decrease the trust rating of the company by 0.5 points.

Based on historical data, the consulting firm identified the maximum success rate for each firm as shown by the graph below. Thus, even though a particular Pill could theoretically improve a rating up to a certain level, the actual improvement would be constrained by the success rate shown in the graph below. For instance, if Company A took a White Pill then, at the most, the consulting firm could have improved the popularity rating by 0.8 points (80% of 1) but the trust rating would still go down by 0.5 points. Also, the amount charged would still be the same though for all the companies for that pill.

What is the minimum number of pills that company K needs to take in order to exceed the position of Company C in both the popularity and trust Marks ratings?

Solution:

**Correct Answer :- B**

**Explanation : T**he current popularity and trust ratings of the two companies are as shown below:

Company C is at -8 on Popularity and -2 on Trust.

Company K is at -9 on Popularity and -8 on Trust.

Since company K wants to overtake company C, the ratings of company C need to be static and the success rate of only company K need to be considered.

Also, since the number of pills is to be minimised, the pill chosen should be such that it either improves ratings on both the parameters simultaneously or does not negatively impact the rating on any parameter.

Therefore, company K needs to take either Black, Red or Blue pills.

Now, note that the success rate for company K is 80%.

Also, company K needs more than 6 points on Trust and more than 1 point on Popularity to exceed Company C.

Therefore, it should take a pill that gives it maximum improvement on the trust rating.

Since a Black Pill does not provide any improvement on trust, company K can only take a Blue or Red pill to improve Trust.

Company K would require 8 Red Pills to exceed company C on trust i.e 8 x 0.8 x 1 = 6.4 points.

However, there would be no improvement in the popularity ratings.

Now, it would need 2 Blue pills to exceed company C on popularity i.e. 2 x 0.8 x 1 = 1.6 points.

Thus, in such a case, company K would need a minimum of 10 pills.

QUESTION: 10

A consulting firm carried out a perception mapping exercise for 15 companies and plotted the results as shown below. The perception mapping was done on the basis of two parameters : the trust of products (made by each company) among the customers and the popularity of the company among customers. The consulting firm plotted popularity on the X-axis and trust on the Y-axis. Each company received a rating from -10 to +10 for both the parameters. A rating of+10 was considered to be the highest while that of-10 was considered to be the lowest.

Each company was given the result and the consulting firm bagged the contract to improve the ratings for these companies. To improve the ratings on each parameter, the consulting firm charged each company as per the tariff structure shown in the table below. It improved the performance of the company based on marketing needs and product manufacturing. To improve the trust ratings, the consulting firm suggested a mechanism to improve the product while it suggested marketing ideas to improve the popularity ratings of the company. The tariff worked on the mechanism of pills wherein each pill would improve a certain parameter for the company as shown below. For example, a White Pill would cost the company Rs. 9 Lakhs and it would improve the popularity rating of the company by 1 point but would decrease the trust rating of the company by 0.5 points

Based on historical data, the consulting firm identified the maximum success rate for each firm as shown by the graph below. Thus, even though a particular Pill could theoretically improve a rating up to a certain level, the actual improvement would be constrained by the success rate shown in the graph below. For instance, if Company A took a White Pill then, at the most, the consulting firm could have improved the popularity rating by 0.8 points (80% of 1) but the trust rating would still go down by 0.5 points. Also, the amount charged would still be the same though for all the companies for that pill.

Which of the following statements is definitely true?

I. Both L and J can take 2 White Pills each.

II. M needs at least 4 pills to exceed the position of A in both the parameters.

III. The cost incurred by F to exceed B on Trust is less than Rs. 25 Lakhs.

Solution:

Consider Statement I:

The popularity and trust rating of company L is 3 and 9 respectively.

Also, its success rate is 75%.

Therefore, if it takes 2 White Pills, its popularity rating would improve by 2 x 1 x 0.75 i.e. 1.5 points, while its trust rating would go down by 2 x 0.5 x 0.75 i.e. 0.75 points.

