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Test: Binary Logic (April 25) - CAT MCQ


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10 Questions MCQ Test Daily Test for CAT Preparation - Test: Binary Logic (April 25)

Test: Binary Logic (April 25) for CAT 2024 is part of Daily Test for CAT Preparation preparation. The Test: Binary Logic (April 25) questions and answers have been prepared according to the CAT exam syllabus.The Test: Binary Logic (April 25) MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Binary Logic (April 25) below.
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Test: Binary Logic (April 25) - Question 1
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Who among the three always tells the truth?

Detailed Solution for Test: Binary Logic (April 25) - Question 1

Let us look at the first statement of Gerald - "Leslie is the truth-teller". This statement implies that Gerald is not the truth-teller as there is only one truth-teller, and if Leslie is the truth-teller, then Gerald cannot be the truth-teller.
Thus, Gerald can either be an alternator or liar.  ......(1)
Let us see the first statement of Leslie - "Gerald is not the alternator". If Leslie is the truth-teller, then Gerald will be a liar, in which case Leslie cannot be the truth-teller.    ......(2)
From (1) and (2), Samuel should be the truth-teller. Now, Leslie can either be the liar or the alternator.
Case (i)
If Leslie is an alternator, his first statement would be true and second statement would be false, and both the statements of Gerald would be false. Hence, it is a possible case. In such a case, the buses of each of the people cannot be determined.
Case (ii)
If Leslie is a liar, both his statements would be false, and the first statement of Gerald would be false and his second statement would be true. As there are no contradictions, this is also a possible case.
In this case, Gerald would be coming from City-B, Samuel would be coming from City-A and Leslie would be coming from City-C.
Hence, Samuel is the truth-teller.

Test: Binary Logic (April 25) - Question 2
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The person in the bus coming from which of the following cities, always alternates between speaking the truth and a lie?

Detailed Solution for Test: Binary Logic (April 25) - Question 2

Let us look at the first statement of Gerald - "Leslie is the truth-teller". This statement implies that Gerald is not the truth-teller as there is only one truth-teller, and if Leslie is the truth-teller, then Gerald cannot be the truth-teller.
Thus, Gerald can either be an alternator or liar.  ......(1)
Let us see the first statement of Leslie - "Gerald is not the alternator". If Leslie is the truth-teller, then Gerald will be a liar, in which case Leslie cannot be the truth-teller.    ......(2)
From (1) and (2), Samuel should be the truth-teller. Now, Leslie can either be the liar or the alternator.
Case (i)
If Leslie is an alternator, his first statement would be true and second statement would be false, and both the statements of Gerald would be false. Hence, it is a possible case. In such a case, the buses of each of the people cannot be determined.
Case (ii)
If Leslie is a liar, both his statements would be false, and the first statement of Gerald would be false and his second statement would be true. As there are no contradictions, this is also a possible case.
In this case, Gerald would be coming from City-B, Samuel would be coming from City-A and Leslie would be coming from City-C.
As seen above, the city from which the alternator is coming cannot be determined.

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Test: Binary Logic (April 25) - Question 3
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Who among the following is coming from City-C?

Detailed Solution for Test: Binary Logic (April 25) - Question 3

Let us look at the first statement of Gerald - "Leslie is the truth-teller". This statement implies that Gerald is not the truth-teller as there is only one truth-teller, and if Leslie is the truth-teller, then Gerald cannot be the truth-teller.
Thus, Gerald can either be an alternator or liar.  ......(1)
Let us see the first statement of Leslie - "Gerald is not the alternator". If Leslie is the truth-teller, then Gerald will be a liar, in which case Leslie cannot be the truth-teller.    ......(2)
From (1) and (2), Samuel should be the truth-teller. Now, Leslie can either be the liar or the alternator.
Case (i)
If Leslie is an alternator, his first statement would be true and second statement would be false, and both the statements of Gerald would be false. Hence, it is a possible case. In such a case, the buses of each of the people cannot be determined.
Case (ii)
If Leslie is a liar, both his statements would be false, and the first statement of Gerald would be false and his second statement would be true. As there are no contradictions, this is also a possible case.
In this case, Gerald would be coming from City-B, Samuel would be coming from City-A and Leslie would be coming from City-C.
Hence, answer option 4 is correct.

