Test: Binary Logic - CAT MCQ

# Test: Binary Logic - CAT MCQ

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## 10 Questions MCQ Test Logical Reasoning (LR) and Data Interpretation (DI) - Test: Binary Logic

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Test: Binary Logic - Question 1

### Directions: Read the question below very carefully and choose the correct answer for the questions that follow: On an island ‘Tristan da Cunha’ the inhabitants always answer any question with two sentences – one of which is always true and the other always false. The Head of the island discovers illegal activities, in order to determine the identity of the culprits and also to know more about the next heist on the basis of a plane. You and what it looks like. This is what they have to say: S: It arrives at 9:00 p.m. The colour of the plane is only red. R: It arrives at 9:00 p.m. The colour of the plane is only red. B: I know at what time the ship arrives. R is lying about the time of arrival. Q. At what time does the plane arrive?

Detailed Solution for Test: Binary Logic - Question 1
• Both S and R say the plane arrives at 9:00 p.m. and the color is red. Since one of them is lying about both parts of the statement, the time could be true or false for either S or R.
• B claims to know the ship's arrival time and says R is lying about the arrival time of the plane. This gives us two possibilities:
• Scenario 1: If B is telling the truth about the ship and R is lying about the  plane arrival time, then the plane doesn't arrive at 9:00 p.m. (because R's statement about the time would be false).
• Scenario 2: If B is lying about the ship and R is telling the truth about the plane arrival time, then the plane does arrive at 9:00 p.m. (because R's statement about the time would be true).
• Looking at both scenarios, the only consistent information is that one of them (S or R) is lying about the plane's arrival time. We cannot determine for sure which one is telling the truth about the time based on the given statements.
• Therefore, we cannot definitively say at what time the plane arrives. We only know it's either 9:00 p.m. or not 9:00 p.m.
Test: Binary Logic - Question 2

### Directions: Read the question below very carefully and choose the correct answer for the questions that follow: On an island ‘Tristan da Cunha’ the inhabitants always answer any question with two sentences – one of which is always true and the other always false. The Head of the island discovers illegal activities, in order to determine the identity of the culprits and also to know more about the next heist on the basis of a plane. You and what it looks like. This is what they have to say: S: It arrives at 9:00 p.m. The colour of the plane is only red. R: It arrives at 9:00 p.m. The colour of the plane is only red. B: I know at what time the ship arrives. R is lying about the time of arrival. Q. What is the color of the plane?

Detailed Solution for Test: Binary Logic - Question 2
1. S and R: Both say the plane arrives at 9:00 p.m. and the color is red. Since one of their statements must be false, the arrival time (9:00 p.m.) could be either true or false, but the color being only red must be false for at least one of them.

2. B:    B claims to know the ship's arrival time. This doesn't tell us anything about the plane.

B also says R is lying about the arrival time.

We now have two possibilities:

Case 1: S is telling the truth about the arrival time (9:00 p.m.): In this case, R must be lying about the arrival time. Since we know one of their statements about color is also false, then the plane's color cannot be only red (as both S and R claim). Therefore, the plane's color must be something other than red.

Case 2: R is telling the truth about the arrival time (9:00 p.m.): Following the same logic, S must be lying about the arrival time. Since their statements about color contradict each other (only red vs. not only red), the plane's color cannot be only red.

In both cases, regardless of who's telling the truth about the arrival time, the information about the plane's color being only red is confirmed to be false.

Therefore, the color of the plane is something other than red.

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Test: Binary Logic - Question 3

### Directions: Read the question below very carefully and choose the correct answer for the questions that follow: There are two types of inhabitants at Hawaii Islands – X type and Y type. The X type of inhabitants always speaks the truth and the Y type of inhabitants always lie. Q John says, “I always lie.” Which type of an inhabitant is he?

Test: Binary Logic - Question 4

Directions: Read the question below very carefully and choose the correct answer for the questions that follow:

There are two types of inhabitants at Hawaii Islands – X type and Y type. The X type of inhabitants always speaks the truth and the Y type of inhabitants always lie.

Q. David says, "According to John. I always speak the truth." Which of the following is a correct conclusion?

Detailed Solution for Test: Binary Logic - Question 4

Explanation: If David is telling the truth, then according to John, David always speaks the truth. This implies that John, who makes the claim about David, must be of type X, as his statement about David's truthfulness aligns with the truth.