Therefore, the new popularity and trust ratings for company L would be 4.5 and 8.25, which are both valid values.

The popularity and trust rating of company J is 9 and -5 respectively. Also, its success rate is 70%.

Therefore, if it takes 2 White Pills, its popularity rating would improve by 2 x l x 0.7 i.e. 1.4 points, while its trust rating would go down by 2 x 0.5 x 0.7 i.e. 0.7 points.

Therefore, the new popularity and trust ratings for company J would be 10.4 and -5.7.

However, the maximum rating that a company have is +10.

Therefore, company J cannot take 2 White Pills.

Therefore, statement I is false.

Hence, option 1 can be eliminated.

Consider Statement II:

The popularity and trust ratings for M are -8 and 5 respectively while the corresponding ratings for company A are -7 and 7 respectively.

Thus, M needs to gain more than 2 points on trust and more than 1 point on popularity.

The success rate of M is 85%.

Thus, it has to take a minimum of 1 Black Pill, 2 Red Pills and 1 Blue Pill to overtake A on both parameters.

Thus, M needs atleast 4 pills to exceed the position of A on both parameters.

Hence, statement II is definitely true.

Hence, option 3 can be eliminated.

Consider Statement III:

The trust ratings for F and B are -7 and -5 respectively.

Thus, F need to improve by more than 2 points.

The success rate of F is 80%

To improve the trust ratings, F can use either the Yellow Pills or the Red Pills.

However, the Yellow Pills are cheaper and so they are used.

F will need 3 Yellow pills and the cost of the same would be 3 x 7 = Rs.

21 lakhs.

However, if the Red Pills are used, the cost is 3 x 12 = Rs. 36 lakhs.

Thus, the cost incurred by F to exceed B on the trust ratings is not necessarily less than Rs. 25 lakhs. Note that the statement does not mention “minimum cost”. Had it mentioned minimum cost, statement III would be definitely true. In the given scenario, statement III may or may not be true.

Hence, only statement II is definitely true.

Hence, option 2.

*Answer can only contain numeric values

QUESTION: 11

Each question is followed by two statements A and B. Answer each question using the following instructions.

Mark (1) if the question can be answered by using statement A alone but not by using statement B alone.

Mark (2) if the question can be answered by using statement B alone but not by using statement A alone.

Mark (3) if the question can be answered by using both the statements together but not by using either of the statements alone.

Mark (4) if the question cannot be answered on the basis of the two statements.

Is quadrilateral ABCD a rhombus?

1. The diagonals of quadrilateral ABCD intersect at 90°.

2. AB is parallel to CD.

Solution:

Using statement A alone:

We cannot conclude whether quadrilateral ABCD is a rhombus or not. This is because the diagonals of a rhombus do indeed intersect at 90°, but not all quadrilaterals with diagonals intersecting at 90° are rhombuses.

Using statement B alone:

We cannot conclude whether A is a rhombus or not. We have freedom to choose the sides of quadrilateral ABCD as we wish.

Combining both the statements A and B:

In a rhombus, the diagonals intersect at 90°. Also, if quadrilateral ABCD is a rhombus, AB is parallel to CD. However, we cannot be sure that a quadrilateral with one pair of opposite parallel sides and diagonals intersecting at 90° is a rhombus. Figure shows an example of a trapezium with the same conditions.

••• We cannot answer the question even after using both the statements A and B.

Answer: 4

*Answer can only contain numeric values

QUESTION: 12

1. Each question is followed by two statements A and B. Answer each question using the following instructions.

Mark (1) if the question can be answered by using statement A alone but not by using statement B alone.

Mark (2) if the question can be answered by using statement B alone but not by using statement A alone.

Mark (3) if the question can be answered by using both the statements together but not by using either of the statements alone.

Mark (4) if the question cannot be answered on the basis of the two statements.

