DIRECTIONS for questions 1 to 3: These questions are based on the following information.
P, Q and R when asked a question give three statements as reply in the following manner.
P - Always replies in only one type of statements - truth or lie.
Q - Never replies in the same type of statements as P.
R - Is neither consistent in all his statement types nor alternates between the two types of statements.
At the bus - stop, I asked: "Which bus goes to the airport?"
Their replies were as follows:
Take the North - bound bus.
The next bus arrives in 15 minutes.
It takes 45 minutes to reach the airport.
Q:
The north - bound bus comes from the airport.
You have to wait for 20 minutes for the bus.
It takes 30 minutes to reach the airport.
R:
Take the South - bound bus.
You have to wait for another quarter of an hour for the bus.
It takes anywhere between 1 hour to 1 hour 30 minutes to reach the airport.
Which of the following represents the reply that R gave?
1. Truth - Truth - Lie
2. Lie - Truth - Truth
3. Lie - Lie-Truth
4. Truth - Lie-Lie
Sol: Option 4 Explanation:
If P always speaks the truth, then Q always lies.
If P always lies R then Q always speaks the truth.
In either case, R cannot be speaking all truths or all lies. R cannot alternate between truth and lies either.
So, we have the following:
Case (i)
I
II
III
P
T
T
T
Q
F
F
F
R
F
T
F
Case (ii)
I
II
III
P
F
F
F
Q
T
T
T
R
T
F
F
In case (i), R becomes an alternator which violates the given condition.
Hence case (ii) is the correct arrangement and the south bound bus goes to the airport. Hence, R replies in the manner: Truth - lie - lie
Which of the following is definitely true?
I. P always lies.
II. Q always lies.
III. The North - bound bus goes to the airport.
1. Only I
2. Only II
3. Only I and II
4. Only II and III
Sol: Option 1 Explanation:
If P always speaks the truth, then Q always lies.
If P always lies R then Q always speaks the truth.
In either case, R cannot be speaking all truths or all lies. R cannot alternate between truth and lies either.
So, we have the following:
Case (i)
I
II
III
P
T
T
T
Q
F
F
F
R
F
T
F
Case (ii)
I
II
III
P
F
F
F
Q
T
T
T
R
T
F
F
In case (i), R becomes an alternator which violates the given condition.
Hence case (ii) is the correct arrangement and the south bound bus goes to the airport. Hence, Only I statement is true.
How long does it take before to reach the airport from the bus-stop?
1. 45 minutes
2. 50 minutes
3. Between 1 hour and 1 hour 30 minutes
4. 30 minutes
Sol: Option 2
If P always speaks the truth, then Q always lies.
If P always lies R then Q always speaks the truth.
In either case, R cannot be speaking all truths or all lies. R cannot alternate between truth and lies either.
So, we have the following:
Case (i)
I
II
III
P
T
T
T
Q
F
F
F
R
F
T
F
Case (ii)
I
II
III
P
F
F
F
Q
T
T
T
R
T
F
F
In case (i), R becomes an alternator which violates the given condition.
Hence case (ii) is the correct arrangement and the south bound bus goes to the airport. Therefore, (20 minutes to wait for the bus) + (30 minutes of travel time) = 50 minutes to reach the airport.
DIRECTIONS for questions 4 to 6: These questions are based on the data given below.
There are four executives A, B, C and D each working in a different organization amongst Microsoft, Oracle, Infosys and IBM, not necessarily in the same order. Each of them gives three replies to any question asked, which are alternately true or false, in any order. When asked to mention the name of the executive and the organization that he works for, they gave the following replies:
A:
C works with Microsoft.
D works with IBM.
B works with Infosys.
B:
A works with IBM.
C works with Infosys.
D works with Oracle.
C:
D works with Microsoft.
B works with Oracle.
A works with Infosys.
D:
B is not working with Infosys.
A is working with IBM.
C is not working with Microsoft.
A definite arrangement can be obtained from the above information. Solve the questions based on the above data.
Who among the following works with Microsoft?
1. A
2. B
3. C
4. D
Sol: Option 1 Explanation:
Each person alternates between truth and lie, then for three statements given by any person, the nature of the statements could be:
True, False, True
or
False, True, False
(i) Assume that the three statements given by A are in the order True, False, True. Then we get the following arrangement:
I
II
III
Organization
A
T
F
T
IBM
B
T
F
T
Infosys
C
F
F
F
Microsoft
D
F
T
F
Oracle
Here, all the three statements given by C become false; hence, we'll try the second combination.
