LR - Binary Logic - Previous Year CAT/MBA Questions
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While Balbir had his back turned, a dog ran into his butcher shop, snatched a piece of meat off the counter and ran out. Balbir was mad when he realised what had happened. He asked three other shopkeepers, who had seen the dog, to describe it. The shopkeepers really didn't want to help Balbir. So each of them made a statement which contained one truth and one lie.
A. Shopkeeper Number 1 said: "The dog had black hair and a long tail."
B. Shopkeeper Number 2 said: "The dog has a short tail and wore a collar."
C. Shopkeeper Number 3 said: "The dog had white hair and no collar."
Based on the above statements, which of the following could be a correct description?
- (a)
The dog had white hair, short tail and no collar.
- (b)
The dog had white hair, long tail and a collar.
- (c)
The dog had black hair, long tail and a collar.
- (d)
The dog had black hair, long tail and no collar.
Answer: Option B
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Text Explanation :
According to the statement of the shopkeeper number 1, the dog had either black hair or a long tail, but definitely not both.
∴ Options 3 and 4 can be eliminated.
According to the statement of shopkeeper number 3, the dog had either white hair or wore a collar, but not both.
∴ Option 1 can be eliminated.
Hence, option (b).
Workspace:
Direction: In each of the following sentences, the main statement is followed by four sentences each. Select a pair of sentences that relate logically to the given statement.
Either Sam is ill, or he is drunk.
A. Sam is ill.
B. Sam is not ill.
C. Sam is drunk.
D. Sam is not drunk.
- (a)
AB
- (b)
DA
- (c)
AC
- (d)
CD
Answer: Option B
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Text Explanation :
Sam is not drunk, so he must be ill. One of the either ... or condition is true.
Workspace:
Refer to the following information and answer the questions that follow.
“Kya – Kya” is an island in the South Pacific. The inhabitants of “Kya – Kya” always answer any question with two sentences, one of which is always true and the other always false.
You find that your boat is stolen. You question three inhabitants of the island and they reply as follows:
John says, “I didn’t do it. Mathew didn’t do it.”
Mathew says. “I didn’t do it. Krishna didn’t do it.”
Krishna says. “I didn’t do it. I don’t know who did it.”
Who stole your boat?
- (a)
John
- (b)
Mathew
- (c)
Krishna
- (d)
None of them
Answer: Option B
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Text Explanation :
The best way to solve these kinds of questions is to assume that one of the statements is either true or false and thus figure out whether there is consistency in what everyone is saying.
Let us assume that John’s first statement is true. So his second statement must be false. This implies that Mathew did it. This makes Mathew’s first statement false. So the second statement has to be true. This implies that Krishna didn’t do it. So Krishna’s first statement is true and his second statement is false. Since all the statements are consistent with each other, the assumption made by us should be the correct one. So it is Mathew who stole the boat.
Workspace:
Refer to the following information and answer the questions that follow.
“Kya – Kya” is an island in the South Pacific. The inhabitants of “Kya – Kya” always answer any question with two sentences, one of which is always true and the other always false.
There is only one pilot on the island. You interview three men, Koik, Lony and Mirna. You also notice that Koik is wearing a cap.
Mirna says, “Lony’s father is the pilot. Lony is not the priest’s son.”
Koik says, “I am the priest. On this island, only priests can wear caps.”
Lony says, “I am the priest’s son. Koik is not the priest.”
Which of the following is true?
- (a)
Lony is not Koik’s son.
- (b)
Koik is the pilot.
- (c)
Mirna is the pilot.
- (d)
Lony is the priest.
Answer: Option B
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Text Explanation :
The best way to solve these kinds of questions is to assume that one of the statements is either true or false and thus figure out whether there is consistency in what everyone is saying.
The key here are the statements made by Koik. Since we know that he is wearing a cap, if his first statement is false, then his second statement cannot be true. So his first statement is true and his second statement is false. This implies that Koik is the priest. This makes Lony’s second statement false and so his first statement is true. So Lony is Koik’s son. This makes Mirna’s second statement false and so his first statement is true. So Lony’s father is a pilot. Thus, Koik is the pilot. (Note: Koik is also the priest).
Workspace:
Refer to the following information and answer the questions that follow.
“Kya – Kya” is an island in the South Pacific. The inhabitants of “Kya – Kya” always answer any question with two sentences, one of which is always true and the other always false.
You are walking on the road and come to a fork. You ask the inhabitants Ram, Laxman and Lila. ”Which road will take me to the village?”
Ram says, “I never speak to strangers. I am new to these parts.”
Laxman says, “I am married to Lila. Take the left road.”
Lila says, “I am married to Ram. He is not new to this place.”
Which of the following is true?
- (a)
Left road takes you to the village.
- (b)
Right road takes you to the village.
- (c)
Lila is married to Laxman.
- (d)
None of these.
Answer: Option A
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Text Explanation :
The best way to solve these kinds of questions is to assume that one of the statements is either true or false and thus figure out whether there is consistency in what everyone is saying.
The first statement of Ram is obviously false, as he is saying that he never speaks to a stranger, when he actually is. So he must be new to those parts. This makes the second statement of Lila false. So she should be married to Ram. This makes the first statement of Ram false. So the left road should take you to the village.
Workspace:
Refer to the following information and answer the questions that follow.
“Kya – Kya” is an island in the South Pacific. The inhabitants of “Kya – Kya” always answer any question with two sentences, one of which is always true and the other always false.
You want to speak to the chief of the village. You question three inhabitants. Amar, Bobby and Charles. Only Bobby is wearing a red shirt.”
Amar says. “I am not Bobby’s son. The chief wears a red shirt.”
Bobby says, “I am Amar’s father. Charles is the chief.”
Charles says, “The chief is one among us. I am the chief.”
Who is the chief?
- (a)
Amar
- (b)
Bobby
- (c)
Charles
- (d)
None of them
Answer: Option B
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Text Explanation :
The best way to solve these kinds of questions is to assume that one of the statements is either true or false and thus figure out whether there is consistency in what everyone is saying.
If you observe Charle’s statement carefully, you will figure out that his first statement is true and second statement is false. For instance, if his first statement is false, then his second statement cannot be true. There would be inconsistency in what he is talking. So Charles is not the chief. This makes Bobby’s second statement false and first statement true. So Bobby is Amar’s father and hence, Amar’s first statement is false. So his second statement must be true. This implies that the chief is wearing the red shirt. So Bobby is the chief.
Workspace:
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