Q. What is the difference in the cubes of the roots of the quadratic equation ax^{2} + bx + c = 0?

1. Sum of the roots of the quadratic equation is known.

2. Product of the roots of the quadratic equation is known.

Solution:

Let ‘α’ and ‘β' be the roots of the quadratic equation ax^{2} + bx + c - 0

**Using statement A alone:**

We know the sum of the roots (i.c. a + p) of the quadratic equation ax^{2} + bx + c = 0

However, from these, we cannot find the difference in the cubes of the roots of ax^{2} + bx + c = 0

Thus, the question cannot be answered using statement A alone.

**Using statement B alone:**

We know the products of the roots (i.e. off) of the quadratic equation ax^{2} + bx + c = 0

However, from these we cannot find the difference in the cubes of the roots of ax^{2} + bx + c = 0

Thus, the question cannot be answered using statement B alone.

**Using both the statements together:**

We know the sum of the roots (i.e α + β) and product of the roots (i.e αβ) of the quadratic equation ax^{2} + bx + c = 0

From these we can find the difference in the roots (i.e. α - β) of the quadratic equation ax^{2} + bx + c = 0

We know, (α^{2} + β^{2} + αβ) = (α + β)^{2} - (αβ)

∴ (α^{3} - β^{3}) = (α - β) x (α^{2} + β^{2} + αβ)

Thus, the difference in the cubes of the roots can be found.

Thus, the question can be answered using both the statements together but not by using cither statement alone.

QUESTION: 13

Group Question

Answer the following question based on the information given below.

There are five energy drink manufacturers—Black Bull, Shockwave, Power Kick, Blue Ox and Kick Start. Each company uses five components Alpha, Beta, Gamma, Tera and Kappa in varied proportions in their drinks.

The table below gives the percentage of each of these components in the drug.

All manufacturers sell their drinks in bottles of 200 ml.

The effectiveness of each unit of components Alpha, Beta, Gamma and Tera is in the ratio 5 : 6 : 4 : 3, while Kappa is just a sweetener. Which of the following drinks is most effective?

Solution:

Let the effectiveness of Alpha, Beta, Gamma and Tera be 5x, 6x, 4x and 3x respectively.

The total effectiveness of all the drinks given in the options is:

Shockwave: (29 x 5x) + (23 x 6x) + (13 x 4x) + (15 x 3jc) = 380x Power Kick: (23 x 5x) + (15 x 6x) + (17 x 4x) + (27 x 3x) = 354x Blue Ox: (20 x 5x) + (28 x 6x) + (12 x 4x) + (25 x 3x) = 391x Kick Start: (17 x 5jc) + (20 x 6x) + (23 x 4x) + (18 x 3x) = 35 lx Therefore the most effective drink is Blue Ox.

Hence, option 3.

QUESTION: 14

There are five energy drink manufacturers—Black Bull, Shockwave, Power Kick, Blue Ox and Kick Start. Each company uses five components Alpha, Beta, Gamma, Tera and Kappa in varied proportions in their drinks.

The table below gives the percentage of each of these components in the drug.

Which drink has the least ratio of content of Gamma to the total content of Beta and Kappa?

Solution:

The required ratio for the drinks given in the options is:

Black Bull: 20/(18 + 27) = 0.4444 Shockwave: 13/(23 + 20) = 0.3023

Power Kick: 17/(15 + 18) = 0.5151 Blue Ox: 12/(28 + 15) = 0.2791

The required ratio is least for Blue Ox.

Hence, option 1.

*Answer can only contain numeric values

QUESTION: 15

Group Question

Answer the following question based on the information given below.

The tables below provide data about the age, expenditure on clothes and expenditure on food for employees of a certain company.

In table A, for the age given in the first column, the second column gives the number of employees not exceeding that age. Thus, as per the first entry, there are 11 employees aged 24 years or less.

Tables B and C are also to be read in a similar manner.

Between two employees, if the age of one person is greater than the other, his expenditure on clothes as well as on food will also be more than the other.

How many employees having an age more than 30 years spent more than 1.5 lakhs on clothes and a maximum of 4.18 lakhs on food?

Solution:

There were 60 employees having an age less than or equal to 30 years and there were 100 employees under consideration.

