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CAT Questions | CAT LR Questions | Linear Arrangement

Linear arrangement is the most common topic under the Logical Reasoning section for entrance exams like IIFT, SNAP, CMAT. Generally, one puzzle on seating arrangement reasoning carries 4-5 questions with a varied difficulty level. Linear arrangement questions analyze a candidate’s analytical mindset in the corporate job and thus need utmost excellency.

Below, the details about the number system for different competitive MBA entrance exams is given: –

CAT:

Linear Arrangement
Year No of Questions Good attempt Difficulty
2017-slot1 4 2 Difficult
2017-slot2 4 2 Difficult

IIFT:

Linear Arrangement
Year No of Questions Good attempt Difficulty
2019 3 3 Easy-Moderate
2017 2 2 Moderate

SNAP:

Linear Arrangement
Year No of Questions Good attempt Difficulty
2018 3 3 Easy-Moderate

Basic Concepts of Linear Arrangement

  • Questions based on single row arrangement
  • Problems involving two-row arrangement with directions also involved
  • Problems based on single row  arrangement question with persons/objects in the question facing different directions
 

CAT Questions | Linear Arrangement in logical reasoning

1. 1000 patients currently suffering from a disease were selected to study the effectiveness of treatment of four types of medicines — A, B, C and D. These patients were first randomly assigned into two groups of equal size, called treatment group and control group. The patients in the control group were not treated with any of these medicines; instead they were given a dummy medicine, called placebo, containing only sugar and starch. The following information is known about the patients in the treatment group. [CAT 2020]

 

a. A total of 250 patients were treated with type A medicine and a total of 210 patients were treated with type C medicine. 

b. 25 patients were treated with type A medicine only. 20 patients were treated with type C medicine only. 10 patients were treated with type D medicine only. 

c. 35 patients were treated with type A and type D medicines only. 20 patients were treated with type A and type B medicines only. 30 patients were treated with type A and type C medicines only. 20 patients were treated with type C and type D medicines only. 

d. 100 patients were treated with exactly three types of medicines. 

e. 40 patients were treated with medicines of types A, B and C, but not with medicines of type D. 20 patients were treated with medicines of types     A, C and D, but not with medicines of type B. 

f. 50 patients were given all the four types of medicines. 75 patients were treated with exactly one type of medicine. 

 

1. How many patients were treated with medicine type B?    

2. The number of patients who were treated with medicine types B, C and D, but not type A was: 

3. How many patients were treated with medicine types B and D only?    

4. The number of patients who were treated with medicine type D were?

As the given questions are based on only second group that is treatment group also there are a lot of data given . So it will be easier to make a venn diagram and fill all the given data and then solve the questions for missing values.

 

Given ,

From statement f) 75 patients were treated with exactly one type of medicine.

So 10+20+x+25 = 75

x = 20

From statement a) A total of 250 patients were treated with type A,

So 25+20+30+40+35+20+50 + y = 250

220 + y = 250

y = 30

From statement d) 100 patients were treated with exactly three types of medicines.

40+20+y+z = 100

60+30+z = 100

z = 10

From statement a) total of 210 patients were treated with type C medicine. So,

20+20+20+30+40+50+b+z = 210

180+b + 10= 210

b = 20

Now as there were total 500 patient in treatment group , so

250+x+b+z+a +20+20+10 = 500

300+20+20+10 + a = 500

a + 350 = 500

a = 150

 

 

1. Number of patients were treated with medicine type B = 20+40+50+y + x+z+a+b = 110+20+30+10+150+20= 340

2. The number of patients who were treated with medicine types B, C and D, but not type A = z = 10

3. The number of patients were treated with medicine types B and D only = a = 150

4. The number of patients who were treated with medicine type D = 20+50+35+y + a+ z + 20+10 = 135+30+10+150 = 325

2. Ten musicians (A, B, C, D, E, F, G, H, I and J) are experts in at least one of the following three percussion instruments: ta mridangam, and ghatam. Among them, three are experts in tabla but not in mridangam or ghatam, another three are experts in mridangam but not in tabla or ghatam, and one is an expert in ghatam but not in tabla or mridangam. Further, two are in tabla and mridangam but not in ghatam, and one is an expert in tabla and ghatam but not in mridangam. 

 [CAT 2020]

The following facts are known about these ten musicians. 

a. Both A and B are experts in mridangam, but only one of them is also an expert in tabla. 

b. D is an expert in both tabla and ghatam. 

c. Both F and G are experts in tabla, but only one of them is also an expert in mridangam. 

d. Neither I nor J is an expert in tabla. 

e. Neither H nor I is an expert in mridangam, but only one of them is an expert in ghatam. 

