# PE 1 - Binary Logic | LR - Binary Logic

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**Answer the next 3 questions based on the information given below:**

The top 3 rankers of the class Akash, Brijesh and Chetan, not necessarily in the same order , made the following statements about their ranks.

**Akash: **

1. I am not the top ranker.

2. Brijesh is not the second ranker.

3. Chetan is the 3^{rd} ranker.

**Brijesh : **

1. Akash’s 1^{st} statement is false.

2. I am the 3^{rd} ranker.

3. I made two false statements.

**Chetan : **

1. Akash is 1^{st} ranker.

2. Brijesh is not the 2^{nd} ranker.

3. I am the 2^{nd} ranker.

It is known that each of Akash and Chetan made only one false statement. Brijesh made only one true statement.

**PE 1 - Binary Logic | LR - Binary Logic**

Who is the 1^{st} ranker?

- (a)
Akash

- (b)
Brijesh

- (c)
Chetan

- (d)
Cannot be determined

Answer: Option B

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**Explanation** :

It is given that Brijesh made only 1 true statement, i.e., he made 2 false statements.

∴ Brijesh’s third statement is true ⇒ Brijesh’s first two statements are false.

⇒ Akash’s first statement is true and Brijest is not third ranker.

Now, since Akash’s first statement is true ⇒ Akash is not the top ranker.

Since Akash is not the top ranker ⇒ Chetan’s first statement is false.

⇒ Chetan’s second and third statement are true.

⇒ Chetan is the 2^{nd} ranker.

Also, since Akash is not the top ranker, it means that Brijesh is the top ranker and Akash is ranked third.

Hence, option (b).

Workspace:

**PE 1 - Binary Logic | LR - Binary Logic**

Which of the following represents the correct order of truth and false statements made by Chetan?

- (a)
True, False, True

- (b)
True, True, False

- (c)
False, True, True

- (d)
Cannot be determined

Answer: Option C

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**Explanation** :

Consider the solution to the first question of this set.

Chetan’s 1^{st} statement is false and other 2 are true.

Hence, option (c).

Workspace:

**PE 1 - Binary Logic | LR - Binary Logic**

Who is the third ranker?

- (a)
Akash

- (b)
Brijesh

- (c)
Chetan

- (d)
Cannot be determined

Answer: Option A

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**Explanation** :

Consider the solution to the first question of this set.

Akash is the 3^{rd} ranker.

Hence, option (a).

Workspace:

**PE 1 - Binary Logic | LR - Binary Logic**

Three sisters are identical triplets, the oldest by minutes is Asha, and Asha always tells anyone the truth. The next oldest is Eesha, and Eesha always will tell anyone a lie. Usha is the youngest of the three. She sometimes lies and sometimes tells the truth.

Victor, and old friend of the family’s, came over one day and as usual he didn’t know who whom was, as he asked each of them one question.

Victor asked the sister that was sitting on the left, “Which sister is in the middle of you three?” and the answer he received was, “Oh, that’s Asha”.

Victor then asked the sister in the middle, “What is your name?” The response given was, “I am Usha”.

Victor turned to the sister on the right, then asked, “Who is that in the middle?” The sister then replied, “She is Eesha”.

This confused Victor; he had asked the same question three times and received three different answers.

Who was actually sitting in the middle?

- (a)
Asha

- (b)
Eesha

- (c)
Usha

- (d)
Cannot be determined

Answer: Option B

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**Explanation** :

Assuming,

**Case 1:** Asha is sitting on the left.

Since Asha is sitting on the left she would’ve answered the question with either Eesha or Usa.

∴ Asha is not sitting on the left.

**Case 2:** Asha is sitting in the middle.

Since Asha is sitting in the middle she would’ve answered the question as Asha.

∴ Asha is not sitting in the middle.

Asha is sitting in the middle and her answer to the question is

**Case 3:** Asha is sitting on the right.

This is the only position left for Asha. Her answer is Eesha which means Eesha is sitting in the middle and Usa is on the left.

∴ Eesha is sitting in the middle.

Hence, option (b).

Workspace:

**PE 1 - Binary Logic | LR - Binary Logic**

In a group of 5, Suraj said “One of us is lying”. Priya said “Exactly two of us are lying”. Harshit said, “Exactly three of us are lying”. Gautam said, “Exactly four of us are lying”. Abhishek said, “Exactly five of us are lying”. Which one said the truth?

- (a)
Gautam

- (b)
Suraj

- (c)
Abhishek

- (d)
Priya

- (e)
Harshit

Answer: Option A

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**Explanation** :

Assuming,

**Case 1**: One of them is lying ⇒ Suraj is saying the truth and other 4 are lying which contradicts the assumption.

**Case 2**: Two of them are lying ⇒ Priya is saying the truth and other 4 are lying which contradicts the assumption.

**Case 3**: Three of them are lying ⇒ Harshit is saying the truth and other 4 are lying which contradicts the assumption.

**Case 4**: Four of them are lying ⇒ Gautam is saying the truth and other 4 are lying which fits well with the assumption.

**Case 5**: Five of them are lying ⇒ Abhishek is saying the truth and other 4 are lying which contradicts the assumption.

∴ Only Gautam is telling the truth.

Hence, option (a).

Workspace:

**PE 1 - Binary Logic | LR - Binary Logic**

Ashok, Eesha, Farookh and Gowri ran a race.

Ashok said, “I did not finish 1^{st} or 4^{th}”.

Eesha said, “I did not finish 4^{th}”.

Farookh said, “I finished 4^{th}”.

Gowri said, “I finished 4^{th}”.

There were no ties in the competition, and exactly three of the children told the truth. Who finished 4^{th}?

- (a)
Ashok

- (b)
Gowri

- (c)
Farookh

- (d)
Cannot be determined

Answer: Option D

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**Explanation** :

Since Farookh and Gowri made the same statement – “I finished 4^{th}”, one of them is lying.

⇒ Ashok, Eesha and one of Farookh / Gowri are telling the truth.

Based on true statements of Ashok and Eesha, either Farookh or Gowri finshied 4^{th} but we don’t know who.

∴ With the information given we cannot determined who finished 4^{th}.

Hence, option (d).

Workspace:

**PE 1 - Binary Logic | LR - Binary Logic**

Ahmed, Babu, Chitra, David and Eesha each choose a large different number.

Ahmed says, “My number is not the largest and not the smallest”.

Babu says, “My number is not the largest and not the smallest”.

Chitra says, “My number is the largest”.

David says, “My number is the smallest”.

Eesha says, “My number is not smallest”.

Exactly one of the five children is lying. The others are telling the truth. Who has the largest number?

- (a)
Eesha

- (b)
David

- (c)
Chitra

- (d)
Babu

Answer: Option A

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**Explanation** :

If we assume Ahmed has the largest number ⇒ Ahmed and Chitra will be lying. This contradicts the fact that only one of them is lying.

∴ Ahmed cannot have the largest number.

Similarly we can make the following table:

From the table we can see that either Chitra or Eesha can have the largest number.

If Chitra has the largest number then it would not be possible to give samllest number to anyone else such that there in only one liar.

∴ Eesah has the largest number.

Hence, option (a).

Workspace:

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