Thus, the number of employees having an age greater than 30 years is 100 - 60 = 40 years.

Similarly, the number of employees who spent more than 1.5 lakhs on clothes and the number of employees who spent more than 4.18 lakhs on food can be found as shown in the table below.

A person who is older than another person also spends more than the other person.

Therefore, the number of employees who are above 30 years and spent more than 1.50 lakhs on clothes is 25.

Out of these 25 employees, 9 spent more than 4.18 lakhs on food.

••• Number of employees having an age more than 30 years, who spent more than 1.50 lakhs on clothes and a maximum of 4.18 lakhs on food = 25-9=16

Answer: 16

*Answer can only contain numeric values

QUESTION: 16

The tables below provide data about the age, expenditure on clothes and expenditure on food for employees of a certain company.

In table A, for the age given in the first column, the second column gives the number of employees not exceeding that age. Thus, as per the first entry, there are 11 employees aged 24 years or less.

Tables B and C are also to be read in a similar manner.

Between two employees, if the age of one person is greater than the other, his expenditure on clothes as well as on food will also be more than the other.

Among employees older than 26 years but not exceeding 32 years, how many spent more than 3.18 lakhs on food?

Solution:

Number all the employees from 1 to 100 in increasing order of their age.

Thus, employees with an age not more than 26 years are numbered 1 to 26

The first employee having an age greater than 26 years is numbered 27.

So, employees with their age greater than 26 years are numbered 27 to 100.

Thus, the last employee whose age does not exceed 32 years is numbered Marks 77.

Thus, employees older than 26 years but not exceeding 32 years are those numbered 27 to 77.

Now, as the employees numbered 1 to 33 spent less than 3.18 lakhs on food, those who spent more than that are employees numbered 34 to 100

Employees who spent more than 3.18 lakhs and are older than 26

years, but not older than 32 years are those numbered from 34 to 77.

Thus, the number of such employees = 77 - 34 + 1 = 44

Answer: 44

QUESTION: 17

Group Question

Answer the following question based on the information given below.

Pankeet and Ajay are playing a word game with each other. The game is such that it involves words of four distinct letters only. A player has to think of a secret word. Then, in turn, the opponent tries to guess the word of the player who gives the number of matches. If the matching letters are on their right positions, they are "bulls", if on different positions, they are "cows"

For example,

Secret Word: MUST

Guess: SUMP

Answer: 2 Cows and 1 Bull

The word must be guessed in the least number of attempts.

Pankeet has now thought of a secret word for Ajay. Ajay has guessed some words and his position is as follows

For the questions below, use the above information to answer them

Which letter is surely present in the secret word thought by Pankeet?

Solution:

From the word MILK, we know that there are no letters out of ‘M’, T, ‘L’ and ‘K’ as 0 Cows and 0 Bulls.

The word MAKE has ‘A’ in 2^{nd} position and it is been given 1 Cow while the word DARK has ‘A’ in 2^{nd} position too but it is given a Bull.

Thus, ‘A’ cannot be present in the secret word.

Now from MAKE, we only have ‘E’ Thus, ‘E’ is surely present

Hence, option 4.

QUESTION: 18

Answer the following question based on the information given below.

Pankeet and Ajay are playing a word game with each other. The game is such that it involves words of four distinct letters only. A player has to think of a secret word. Then, in turn, the opponent tries to guess the word of the player who gives the number of matches. If the matching letters are on their right positions, they are "bulls", if on different positions, they are "cows"

For example,

Secret Word: MUST

Guess: SUMP

Answer: 2 Cows and 1 Bull

The word must be guessed in the least number of attempts.

Pankeet has now thought of a secret word for Ajay. Ajay has guessed some words and his position is as follows

What is the probability of letter ‘P’ to be present in the secret word?

Solution:

From above argument we know that ‘E’ is present in the secret word.