Test: Binary Logic (April 25) - Question 4
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Who among the following is a liar?
Detailed Solution for Test: Binary Logic (April 25) - Question 4

Let us look at the first statement of Gerald - "Leslie is the truth-teller". This statement implies that Gerald is not the truth-teller as there is only one truth-teller, and if Leslie is the truth-teller, then Gerald cannot be the truth-teller.
Thus, Gerald can either be an alternator or liar.  ......(1)
Let us see the first statement of Leslie - "Gerald is not the alternator". If Leslie is the truth-teller, then Gerald will be a liar, in which case Leslie cannot be the truth-teller.    ......(2)
From (1) and (2), Samuel should be the truth-teller. Now, Leslie can either be the liar or the alternator.
Case (i)
If Leslie is an alternator, his first statement would be true and second statement would be false, and both the statements of Gerald would be false. Hence, it is a possible case. In such a case, the buses of each of the people cannot be determined.
Case (ii)
If Leslie is a liar, both his statements would be false, and the first statement of Gerald would be false and his second statement would be true. As there are no contradictions, this is also a possible case.
In this case, Gerald would be coming from City-B, Samuel would be coming from City-A and Leslie would be coming from City-C.
We cannot determine which city the liar is coming from.
Hence, answer option 4 is correct.

Test: Binary Logic (April 25) - Question 5
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Who among the following lives in the bunglow?
Detailed Solution for Test: Binary Logic (April 25) - Question 5

It is known that Harold lives in the villa, which means that the 2nd statement made by Owen must be true, whereas the 2nd statement made by Harold must be false. As Roger says that he and Adrian both live in the bunglow, Roger cannot be the person who always speaks the truth, as each person lives in exactly one type of house and exactly one type of house is occupied by one friend. This means only Adrian can always speak the truth, as there must be at least one person who always speaks the truth.
We take this as the basis and get the arrangement as given below:

Hence, Owen lives in the bunglow, which means option 2 is correct.

Test: Binary Logic (April 25) - Question 6
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Who among the following always speaks the truth?
Detailed Solution for Test: Binary Logic (April 25) - Question 6

It is known that Harold lives in the villa, which means that the 2nd statement made by Owen must be true, whereas the 2nd statement made by Harold must be false. As Roger says that he and Adrian both live in the bunglow, Roger cannot be the person who always speaks the truth, as each person lives in exactly one type of house and exactly one type of house is occupied by one friend. This means only Adrian can always speak the truth, as there must be at least one person who always speaks the truth.
We take this as the basis and get the arrangement as given below:

Adrian always speaks the truth.
Hence, answer option 3 is correct.

Test: Binary Logic (April 25) - Question 7
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Who always alternate(s) between telling the truth and lying?
Detailed Solution for Test: Binary Logic (April 25) - Question 7

It is known that Harold lives in the villa, which means that the 2nd statement made by Owen must be true, whereas the 2nd statement made by Harold must be false. As Roger says that he and Adrian both live in the bunglow, Roger cannot be the person who always speaks the truth, as each person lives in exactly one type of house and exactly one type of house is occupied by one friend. This means only Adrian can always speak the truth, as there must be at least one person who always speaks the truth.
We take this as the basis and get the arrangement as given below:

Thus, it can be concluded that Harold and Owen alternate between telling the truth and lying.
Hence, answer option 3 is correct.

Test: Binary Logic (April 25) - Question 8
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Who lives in the apartment?
Detailed Solution for Test: Binary Logic (April 25) - Question 8

It is known that Harold lives in the villa, which means that the 2nd statement made by Owen must be true, whereas the 2nd statement made by Harold must be false. As Roger says that he and Adrian both live in the bunglow, Roger cannot be the person who always speaks the truth, as each person lives in exactly one type of house and exactly one type of house is occupied by one friend. This means only Adrian can always speak the truth, as there must be at least one person who always speaks the truth.
We take this as the basis and get the arrangement as given below:

Thus, it can be concluded that Adrian lives in the apartment.
Hence, answer option 3 is correct.

Test: Binary Logic (April 25) - Question 9
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Who among the following ate black pudding?
Detailed Solution for Test: Binary Logic (April 25) - Question 9

Each person alternates between a truth and a 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 Walter are in the order, True, False, True. Then, we get the following arrangement:

Here, all the three statements given by Neil become false. Hence, we'll try the second combination.
(ii) Assume that the three statements given by Walter are in the order False, True, False.
Then, we get the following arrangement:


Thus, Walter ate the black pudding.
Hence, answer option 1 is correct.

Test: Binary Logic (April 25) - Question 10
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Roy ate
Detailed Solution for Test: Binary Logic (April 25) - Question 10

Each person alternates between a truth and a 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 Walter are in the order, True, False, True. Then, we get the following arrangement:

Here, all the three statements given by Neil become false. Hence, we'll try the second combination.
(ii) Assume that the three statements given by Walter are in the order False, True, False.
Then, we get the following arrangement:


Thus, it can be concluded that Roy ate Kippers.
Hence, answer option 4 is correct.

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