Binary Logic Questions for CAT with Answers PDF

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.

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.

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.

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.

It is known that Harold lives in the villa, which means that the 2^nd statement made by Owen must be true, whereas the 2^nd 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.

It is known that Harold lives in the villa, which means that the 2^nd statement made by Owen must be true, whereas the 2^nd 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.

It is known that Harold lives in the villa, which means that the 2^nd statement made by Owen must be true, whereas the 2^nd 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.

It is known that Harold lives in the villa, which means that the 2^nd statement made by Owen must be true, whereas the 2^nd 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.

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.

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.

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 Gavin spoke spoke the maximum number of truths, i.e. 2.
Hence, answer option 4 is correct.

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:


It can be observed from the arrangement made above that option (4) is false.

 Let Henry be the truth-teller. From Henry's first statement, Daniel is not the alternator. Hence, Daniel must be the liar. As per Henry's second statement, Henry must be travelling in Coach-B because he is the truth-teller.
Since Daniel is a liar, from his first statement, the alternator is not travelling in Coach-C. Hence, the alternator must be travelling in Coach-A. The liar must be travelling in Coach-C. In this case, Hugh must be the alternator. Hugh's second statement is false and first statement is true. Hence, this is one possible case.
Let Daniel be the truth-teller. From Daniel's first statement, the alternator is travelling in Coach-C. Since Daniel is the truth-teller, Henry's first statement is true. Hence, Henry must be the alternator. His second statement must be false. Hence, the truth-teller is not travelling in Coach-B. Since the alternator is travelling in Coach-C, the truth-tellers is travelling in Coach-A and the liar must be travelling in Coach-B. Since Daniel is the truth-teller and Henry is the alternator, Hugh must be the liar. However, Hugh's first statement is true as Henry is not travelling in Coach-A (since Henry is the alternator, he must be travelling in Coach-C). Hence, Hugh cannot be the liar. Therefore, this case is not possible.
Let Hugh be the truth-teller. Daniel is the alternator and Henry is the liar. Daniel's second statement is false and hence, his first statement must be true. Therefore, the alternator is travelling in Coach-C. Since Henry is the liar, the truth-teller cannot be travelling in Coach-B. Hence, the truth-teller must be travelling in Coach-A and the liar must be travelling in Coach-B. This is one possible case.

Thus, it can be concluded that Hugh is travelling in Coach-A.
Hence, answer option 1 is correct.

 Let Henry be the truth-teller. From Henry's first statement, Daniel is not the alternator. Hence, Daniel must be the liar. As per Henry's second statement, Henry must be travelling in Coach-B because he is the truth-teller.
Since Daniel is a liar, from his first statement, the alternator is not travelling in Coach-C. Hence, the alternator must be travelling in Coach-A. The liar must be travelling in Coach-C. In this case, Hugh must be the alternator. Hugh's second statement is false and first statement is true. Hence, this is one possible case.
Let Daniel be the truth-teller. From Daniel's first statement, the alternator is travelling in Coach-C. Since Daniel is the truth-teller, Henry's first statement is true. Hence, Henry must be the alternator. His second statement must be false. Hence, the truth-teller is not travelling in Coach-B. Since the alternator is travelling in Coach-C, the truth-tellers is travelling in Coach-A and the liar must be travelling in Coach-B. Since Daniel is the truth-teller and Henry is the alternator, Hugh must be the liar. However, Hugh's first statement is true as Henry is not travelling in Coach-A (since Henry is the alternator, he must be travelling in Coach-C). Hence, Hugh cannot be the liar. Therefore, this case is not possible.
Let Hugh be the truth-teller. Daniel is the alternator and Henry is the liar. Daniel's second statement is false and hence, his first statement must be true. Therefore, the alternator is travelling in Coach-C. Since Henry is the liar, the truth-teller cannot be travelling in Coach-B. Hence, the truth-teller must be travelling in Coach-A and the liar must be travelling in Coach-B. This is one possible case.

In both the cases, Hugh spoke at least one true statement.
Hence, answer option 3 is correct.

 Let Henry be the truth-teller. From Henry's first statement, Daniel is not the alternator. Hence, Daniel must be the liar. As per Henry's second statement, Henry must be travelling in Coach-B because he is the truth-teller.
Since Daniel is a liar, from his first statement, the alternator is not travelling in Coach-C. Hence, the alternator must be travelling in Coach-A. The liar must be travelling in Coach-C. In this case, Hugh must be the alternator. Hugh's second statement is false and first statement is true. Hence, this is one possible case.
Let Daniel be the truth-teller. From Daniel's first statement, the alternator is travelling in Coach-C. Since Daniel is the truth-teller, Henry's first statement is true. Hence, Henry must be the alternator. His second statement must be false. Hence, the truth-teller is not travelling in Coach-B. Since the alternator is travelling in Coach-C, the truth-tellers is travelling in Coach-A and the liar must be travelling in Coach-B. Since Daniel is the truth-teller and Henry is the alternator, Hugh must be the liar. However, Hugh's first statement is true as Henry is not travelling in Coach-A (since Henry is the alternator, he must be travelling in Coach-C). Hence, Hugh cannot be the liar. Therefore, this case is not possible.
Let Hugh be the truth-teller. Daniel is the alternator and Henry is the liar. Daniel's second statement is false and hence, his first statement must be true. Therefore, the alternator is travelling in Coach-C. Since Henry is the liar, the truth-teller cannot be travelling in Coach-B. Hence, the truth-teller must be travelling in Coach-A and the liar must be travelling in Coach-B. This is one possible case.

If Henry is not the liar, then Henry is the truth-teller.
Hence, answer option 2 is correct.