From the word LEAN, we know that ‘E’ is on the 2^{nd} position while ‘N’ is also not there in the secret word since it is only 1 Bull (for letter ‘E’)

Thus, from the word NEAR, we see that ‘R’ is also present but not in the right position (1 Bull for ‘E’ and 1 Cow for ‘R’)

From the word DARK, thus we see that ‘R’ is on the 3^{rd} position (1 Bull) Thus, we have “_ER_“

Thus, ‘P’ can occupy either of 2 positions

The alphabets which are remaining are [26 - (‘M’, ‘A’, ‘K’, ‘L’, T, ‘N’, ‘D', ‘E', ‘R’)] = 17

Each of the alphabets can occupy either of 2 positions.

Thus probability of "P" being present in secret word is 1/17

QUESTION: 19

Pankeet and Ajay are playing a word game with each other. The game is such that it involves words of four distinct letters only. A player has to think of a secret word. Then, in turn, the opponent tries to guess the word of the player who gives the number of matches. If the matching letters are on their right positions, they are "bulls", if on different positions, they are "cows"

For example,

Secret Word: MUST

Guess: SUMP

Answer: 2 Cows and 1 Bull

The word must be guessed in the least number of attempts.

Pankeet has now thought of a secret word for Ajay. Ajay has guessed some words and his position is as follows

Ajay attempted the following guesses after those 5 guesses.

What will Pankeet say if Ajay attempts the word “WORK”?

Solution:

We know that ‘R’ and ‘E’ are present in the secret word and they are in 3^{rd }and 2^{nd} position respectively.

Thus, from the answer for PYRE, we know that ‘P* and ‘ Y’ are not present

From the answer for word ZEAL, we can infer that ‘Z’ is present as ‘A’ and ‘L’ are not present

Since it was 2 Bulls, we know that ‘Z’ is present in the 1^{st} place.

From POSE, SAID and BALD we see that ‘O’ is present and it can occupy only 4^{th} place.

Thus the word is “ZERO”

If Ajay attempts WORK, then Pankeet will say 1 Cow and 1 Bull as ‘O’ is in the wrong place and ‘R’ is in the right place.

Hence, option 4.

QUESTION: 20

For example,

Secret Word: MUST

Guess: SUMP

Answer: 2 Cows and 1 Bull

The word must be guessed in the least number of attempts.

Pankeet has now thought of a secret word for Ajay. Ajay has guessed some words and his position is as follows

A hit percentage is defined as average of Bull percentage of all words guessed.

Continuing from the previous questions, what is the hit percentage till now? Round off the answer to the nearest integer.

Solution:

Average Bull percentage is 13.64%

Thus, rounding off the answer to the nearest integer gives us 14%

Hence, option 4.

QUESTION: 21

Group Question

Answer the following question based on the information given below.

Seven girls Abhilasha, Aditi, Akhila, Alka, Ambuja, Amshula and Amrita sit in a row satisfying the following conditions. Amshula is to the right of Aditi and Abhilasha and is to the immediate left of Ambuja. Amrita is not to the right of Aditi. There are same number of girls sitting between Akhila and Amshula as there are between Akhila and Alka, also Akhila is to the left of Abhilasha. Alka is to the immediate right of Amrita.

Q. Who is sitting at the centre?

Solution:

It is given that Amshula is to the right of Aditi and Abhilasha, and is to the immediate left of Ambuja.

The possible orders can be,

1. Aditi, Abhilasha, Amshula, Ambuja

2. Abhilasha, Aditi, Amshula, Ambuja

It is given that the number of girls between Akhila and Amshula is the same as Akhila and Alka, also Akhila is to the left of Abhilasha.

It is also given that Aditi and Abhilasha are to the left of Amshula.

Alka is to the left of Akhila and Amshula is to the right of Akhila.

There cannot be 2 girls between Akhila and Alka and between Akhila and Amshula.

Also if there are no girls between them then Amrita cannot be to the left of Alka.

••• There has to be one girl i.e. Abhilasha between Akhila and Alka and one girl between Akhila and Amshula.

The only girl remaining is Aditi.

••• The only possible order now will be:

Amrita, Alka, Aditi, Akhila, Abhilasha, Amshula, Ambuja.

