# LR - Venn Diagram - Previous Year CAT/MBA Questions

You can practice all previous year OMET questions from the topic LR - Venn Diagram. This will help you understand the type of questions asked in OMET. It would be best if you clear your concepts before you practice previous year OMET questions.

**Answer the questions based on the information given below.**

In an organisation with three departments i.e. Marketing, Finance and HR, it was decided to shuffle the 70 employees between departments. To make optimum use of resources, the management assesses their capability based on their qualification. 3 employees can work in every department. 7 employees can work in Finance and Marketing only. 10 can work only in HR while the number of employees only in Marketing is double of that in only Finance. Employees in only Finance cannot be less than 10 while employees in Finance and HR only are three times of two less than that of Marketing and HR only. The organization has employees with all possible combinations of their capabilities.

**IIFT 2019 LRDI | LR - Venn Diagram**

How many employees at the maximum are capable to work in Finance ?

- A.
31

- B.
33

- C.
28

- D.
32

Answer: Option A

**Explanation** :

Let the employees who can work only oin Finance be x, therefore employees who can work only in Marketing is 2x.

Also let the employees who can work in Marketing and HR only be a, therefore employees who can work in Finance and Hr only is 3(a – 2) = 3a – 6

∴ 2x + x + 7 + 3 + 10 + a + 3a – 6 = 70

∴ 3x + 4a = 56

As no. of employees inFinance can't be less than 10, so there are two possible solutions, where x = 12 and K = 5 and x = 16 and k = 2. But of K is 2 then the employees who can work Finance and HR only will be zero.

Therefore x = 12 and K = 5

So no. of employees who can work only in Finance are 12 and no. of employees who can work only in Marketing are 24.

No. of employees who can work in Marketing and HR only are 5 and no. of employees who cana work in Finance and HR only are 3a – 6 = 9

no. of Employees capable of working in Finance = 7 + 3 + 9 + 12 = 31

Hence,option 1.

Workspace:

**IIFT 2019 LRDI | LR - Venn Diagram**

How many employees are capable to work in Marketing and HR only ?

- A.
1

- B.
5

- C.
9

- D.
7

Answer: Option B

**Explanation** :

Let the employees who can work only oin Finance be x, therefore employees who can work only in Marketing is 2x.

Also let the employees who can work in Marketing and HR only be a, therefore employees who can work in Finance and Hr only is 3(a – 2) = 3a – 6

∴ 2x + x + 7 + 3 + 10 + a + 3a – 6 = 70

∴ 3x + 4a = 56

As no. of employees inFinance can't be less than 10, so there are two possible solutions, where x = 12 and K = 5 and x = 16 and k = 2. But of K is 2 then the employees who can work Finance and HR only will be zero.

Therefore x = 12 and K = 5

So no. of employees who can work only in Finance are 12 and no. of employees who can work only in Marketing are 24.

No. of employees who can work in Marketing and HR only are 5 and no. of employees who cana work in Finance and HR only are 3a – 6 = 9

Number of employees capable of Working in Marketing and HR only are 5.

Hence, option 2.

Workspace:

**Answer the following question based on the information given below.**

A consultant to Department of Commerce, Government of Bianca has suggested 30 products which have high export potential. Dora an entrepreneur and prospective3 exporter notices that these products can be grouped in three ways- Machine made goods, Handmade goods and intermediate goods. Among these 30 products some products are both machine made and intermediate goods but not intermediate goods. Some products are handmade and not intermediate goods but not machine made goods. Further it is seen that handmade-machine made goods are 1 less than machine made-intermediate goods. Similarly the total number of handmade-intermediate goods is 1 less than machine made-intermediate goods. There are just 4 products common across all products groups i. e. machine made-handmade- intermediate goods. Apart from this the number of only handmade goods is same as only machine made goods but less than only intermediate goods. Each product group/combination has at least one product.

Dora prefers to export machine made goods and avoid hand made goods. She finds out that only handmade goods are twice the machine made-intermediate goods and the number of only intermediate goods is an even number. Whereas her close friend Sara prefers to export intermediate goods followed by only handmade goods.

