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Dhana Satyan

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· 1 Months ago

in a simple way step by step

Question:

DIRECTIONS: These questions are based on the information given below.


Five persons — Atul, Vimal, Kamal, Ballu and Sanju, who are of different ages met at a place, Each of them made two statements, but each person will make at least one false statement. The following are the statements made by them.


Atul:    I am older than Sanju.

          Ballu is older than Vimal.

Ballu:  Vimal is older than Atul.

          I am younger than Kamal.

Kamal: I am younger than Sanju.

          Vimal is older than Ballu.

Vimal: Sanju is older than Atul.

          I am older than Sanju.

Sanju: Kamal is younger than Ballu.

          Kamal is older than Atul. 


If Sanju is younger than Ballu and Vimal is older than Ballu, then according to the statements made by them, how many such cases are possible?

Options:
A) 6
B) 7
C) 8
D) 9
E) 10
Solution:
The given statements are:


Person

I statement

II statement

Atul

A > S

B > V

Ballu

V > A

B < K

Kamal

K < S

V > B

Vimal

S > A

V > S

Sanju

K < B

K > A


In the above table, each person is represented by the first letter of his name.

It is given that B > S and V > B

We have the following possibilities


A:

I. A > S

T

T

T

T

-

II. B > V

F

F

F

F

B:

I. V > A

F

F

T

T

-

II. B < K

T

T

F

F

K:

I. K < B

F

F

F

F

-

II. V > B

T

T

T

T

V:

I. S > A

F

F

F

F

-

II. K < B

F

F

T

T

S:

I. K < B

F

F

T

T

-

II. K > A

T

F

F

F


From (a), we get the following sequences:

K > A > V > B > S.

From (b) we get

(1) A > K > V > B > S

(2) A > V > K > B > S

(3) A > V > B > K > S

From (c), we get

(1) V >A B > K > S

(2) V > B > A > K > S

(3) A > V > B > K > S

From (d), we get

A > V > B > K > S

There are eight such sequences are possible.

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