Test: Binary Logic - Question 5

Directions: Read the question below very carefully and choose the correct answer for the questions that follow:

There are two types of inhabitants at Hawaii Islands – X type and Y type. The X type of inhabitants always speaks the truth and the Y type of inhabitants always lie.

Q. Mike says. "Albert and I are of the same type." Which of the following is a correct conclusion?

Detailed Solution for Test: Binary Logic - Question 5

Explanation: If Mike is of type X and tells the truth, then Albert must also be of type X, which would make Mike's statement true. However, if Mike is of type Y and lies, then Albert must be of type X to make Mike's statement false, which means Mike and Albert are not of the same type. Therefore, in either case Albert has to be of type X.

Test: Binary Logic - Question 6

Directions: Read the question below very carefully and choose the correct answer for the questions that follow:

There are two types of inhabitants at Hawaii Islands – X type and Y type. The X type of inhabitants always speaks the truth and the Y type of inhabitants always lie.

Q. Rolly says "Soni and I are of different types." Which of the following is a correct conclusion?

Detailed Solution for Test: Binary Logic - Question 6

Different means not the same as another or each other so evidently if Rolly is Type A then Soni would be Type B.

Test: Binary Logic - Question 7

Directions: Read the question below very carefully and choose the correct answer for the questions that follow:

There are two types of inhabitants at Hawaii Islands – X type and Y type. The X type of inhabitants always speaks the truth and the Y type of inhabitants always lie.

Q. Mike says, "At least one person among Albert and I always lies." What types are Mike and Albert-respectively?

Detailed Solution for Test: Binary Logic - Question 7

Mike says, "At least one person among Albert and I always lies.
Let Assume Mike is Y type of inhabitant who always Lies
then Mike Says . "At least one person among Albert and I always lies"
, we Have already assumed that Milke Always lies Hence Mike is speaking truth by saying  At least one person among Albert and Mike always lies   as Mike Always lies is assumed
Hence our Assumption is Wrong,
=> Mike is not Y type
=>   Mike is X type of inhabitant who always Speak Truth
Now Mike is saying that At least one person among Albert and Mike always lies.
But we Know That Mike always speak truth
hence Albert has to speak always lie
=> Albert is Y  type of inhabitant who always Lies
Mike - X Type  of inhabitant who always Speak Truth
Albert - Y type of inhabitant who always Lies

Test: Binary Logic - Question 8

Directions: Refer to the passage below and answer questions given below it.

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 3rd ranker.

Brijesh :
1. Akash's 1st statement is false.
2. I am the 3rd ranker.
3. I made two false statements.

Chetan :
1. Akash is 1st ranker.
2. Brijesh is not the 2nd ranker.
3. I am the 2nd ranker.

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

Who is the 1st ranker?

Detailed Solution for Test: Binary Logic - Question 8

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 2nd ranker.
• Also, since Akash is not the top ranker, it means that Brijesh is the top ranker and Akash is ranked third.

Hence, option (c).

Test: Binary Logic - Question 9

Directions: Refer to the passage below and answer questions given below it.

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 3rd ranker.

Brijesh :
1. Akash's 1st statement is false.
2. I am the 3rd ranker.
3. I made two false statements.

Chetan :
1. Akash is 1st ranker.
2. Brijesh is not the 2nd ranker.
3. I am the 2nd ranker.

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

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

Detailed Solution for Test: Binary Logic - Question 9

Consider the solution to the first question of this set.
Chetan's 1st statement is false and other 2 are true.
Hence, option (B).

Test: Binary Logic - Question 10

Directions: Refer to the passage below and answer questions given below it.

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 3rd ranker.

Brijesh :
1. Akash's 1st statement is false.
2. I am the 3rd ranker.
3. I made two false statements.

Chetan :
1. Akash is 1st ranker.
2. Brijesh is not the 2nd ranker.
3. I am the 2nd ranker.

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

Who is the third ranker?

Detailed Solution for Test: Binary Logic - Question 10

Solution :

Consider the solution to the first question of this set.
Akash is the 3rd ranker.
Hence, option (a).

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## Logical Reasoning (LR) and Data Interpretation (DI)

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