**IIFT 2018 LR | LR - Venn Diagram**

Sara and Dora prefer to exports as many common products as possible in order to understand the regulatory conditions. Keeping their preferences intact, what is the maximum number of common products which can be exported by both of them?

- A.
2

- B.
4

- C.
14

- D.
Data Inadequate

Answer: Option A

**Explanation** :

2a + a – 1 + 4 + a + 2a + a – 1 + b = 30

7a + b = 28

b has to be a multiple of 7.

if b = 7, ⇒ a = 3

if b = 14, ⇒ a = 2

if b = 21, ⇒ a = 1

Given, b = even, Thus, b = 14, a = 2

Products common to M & I = 2.

Hence, option 1.

Workspace:

**IIFT 2018 LR | LR - Venn Diagram**

If another exporter Abeer prefers to export only intermediate goods, then the total number of products which both Abeer and Dora export are

- A.
24

- B.
20

- C.
22

- D.
21

Answer: Option B

**Explanation** :

(Intermediate + Machine) – Handmade

= 14 + 2 + 4 = 20

Hence, option 2.

Workspace:

**IIFT 2018 LR | LR - Venn Diagram**

If the entry code for the show at 7 pm is

'Do things to help others in difficulty '

Then the code for entry ticket for the show at 12 noon of that day was

- A.
Do things others help to in difficulty

- B.
Do things to help others in difficulty

- C.
Do things to help in difficulty others

- D.
Do things difficulty help to others in

Answer: Option B

**Explanation** :

There are 4 shows between 7 pm show and noon show.

Reverse patterns : 1 – 3 – 6 – 5 – 7 – 1. So after every 4 shows, the pattern will be same. So the code for entry ticket for the show at 12 noon will be same as 7 pm show.

Hence, option 2.

Workspace:

**IIFT 2016 LRDI | LR - Venn Diagram**

The diagram below, explains which of the given relationship

- A.
Judge, Thief, Criminal

- B.
Tea, Coffee, Beverages

- C.
Males, Fathers, Doctors

- D.
Cabinet, Minister, Home Minister

Answer: Option C

**Explanation** :

Every father is a male, but every male need not be a father. Hence, the set of fathers is the subset of the set of males.

Some males are doctors and some fathers are doctors, and vice versa. Hence, the set of doctors partially intersects the set of males as well as fathers.

Hence, the given diagram corresponds to Males, Fathers, Doctors.

Hence, option 3.

Workspace:

**IIFT 2014 LRDI | LR - Venn Diagram**

**In each question given below, there are three statements followed by four conclusions numbered I, II, III and IV. You have to take the given statements to be true even if they seem to be at variance with commonly known facts and then decide which of the conclusion(s) logically follows from the given statements.**

**Statements:**

a. All tigers are lions.

b. All lions are horses.

c. No horses are monkeys.

**Conclusions:**

I. All tigers are horses.

II. No tigers are monkeys.

III. Some lions are tigers.

IV. Some monkeys are not tigers

- A.
All follows

- B.
Only I, II, and III follow

- C.
Only I, II, and IV follow

- D.
Only II, III and IV follow

Answer: Option A

**Explanation** :

It can be seen from the diagram that all conclusions follow.

Hence, option 1.

Workspace:

**IIFT 2014 LRDI | LR - Venn Diagram**

**In each question given below, there are three statements followed by four conclusions numbered I, II, III and IV. You have to take the given statements to be true even if they seem to be at variance with commonly known facts and then decide which of the conclusion(s) logically follows from the given statements.**

**Statements:**

a. Some shirts are pants.

b. All shoes are shirts.

c. All pants are gloves.

**Conclusions:**

I. Some shoes are gloves.

II. Some shirts are gloves.

III. No pants are shoes.

IV. All gloves are shirts.

- A.
Only II follows

- B.
Both I and III follow

- C.
Only III follows

- D.
Only I and IV follow

Answer: Option A

**Explanation** :

From the above diagram, conclusions I, IV do not follow.

From the above diagram, III does not follow.

Hence, only II follows.

Hence, option 1.

Workspace:

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