Akhila is sitting at the centre.

Hence, option 3.

QUESTION: 22

Seven girls Abhilasha, Aditi, Akhila, Alka, Ambuja, Amshula and Amrita sit in a row satisfying the following conditions. Amshula is to the right of Aditi and Abhilasha and is to the immediate left of Ambuja. Amrita is not to the right of Aditi. There are same number of girls sitting between Akhila and Amshula as there are between Akhila and Alka, also Akhila is to the left of Abhilasha. Alka is to the immediate right of Amrita.

Who is sitting next to Amrita?

Solution:

From the answer to the first question of the set, Alka is next to Amrita. Hence, option 3.

QUESTION: 23

Seven girls Abhilasha, Aditi, Akhila, Alka, Ambuja, Amshula and Amrita sit in a row satisfying the following conditions. Amshula is to the right of Aditi and Abhilasha and is to the immediate left of Ambuja. Amrita is not to the right of Aditi. There are same number of girls sitting between Akhila and Amshula as there are between Akhila and Alka, also Akhila is to the left of Abhilasha. Alka is to the immediate right of Amrita.

Without violating any condition, in how many ways can we arrange them?

Solution:

Without violating any conditions, there is only one possble arrangement.

Hence, option 4.

QUESTION: 24

Group Question

Answer the following question based on the information given below.

Amika, Johny, Niharika, Dimple, and Param were the top five finishers in the Indore Harmony Race.

They drove yellow, orange, green, red, and blue race cars, but not necessarily in that order.

Further information on them is given below:

A. Neither Dimple nor Param drove the green car.

B. Dimple finished faster than Amika and Param.

C. The blue car finished earlier than Param's car and Niharika's car.

D. The yellow car finished faster than the green car and the orange car.

E. Amika's car and Param's car finished better than the orange car.

F. Johny's car finished earlier than the blue car and the yellow car.

Who was the 3^{rd} to finish the race?

Solution:

If A finishes faster than B, we will denote it by A > B.

Dimple > Amika Dimple > Param.

Thus, Dimple has to be in the top 3.

Blue Car > Param

Blue Car > Niharika

Now, Param > Orange Car

••• Blue Car > Param > Orange Car

Now, Johny > Blue Car

Johny > Blue Car > Param > Orange Car

Also, Johny > Yellow Car and Yellow Car > Green Car

Now, the two statements given above can be true simultaneously only if Param drives the Yellow car and is 3^{rd} in the race.

Therefore, the Blue car is 2^{nd} in the race and the Orange and green cars are 4^{th} and 5^{th} in the race (in no particular order).

Consequently, Johny drives the Red car, which finishes the race in the 1^{st }place.

Thus, Dimple is 2^{nd} and drives the Blue car.

Now, Amika > Orange car.

Thus, Amika has to be in 4^{th} place and should drive the Green car while Niharika has to be last and has to drive the Orange car.

Thus, the final arrangement is as shown below.

1^{st} - Johny - Red 2^{nd} - Dimple - Blue 3^{rd} - Param - Yellow 4^{th} - Amika - Green 5th _ Niharika - Orange

Thus, it is clear that Param was the 3^{rd} to complete the race.

Hence, option 3.

QUESTION: 25

Amika, Johny, Niharika, Dimple, and Param were the top five finishers in the Indore Harmony Race.

They drove yellow, orange, green, red, and blue race cars, but not necessarily in that order.

Further information on them is given below:

1. Neither Dimple nor Param drove the green car.

2. Dimple finished faster than Amika and Param.

3. The blue car finished earlier than Param's car and Niharika's car.

4. The yellow car finished faster than the green car and the orange car.

5. Amika's car and Param's car finished better than the orange car.

6. Johny's car finished earlier than the blue car and the yellow car.

Q. Which of the following combinations is correct?

Solution:

Consider the arrangement obtained in the solution to the first question. As per this arrangement, Param and Yellow is a correct combination.

Hence, option 4.