 

1. Who among the following is DEFINITELY an expert in tabla but not in either mridangam or ghatam? 

               A) C           B) F         C) H D) A 

 

2. Who among the following is DEFINITELY an expert in mridangam but not in either tabla or ghatam? 

                  A) B           B) E         C) J D) G

 

3. Which of the following pairs CANNOT have any musician who is an expert in both tabla and mridangam but not in ghatam? 

                  A) A and B   B) F and G         C) C and E    D) C and F

 

4. If C is an expert in mrindagam and  is not, then which are the three musicians who are experts in table but not in either mrindagam or ghatam?

 

                        A) E, F and H   B) C, E and G       C) E, G and H    D) C, G and H  

1. As it is given in point 4) and 5) Neither I nor J is an expert in tabla. And Neither H nor I is an expert in mridangam, but only one of them is an expert in ghatam, it mean I is an expert in ghatam only. Which also mean H is an expert of Tabla and J is an expert of mridangam.

From the given options , we know A is an expert of mridangam but we don’t know whether he is an expert of tabla or not.

Similarly F is an expert of tabla but he can also be an expert of mridangam .

We can’t say anything about C. Thus option 3) H is the suitable answer.

2. As it is given in point 4) and 5) Neither I nor J is an expert in tabla. And Neither H nor I is an expert in mridangam, but only one of them is an expert in ghatam, it mean I is an expert in ghatam only. Which also mean H is an expert of Tabla and J is an expert of mridangam.

From the given options , we know B is an expert of mridangam but we don’t know whether he is an expert of tabla or not.

Similarly G is an expert of tabla but he can also be an expert of mridangam .

We can’t say anything about E. Thus option 2) J is the suitable answer.

3. From statement point 1) and statement point 3) option 1) and option 2) can not be the correct choice as at least one among each of A and B , and one among F and G are expert in Tabla as well as mridangam.

Same is true for option 4) F can be an expert in both tabla and mridangam but not in ghatam.

Thus option 3) is our correct choice.

4. As it is given in point 4) and 5) Neither I nor J is an expert in tabla. And Neither H nor I is an expert in mridangam, but only one of them is an expert in ghatam, it mean I is an expert in ghatam only. Which also mean H is an expert of Tabla and J is an expert of mridangam.

Let us represent the given data in a table as below:

 

Number of experts

 

Only tabla

3

H, F or G

Only mridangam

3

J, A or B

Only  Ghatam

1

I

Only Ghatam and tabla

1

D

Only Tabla and mridangam

2

A or B  and F or G

If C is an expert in mridangam and F is not means  E will be expert in Tabla and G will be expert in mridangam as well as Tabla . F will be expert only in Tabla.

Following table will be made .

Only
tabla

3

H,
F , E

Only
mridangam

3

J,
A or B, C

Only 
Ghatam

1

I

Only
Ghatam and tabla

1

D

Only
Tabla and mridangam

2

 A
or B  and G

Option A is correct answer.

3. The first year students in a business school are split into six sections. In 2019 the Business Statistics course was taught in these six sections by Annie, Beti, Chetan, Dave, Esha, and Fakir. All six sections had a common midterm (MT) and a common endterm (ET) worth 100 marks each. ET contained more questions than MT. Questions for MT and ET were prepared collectively by the six faculty members. Considering MT and ET together, each faculty member prepared the same number of questions. Each of MT and ET had at least four questions that were worth 5 marks, at least three questions that were worth 10 marks, and at least two questions that were worth 15 marks. In both MT and ET, all the 5-mark questions preceded the 10-mark questions, and all the 15- mark questions followed the 10-mark questions.

[CAT 2019]

The following additional facts are known.

a. Anie prepared the fifth question for both MT and ET. For MT, this question carried 5 marks.

b. Annie prepared one question for MT. Every other faculty member prepared more than one questions for MT.

c. All questions prepared by a faculty member appeared consecutively in MT as well as ET.

d. Chetan prepared the third question in both MT and ET; and Esha prepared the eighth question in both.

e. Fakir prepared the first question of MT and the last one in ET. Dave prepared the last question of MT and the first one in ET.