(ii) Assume that the three statements given by A are in the order False, True, False.
Then we get the following arrangement:
I
II
III
Organization
A
F
T
F
(x IBM) Microsoft
B
F
T
F
(x Infosys) Oracle
C
F
T
F
(x Microsoft) Infosys
D
T
F
T
IBM
Hence, here we get a definite arrangement. Therefore, A works with Microsoft.
B works with
1. IBM
2. Infosys
3. Microsoft
4. Oracle
Sol: Option 4 Explanation:
Each person alternates between truth and lie, then for three statements given by any person, the nature of the statements could be:
True, False, True
or
False, True, False
(i) Assume that the three statements given by A are in the order True, False, True. Then we get the following arrangement:
I
II
III
Organization
A
T
F
T
IBM
B
T
F
T
Infosys
C
F
F
F
Microsoft
D
F
T
F
Oracle
Here, all the three statements given by C become false; hence, we'll try the second combination.
(ii) Assume that the three statements given by A are in the order False, True, False.
Then we get the following arrangement:
I
II
III
Organization
A
F
T
F
(x IBM) Microsoft
B
F
T
F
(x Infosys) Oracle
C
F
T
F
(x Microsoft) Infosys
D
T
F
T
IBM
Hence, here we get a definite arrangement. Therefore, B works with Oracle.
Which of the following statements must be false?
1. D is working with IBM.
2. The first statements made by A, B and C are false.
3. C is working in Infosys.
4. The second statements made by A, B and C are false.
Sol: Option 4 Explanation:
Each person alternates between truth and lie, then for three statements given by any person, the nature of the statements could be:
True, False, True
or
False, True, False
(i) Assume that the three statements given by A are in the order True, False, True. Then we get the following arrangement:
I
II
III
Organization
A
T
F
T
IBM
B
T
F
T
Infosys
C
F
F
F
Microsoft
D
F
T
F
Oracle
Here, all the three statements given by C become false; hence, we'll try the second combination.
(ii) Assume that the three statements given by A are in the order False, True, False.
Then we get the following arrangement:
I
II
III
Organization
A
F
T
F
(x IBM) Microsoft
B
F
T
F
(x Infosys) Oracle
C
F
T
F
(x Microsoft) Infosys
D
T
F
T
IBM
Hence, here we get a definite arrangement. As can be observed from the arrangement made above, it is option (4) which is false.
DIRECTIONS for questions 7 to 9: Solve questions are based on the following information.
Each of the three persons - Joe, Jack and John-belonged to exactly one of different cities amongst New York, Los Angeles and Chicago. Each person always gives two replies to any question asked. Out of these three, exactly one person always speaks the truth, other always lies and another always alternates between truth and lie, in any order. When each was asked "Which city do you belong to?” the following were their replies:
Joe: I am from New York. Jack is from Los Angeles.
Jack: I am from New York. John is from Chicago.
John: Joe is from Los Angeles. Jack is from New York.
Based on the above, Solve the following questions:
From case(i),it is concluded that John must be from Chicago.
Which city did Jack belong to?
1. New York
2. Los Angeles
3. Chicago
4. Chicago or New York
Option: 2 Explanation:
(i) Assuming Joe always speaks the truth:
I
II
City
Joe
T
T
New York
Jack
F
T
Los Angeles
John
F
F
Chicago
(ii) Assuming Jack always speaks the truth:
I
II
City
Joe
F
F
Los Angeles
Jack
T
T
New York
John
T
T
Chicago
(iii) Assuming John always speaks the truth:
I
II
City
Joe
F
F
Los Angeles
Jack
T
T
New York
John
T
T
Chicago
Arrangement (i)is helping in answering the question. Hence, Jack belongs to Los Angeles.
If there are exactly two persons who always tell the truth and the third person either always lies or alternates between truth and lie, then which of the following statements must be false?
1. John is not from Los Angeles
2. Joe is not from New York.
3. John is not from Chicago.
4. Jack is from New York
Sol: Option 3 Explanation:
(i) Assuming Joe always speaks the truth:
I
II
City
Joe
T
T
New York
Jack
F
T
Los Angeles
John
F
F
Chicago
(ii) Assuming Jack always speaks the truth:
I
II
City
Joe
F
F
Los Angeles
Jack
T
T
New York
John
T
T
Chicago
(iii) Assuming John always speaks the truth:
I
II
City
Joe
F
F
Los Angeles
Jack
T
T
New York
John
T
T
Chicago
From all the three situations, it is concluded that John is not from Chicago is false.
