CRE 1 - Basics | LR - Binary Logic
Answer the next 5 questions based on the information give below:
On an island there are three kinds of people
Truth-tellers: who always speak truth.
Liars: who always lie.
Alternators: who can either tell the truth or lie.
Tarun says: “I am a truth-teller”. Trun is a/an:
- A.
Truth-teller
- B.
Liar
- C.
Alternator
- D.
Cannot be determined
Answer: Option D
Explanation :
Any of truth-teller, liar or alternator can say “I am a truth-teller”
Hence, option (d).
Workspace:
Arun says: “I am a liar”. Arun is a/an:
- A.
Truth-teller
- B.
Liar
- C.
Alternator
- D.
Cannot be determined
Answer: Option C
Explanation :
A truth-teller will never say “I am a liar” because that would be a lie and he cannot speak a lie.
A liar will never say “I am a liar” because that would be true and he cannot speak the truth.
∴ Only an alternator can say “I am a liar”.
Hence, option (c).
Workspace:
Varun says: “I am an alternator”. Varun is definitely not a/an:
- A.
Truth-teller
- B.
Liar
- C.
Alternator
- D.
Cannot be determined
Answer: Option A
Explanation :
A truth-teller will never say “I am an alternator” because that would be a lie and he cannot speak a lie.
A liar can say “I am an alternator” because that would be a lie.
An alternator can say anything.
∴ Varun cannot be a truth-teller.
Hence, option (a).
Workspace:
Three persons (of different kinds) from this island give these statements.
GAUTAM: Umesh is a truth-teller. I am an alternator.
BHEEM: Gautam is a liar. I am a truth-teller.
UMESH: Bheem is a liar. I am an alternator.
Gautam belongs to which tribe?
- A.
Truth-teller
- B.
Liar
- C.
Alternator
- D.
Either (a) or (c)
Answer: Option B
Explanation :
Assuming,
Case 1: Gautam is truth teller i.e., his both statements should be correct.
But his first statemen says that Umesh is the truth-teller which cannot be the case since they are all of different kinds.
∴ Gautam is not the truth-teller.
Case 2: Bheem is the truth-teller i.e, his both statements should be correct.
⇒ His second statement is true and his first statement indicates that Gautam is the liar and Umesh is the alternator.
Checking for statements of Gautam (liar): His both statements are false, which fits well with our assumption.
Checking for statements of Umesh (alternator): His first statement is false and second is true, which also fits well with our assumption.
∴ Gautam is liar, Bheem is truth-teller and Umesh is alternator.
Case 3: Umesh is the truth-teller i.e, his both statements should be correct.
This cannot be case because Umesh’s second statement is contradictory.
∴ Gautam is liar.
Hence, option (b).
Workspace:
While searching for a Mechanic, Pranjal met three locals - Harsh, Akash and Raju - who always gave two replies to any question. Among them one is a truth teller, one is a liar and one is an alternator. When Pranjal asked them, "Who among you is the Mechanic?", their replies were :
Harsh: I am the Mechanic. Akash is a liar
Akash: I am the Mechanic. Raju is a liar
Raju: Akash is the Mechanic. Harsh is a liar.
Who is the mechanic?
- A.
Harsh
- B.
Akash
- C.
Raju
- D.
Either (b) or (c)
Answer: Option B
Explanation :
Assuming,
Case 1: Harsh is the truth-teller i.e., both his statements are correct.
∴ Harsh is the mechanic, Akash is liar and Raju is alternator.
Checking for statements of Akash (liar): His both statements are false, which fits well with our assumption.
Checking for statements of Raju (alternator): His both statements are false, which contradicts our assumption.
∴ Harsh cannot be the truth-teller.
Case 2: Akash is the truth-teller i.e., both his statements are correct.
∴ Akash is the mechanic, Raju is liar and Harsh is alternator.
Checking for statements of Raju (liar): His first statement is true which contradicts our assumption.
∴ Akash cannot be the truth-teller.
Case 3: Raju is the truth-teller i.e., both his statements are correct.
∴ Akash is the mechanic, Harsh is liar and Akash is alternator.
Checking for statements of Harsh (liar): His both statement are false, which fits well with our assumption.
Checking for statements of Akash (alternator): His first statement is true and second statement is false, which fits well with our assumption
∴ Akash is the mechanic.
Hence, option (b).