QUESTION: 26

Amika, Johny, Niharika, Dimple, and Param were the top five finishers in the Indore Harmony Race.

They drove yellow, orange, green, red, and blue race cars, but not necessarily in that order.

Further information on them is given below:

1. Neither Dimple nor Param drove the green car.

2. Dimple finished faster than Amika and Param.

3. The blue car finished earlier than Param's car and Niharika's car.

4. The yellow car finished faster than the green car and the orange car.

5. Amika's car and Param's car finished better than the orange car.

6. Johny's car finished earlier than the blue car and the yellow car.

Q. What is the correct order of the people who finished in the first three positions in the race?

Solution:

Consider the final arrangement obtained in the solution to the first question.

As per this arrangement, Johny, Dimple and Param respectively finished the race in the first three places.

Hence, option 2.

QUESTION: 27

Group Question

Answer the following question based on the information given below.

On the occasion of New Year, four families from RamVihar Society participated in a music competition.

The four families were ranked according to their scores at the end of the competition.

The following things are known about the four families.

1. Among the four couples, only one couple had no children.

2. Ranks of Mr.Suraj and Mr.Rahul were not adjacent to each other.

3. Priya who had only one kid stood third in the competition.

4. Sons of only Swapna and Seeta studied in the first standard.

5. Raj scored the least as his wife Seeta sang the wrong song twice.

6. Mr.Ram had no children and Mr.Rahul did not stand first.

Q. If Anita is one of the participants, then who is her husband?

Solution:

Let’s organize the given information in a table.

From statement 3, Priya had one kid and stood third.

From statement 5, Raj and Seeta were a couple and they stood fourth. Thus we have:

From statement 2, ranks of Rahul and Suraj were not adjacent to each other.

Suraj and Rahul were ranked 1 and 3 in some order. But from statement 6, Rahul did not stand first.

••• Suraj stood first and Rahul stood third.

It thus follows that Ram stood second.

Also, from statement 6, Ram had no children.

From 4, Swapna and Seeta both had a son.

••• Swapna cannot be Rani’s wife.

Swapna is Suraj’s wife.

Thus we have:

Ram is the husband of Anita.

Hence, option 4.

QUESTION: 28

On the occasion of New Year, four families from RamVihar Society participated in a music competition.

The four families were ranked according to their scores at the end of the competition.

The following things are known about the four families.

1. Among the four couples, only one couple had no children.

2. Ranks of Mr.Suraj and Mr.Rahul were not adjacent to each other.

3. Priya who had only one kid stood third in the competition.

4. Sons of only Swapna and Seeta studied in the first standard.

5. Raj scored the least as his wife Seeta sang the wrong song twice.

6. Mr.Ram had no children and Mr.Rahul did not stand first.

Q. Whose sons study in the first standard?

Solution:

Sons of Swapna and Seeta study in the first standard. Their husbands are Suraj and Raj respectively.

Hence, option 3.

*Answer can only contain numeric values

QUESTION: 29

Group Question

Answer the following question based on the information given below.

Abdul is a roadside vendor selling pins, handkerchiefs, paper-pins, pens, pencils, sharpeners, clips, bands and erasers. Each item has a different cost from Rs. 1 to Rs. 9. The following is also known.

1. The total cost of a pencil and a clip is less than the individual cost of a handkerchief and a paper-pin only.

2. The product of the costs of a clip and a pin is a prime number.

3. The cost of an eraser is Rs. 3 more than that of a band and Rs. 3 less than that of a handkerchief.

4. The cost of a pencil is a perfect square.

Q. How much does a clip cost (in Rs.)?

Solution:

Since the total cost of a pencil and clip combined is less than the individual cost of only a handkerchief and a paper-pin, this total cost must be Rs. 7.

Thus, the sum of costs of a pencil and clip is Rs. 7.

Also, the cost of a handkerchief and a paper pin will be one of Rs. 8 and 9.

Now, the cost of a pencil, which is a perfect square, can be either Rs. 1 or Rs. 4.