 

1. The second question in ET was prepared by:

1. Chetan

2. Esha

3. Beti

4. Dave

 

2. How many 5- mark questions were there in MT and ET combined?

1. 13

2. 10

3. 12

4. Cannot be determined

 

3. Who prepared 15-mark questions for MT and ET?

1. Only Dave, Esha and Fakir

2. Only Beti, Dave, Esha and Fakir

3. Only Esha and Fakir

4. Only Dave and Fakir

 

4. Which of the following questions did Beti prepare in ET?

1. Tenth question

2. Ninth question

3. Fourth question

4. Seventh question

As both MT and ET has atleast 4 questions of 5 marks, atleast 3 ques of 10 marks, and 2 questions of 15 marks

Marks covered by these = 5×4 + 10×3 + 15×2 = 80

Marks left = 20

20 can be divided as (5,5,5,5) (5,5,10) (5,15) (10,10)

Order of question = 5 marks, 10 marks, 15 marks

Since it is given that 5th question is a 5 mark question case of 10,10 marks is rued out

As everyone prepared an equa number of questions the number has to be a factor of 6 greater than 18 and the only possible number here is 24.

Hence the only possible cases are (5,5,5,5) (5,15)Thus ET has 13 questions and MT has 11 questions

 

1. Option 4

2. Option 1

3. Option 1

4. Option 1

 

4.  Adriana, Bandita, Chitra, and Daisy are four female students, and Amit, Barun, Chetan, and Deb are four male students. Each of them studies in one of three institutes – X, Y, and Z. Each student majors in one subject among Marketing, Operations, and Finance, and minors in a different one among these three subjects. The following facts are known about the eight students: [CAT 2018]

 

a. Three students are from X, three are from Y, and the remaining two students, both female, are from Z.

b. Both the male students from Y minor in Finance, while the female student from Y majors in Operations.

c. Only one male student majors in Operations, while three female students minor in Marketing.

d. One female and two male students major in Finance.

e. Adriana and Deb are from the same institute. Daisy and Amit are from the same institute.

f. Barun is from Y and majors in Operations. Chetan is from X and majors in Finance.

g. Daisy minors in Operations.

 

1. Who are the students from the institute Z?

1. Adriana and Bandita

2. Adriana and Daisy

3. Bandita and Chitra

4. Chitra and Daisy

 

2. Which subject does Deb minor in?

1. Cannot be determined uniquely from the given information

2. Marketing

3. Operations

4. Finance

 

3. Which subject does Amit major in?

1. Operations

2. Marketing

3. Cannot be determined uniquely from the given information

4. Finance

 

4. If Chitra majors in Finance, which subject does Bandita major in?

1. Cannot be determined uniquely from the given information

2. Marketing

3. Finance

4. Operations

Let Daisy and Amit are from some institute A . Adriana and Ded be from the some institute B. So Bandita and Chitra must be from same institute (let’s say C) but as only two females are from Z so Bandita and Chitra must be from Z. Now the given information can be tabulated as bellow –

Name

Gender

Institute

Major

Minor

Adriana

Female

B

  

Bandita

Female

Z

  

Chitra

Female

Z

  

Daisy

Female

A

 

O

Amit

Male

A

  

Barun

Male

Y

O

 

Chetan

Male

X

F

 

Deb

Male

B

  

 

From point 3) three female students minor in Marketing and Daisy minors in operations (O) so other three must have minored in Marketing (M)

From point 2) Female student from Y majors in operations so Daisy cannot be from Y so Daisy is from X so is Amit. So Adriana and Deb are form Y. Also Barun and Deb both will miner in Finance (F) and Adrina will major in Operation (O).

Now the table will look like ,

Name

Gender

Institute

Major

Minor

Adriana

Female

Y

O

M

Bandita

Female

Z

F/O

M

Chitra

Female

Z

F/O

M

Daisy

Female

X

F/M

O

Amit

Male

X

F

O/M

Barun

Male

Y

O

F

Chetan

Male

X

F

O/M

Deb

Male

Y

M

F

Now all the questions can be answered.

1. a) Bandita and Chitra

2. c) Finance

3. a) Finance

4. b) operation

 

How to prepare for Linear Arrangement questions

Level 1

Level 2

  • Topics covering multiple concepts like blood relation questions involving 2-3 variables are usually asked in the exams.
  • Candidates must try to cover the questions from DILR for CAT based on these questions by keeping a time limit so that they get acquainted with these concepts. Practice MBAP Topic wise Previous Year CAT paper.

Level 3

  • To gain mastery over the linear arrangement questions for CAT with higher difficulty, the candidates must look into the previous papers like IIFT, SNAP. And solve topic-based tests from MBAP CAT Advance E books on these concepts, so that the student will be able to solve questions involving 2-3 variable in a timed manner.

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