Distribution

Distribution: 1

Distribution:

Distribution sets in Logical Reasoning are a kind that are the most frequently encountered in CAT or other B-school entrance exams. Distribution sets entail a lot of information that needs to be matched and are sometimes best represented in a tabular format. The sets can contain two variables or three or sometimes more than four. As the number of variables is increased, the level of difficulty is substantially raised. Sometimes the sets also contain numbers and calculations are also involved in such sets. The best way to deal with sets based on distribution is to represent the information in a tabular format and try to find the links joining the information. Keep filling up the table to eventually crack the set. One by one we shall see some sets based on distribution and the approach to crack them.

Example1: Six students of Kitabee - Bakul, Praveen, Pratik, Mohak, Sunny and Rahul work with six banks- SBI, Bank of Baroda, Yes Bank, ICICI, HDFC and PNB, not necessarily in the same order. They students are into six different hobbies- Sketching, Dancing, Gardening, Cooking, Singing and Reading without any order and each one of them has only one hobby. Further, it is known that:

a. Bakul works in Yes Bank and the one who likes cooking works with ICICI bank.

b. Mohak doesn’t work with HDFC or SBI but likes Reading.

c. The one who likes Sketching is not Praveen or Rahul and doesn’t work with Yes Bank.

d. Rahul & Sunny work with HDFC and SBI not necessarily in the same order.

e. The one who likes Singing works with SBI while Praveen likes dancing.

1. Who works with Bank of Baroda?

A. Praveen         B. Mohak  C. Pratik D. Cannot be determined

2. Who likes gardening?

A. Bakul             B. Pratik C. Sunny              D. Rahul

3. What is the hobby of the one who works with HDFC?

A. Dancing              B. Gardening C. Sketching          D. Cooking

Solution:  This set is a perfect example of Distribution with three variables – Names, Banks and Hobbies.

From (a) and (b) we get

Name

 Bank

Hobby

Bakul

Yes bank

 
 

ICICI

Cooking

Mohak

PNB/ Bank of Baroda

 
     
     
     

(As Mohak likes reading so he won’t be working with ICICI )

From (e), we get Praveen likes dancing and the one who works with SBI likes singing.

Name

 Bank

Hobby

Bakul

Yes bank

 
 

ICICI

Cooking

Mohak

PNB/ Bank of Baroda

Reading

Praveen

 

Dancing

 

SBI

Singing

     

 

From (c), we get Praveen and Rahul don’t like Sketching and the one who likes Sketching doesn’t work with Yes bank . So, either Sunny or Pratik likes Sketching.

Name

 Bank

Hobby

Bakul

Yes bank

 
 

ICICI

Cooking

Mohak

PNB/ Bank of Baroda

Reading

Praveen

 

Dancing

 

SBI

Singing

Sunny/Pratik

 

Sketching

 

From (d) Rahul and Sunny work with HDFC and SBI (not necessarily in the same order )

As Praveen doesn’t work with HDFC (It has to be either Sunny or Rahul),

Name

 Bank

Hobby

Bakul

Yes bank

 
 

ICICI

Cooking

Mohak

PNB/ Bank of Baroda

Reading

Praveen

 

Dancing

 

SBI

Singing

Sunny/Pratik

HDFC

Sketching

And also Pratik cannot be working in HDFC or SBI, so he works with ICICI leaving Sunny with HDFC and Rahul with SBI bank. Also, this means Bakul likes gardening.

Name

 Bank

Hobby

Bakul

Yes bank

Gardening

Pratik

ICICI

Cooking

Mohak

PNB/ Bank of Baroda

Reading

Praveen

Bank of Baroda/PNB

Dancing

Rahul

SBI

Singing

Sunny

HDFC

Sketching

 

1. Either Mohak or Praveen works with Bank of Baroda. So option (D) is correct.

2. Bakul likes gardening. So, option (A) is correct.

3. The one working with HDFC likes sketching. So, option (C) is correct.

Example 2: Anushka and Alia are two female actresses and Varun and Siddharth are two male actors selected for the shooting of four movies of Dhanraj Productions- Pyaar Alvida, Love Ultimate, Sanam Dilwale and Ishq Fever. Each actor/actress will feature in only two different movies. Each movie features one male actor and one female actress. No two movies have the same pair. Also, the movies are to be shooted in four different locations- London, Seychelles, Paris and Dubai. Following information is further known about them:

1. The male actor scheduled to shoot in London and Dubai does not feature in the movies –Love Ultimate and Sanam Dilwale.