Workspace:
Below are three statements by snooker players. At least one of the statements is false and at least one is true:
- Sachin: Sourav did not pot the black.
- Sourav: I did not pot the black.
- Vinod: I potted the black.
If only one of them potted the ball, who potted the black?
- A.
Sachin
- B.
Sourav
- C.
Vinod
- D.
Both Sachin and Sourav
Answer: Option A
Explanation :
Assuming,
Case 1: Sachin potted the ball ⇒ Saching and Sourav’s statements are correct and Vinod’s statement is false.
Case 2: Sourav potted the ball ⇒ All three statements are false.
Case 3: Vinod potted the ball ⇒ All three statements are true.
Since there has to be at least one true and one false statement, case 1 is applicable here.
Hence, option (a).
Workspace:
Three persons A, B and C gave the following statements:
A says: Either BJP or Congress won the elections.
B says: BJP won.
C says: Neither BJP nor Congress won the elections.
Of these persons, only one person is wrong. Who won the elections?
- A.
BJP
- B.
Congress
- C.
Cannot be determined
- D.
None of these
Answer: Option A
Explanation :
Assuming,
Case 1: BJP wins the election ⇒ Now only C would be wrong.
Case 2: Congress wins the electio ⇒ Now B and C would be wrong.
Case 3: None of them wins the election ⇒ Now A and B would be wrong.
Since only 1 of them is wrong hence, Case 1 is applicable here.
∴ BJP wins the election.
Hence, option (a).
Workspace:
The police rounded up Ankush, Mahesh and Ganesh yesterday because one of them was suspected of robbing the local bank. The 3 suspects gave following statements after intensive questioning:
Ankush: I’m innocent.
Mahesh: I’m innocent.
Ganesh: Mahesh is the guilty one.
Who robbed the bank among the three persons, if only one of the statements will be true?
- A.
Mahesh
- B.
Ankush
- C.
Ganesh
- D.
None of these
Answer: Option B
Explanation :
Assuming,
Case 1: Ankush robbed the bank ⇒ only Mahesh is telling the truth.
Case 2: Mahesh robbed the bank ⇒ Ankush and Ganesh are is telling the truth.
Case 3: Ganesh robbed the bank ⇒ Ankush and Mahesh are telling the truth.
Since only one of them is telling the truth Case 1 is applicable here.
∴ Ankush robbed the bank.
Hence, option (b).
Workspace:
A king’s durbar consists of a knight, a spy and a knave.
Knight speaks only truth, spy can speak either a truth or a lie and the knave speaks only lies.
From the following statements made by 3 people A, B and C comprising the knight, spy and knave though not necessarily in that order, identify the spy.
A: I am knight.
B : A is not knave.
C: If you had asked me, I would say A is the spy.
- A.
A
- B.
B
- C.
C
- D.
Cannot be determined
Answer: Option D
Explanation :
Assuming,
Case 1: A is the knight ⇒ B and C can be spy or knave.
This fits wells with statements made by B and C.
Case 2: B is the knight ⇒ A is spy and C is knave.
This fits wells with statements made by A and C.
Case 3: A is the knight ⇒ A is spy and B is knave.
This contradicts statement made by B.
∴ Based on case 1 and 2, any three of them can be the spy.
Hence, option (d).
Workspace:
Asha and Eesha – Eesha lies on Monday, Tuesday and Wednesday. Asha lies on Thursday, Friday and Saturday. Other days they will say the truth. Professor forgot and asked them what day it is. Both of them said, yesterday I was lying and then professor got the day. What day it is?
- A.
Tuesday
- B.
Thursday
- C.
Friday
- D.
Cannot be determined
Answer: Option B
Explanation :
Eesha lies on Monday, Tuesday and Wednesday whereas Asha lies on Thursday, Friday and Saturday. Other days they will say the truth. We can make the following table :
Asha | Esha | |
Monday | ✔️ | ✖ |
Tuesday | ✔️ | ✖ |
Wednesday | ✔️ | ✖ |
Thursday | ✖ | ✔️ |
Friday | ✖ | ✔️ |
Saturday | ✖ | ✔️ |
Sunday | ✔️ | ✔️ |
Asha can say I was lying yesterday only on Thursday and Sunday.
Esha can say I was lying yesterday only on Thursday and Monday.
∴ Both of them can say yesterday I was lying at the same time only on Thursday.
Hence, option (b).
Workspace:
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