Also, since the product of costs of the clip and pin is a prime number, one of them must cost Rs. 1

So the pencil cannot cost Rs. 1.

Thus, the cost of a pencil is Rs. 4

••• The cost of a clip = 7 - 4 = Rs. 3

Answer: 3

*Answer can only contain numeric values

QUESTION: 30

Abdul is a roadside vendor selling pins, handkerchiefs, paper-pins, pens, pencils, sharpeners, clips, bands and erasers. Each item has a different cost from Rs. 1 to Rs. 9. The following is also known.

1. The total cost of a pencil and a clip is less than the individual cost of a handkerchief and a paper-pin only.

2. The product of the costs of a clip and a pin is a prime number.

3. The cost of an eraser is Rs. 3 more than that of a band and Rs. 3 less than that of a handkerchief.

4. The cost of a pencil is a perfect square.

Q. What is the cost (in Rs.) of 3 pencils, 5 pins and 7 paper-pins?

Solution:

From the solution to the previous question, the cost of a pencil and a clip is Rs. 4 and 3 respectively.

Since either a pin or a clip costs Rs. 1, the cost of a pin is Rs. 1.

Now, the cost of an eraser is 3 more than that of a band and 3 less than that of a handkerchief.

Thus, the cost of a band is 6 less than the cost of a handkerchief.

Thus, the maximum cost of a band can be Rs. 3

As seen earlier, a handkerchief costs one of Rs. 8 or 9.

So, the cost of a band must be Rs. 2 or 3.

Since the cost of a clip is Rs. 3, the band must cost Rs. 2.

So, the cost of an eraser and that of a handkerchief is Rs. 5 and Rs. 8 respectively.

Thus, the cost of a paper-pin will be Rs. 9.

.*• The cost of 3 pencils, 5 pins and 7 paper-pins =3x4+5xl+7x9

= 12 + 5 + 63 = Rs. 80

Answer: 80

QUESTION: 31

Group Question

Answer the following question based on the information given below.

Given below is a layout of streets in a certain area of a city.

There are two days before the monsoon is expected to arrive in the city. In these two days, certain repairs and other issues related to the street roads have to be completed. The issues and the routes on which it is to be done are given below:

Repairing telephone cables - P-R-S-T Repairing the drainage pipelines - P-Q-S-T

Repairing the manholes - P-Q-R-T

Painting the roads - Q-R-T

Fixing neon lights on the road - P-R-S

It is not possible to carry out more than one activity on the same street on the same day. However, all these activities have to be completed within these two days only. The road Q-S is closed on the first day due to a religious procession.

When can the neon lights be fixed?

Solution:

Since the stretch Q-R-T is common to the routes Q-R-T and P-Q-R-T, painting of the roads and manhole repairs cannot be done on the same day.

Road Q-S is closed on the first day => Drainage pipelines on (P-Q-S-T) has to be done on the second day.

Any activity that has to be done on the roads P-Q, Q-S or S-T cannot be done on the second day.

••• Telephone cables are to be repaired on the route P-R-S-T on the first day.

Similarly, repairing the manholes has to done on the first day.

Consequently, painting the roads and fixing the neon lights on the road has to be done on the second day.

Thus, the overall schedule of activities is as shown below.

So, the neon lights can be fixed on the second day.

Hence, option 2.

QUESTION: 32

Given below is a layout of streets in a certain area of a city.

There are two days before the monsoon is expected to arrive in the city. In these two days, certain repairs and other issues related to the street roads have to be completed. The issues and the routes on which it is to be done are given below:

Repairing telephone cables - P-R-S-T Repairing the drainage pipelines - P-Q-S-T

Repairing the manholes - P-Q-R-T

Painting the roads - Q-R-T

Fixing neon lights on the road - P-R-S

It is not possible to carry out more than one activity on the same street on the same day. However, all these activities have to be completed within these two days only. The road Q-S is closed on the first day due to a religious procession.

Which of the following is true?

Solution:

From the table given in the solution to the first question of the set, it is clear that repairing the manholes can only be done on the first day.

Hence, option 4.

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