2. Anushka is scheduled to shoot in Paris but does not feature in the movie Love Ultimate.

3. Pyaar Alvida does not feature Siddharth.

 

1. In which location is the movie Sanam Diljale scheduled to be shot?

A. London          B. Dubai C. Seychelles         D. Paris

2. Which pair out of the following is correct?

A. Varun- Alia – Seychelles   B. Siddharth- Anushka – Seychelles

C. Siddharth – Alia- Seychelles      D. Siddharth- Alia- Paris

3. How many different combinations are possible?

A. 2         B. 4  C. 6 D. 8

Solution:  From (3) we get:

 Name

Pyaar Alvida

 Love Ultimate

Sanam Diljale

Ishq Fever

Anushka

       

Alia

       

Varun

     

Siddharth

  X

     

Location:

       

 

From (1) we get The male actor scheduled to shoot in London and Dubai does not feature in the movies –Love Ultimate and Sanam Dilwale. So, this male actor must be Varun and so he shoots in London and Dubai which further means Siddharth shoots for Love Ultimate and Sanam Diljale



 

 Name

Pyaar Alvida

 Love Ultimate

Sanam Diljale

Ishq Fever

Anushka

       

Alia

       

Varun

  X

  X


Siddharth

  X


 X

Location:

London/Dubai

   

London Dubai

 

From (2)  Anushka is scheduled to shoot in Paris but does not feature in the movie Love Ultimate, this implies that Anushka shoots for the movie Sanam Diljale and Alia shoots for the movie Love Ultimate. Also, this implies Love Ultimate is scheduled to be shot at Seychelles. Thus, the final distribution becomes:

 Name

Pyaar Alvida

 Love Ultimate

Sanam Diljale

Ishq Fever

Anushka

 

  X


 

Alia

 

 X

 

Varun

  X

  X


Siddharth

  X


 X

Location:

London/Dubai

Seychelles

Paris

London Dubai

 

1.  Sanam Diljale is scheduled to be shot at Paris. Thus, option (D) is correct.

2. Siddharth- Alia- Seychelles is the correct combination. Thus, option (C) is correct.

3.  Four different combinations are possible

As Alia/Anushka or Anushka/Alia could feature in Pyaa Alvia/Ishq Fever. Also the films could either be shot at London/Dubai locations. Thus, option (B) is correct.

Example 3:

Image result for characters of chhota bheem

Source: The Indian Express

On the occasion of Holi, five races were held in Dholakpur village in which only five kids-Bheem, Chutki, Jaggu, Dholu and Bholu participated. In each of the race all the five occupied a different position while in no race the five participants occupied the same position. It is further known that:

A. In the third race, the one who came first came last in the first race while Jaggu came last in the third race.

B. Chutki came before Bholu who came before Dholu in the second race.

C. Bheem came first in the second race while he came last in the fourth race.

D. Dholu just came before Chutki in the third race while Dholu came 2nd in the first race.

E. Chutki came 1st in the first race.

F. The one who came 2nd in the second race got the first rank in the fourth race.

1. Who occupied the fifth position in race V?

A. Bholu        B. Bheem C. Dholu         D. Chutki

2. Who occupied the third position in race IV?

A. Bholu     B. Dholu  C. Bheem D. Jaggu

 

3. What was the position of Bheem in the third race?

A. First      B. Second   C. Third D. Fourth



 

Solution : We’ll first fill the table with the direct information that has been given to us.

Position

I race

II race

III race

IV race

V race

First

Chutki

Bheem

     

Second

Dholu

       

Third

         

Fourth

         

Fifth

   

Jaggu

Bheem

 

From the table, it is clear that Bholu came fifth in the I race.Also, from statement A, we get Bholu came first in the third race.

Position

I race

II race

III race

IV race

V race

First

Chutki

Bheem

Bholu

   

Second

Dholu

       

Third

Bheem/Jaggu

       

Fourth

Jaggu/Bheem

       

Fifth

Bholu

 

Jaggu

Bheem

 

 

From statement F, we get the one who came second in the second race came first in the fourth race. This person cannot be Chutki, Bheem. Bholu or Dholu (As Dholu already came second in the second race while Chutki, Bheem and Bholu came first in the I,II and III race). So, this person is Jaggu which implies Dholu came first in the V race.

Position

I race

II race

III race

IV race

V race

First

Chutki

Bheem

Bholu

Jaggu

Dholu

Second

Dholu

Jaggu

     

Third

Bheem/Jaggu

       

Fourth

Jaggu/Bheem

       

Fifth

Bholu

 

Jaggu

Bheem

 

From statement B we get, Chutki came before Bholu who came before Dholu.



 

Position

I race

II race

III race

IV race

V race

First

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