Binary logic || Logical reasoning || CAT 2021 || 31 May (App update required to attempt this test) for CAT & MBA Exams

Question 1

Directions: In a country there are categories of persons – truth tellers, liars and alternators. P met three people, H, B and C from that country. Each of these belong to a different category and made the following statements –
H – City X is 30 km to the North of City Y. I am a liar.
B – City W is 50 km away to the West of City Z. City M is 50 km away to the south of city W.
C – City Y is not to the west of city z. H is a truth-teller.

In which direction is city X with respect to city M?

Question 2

Directions: In a country there are categories of persons – truth tellers, liars and alternators. P met three people, H, B and C from that country. Each of these belong to a different category and made the following statements –
H – City X is 30 km to the North of City Y. I am a liar.
B – City W is 50 km away to the West of City Z. City M is 50 km away to the south of city W.
C – City Y is not to the west of city z. H is a truth-teller.

If the distance between city Y and city Z is 10 km, then how far is city W from city X?

Question 3

Directions: In a country there are categories of persons – truth tellers, liars and alternators. P met three people, H, B and C from that country. Each of these belong to a different category and made the following statements –
H – City X is 30 km to the North of City Y. I am a liar.
B – City W is 50 km away to the West of City Z. City M is 50 km away to the south of city W.
C – City Y is not to the west of city z. H is a truth-teller.

Who among the following is the truth-teller?

Question 4

Directions: Read the following information carefully and answer the questions based on it.

4 persons, P, N, M and S are the top four rankers of the subject Math, Physics, Chemistry and commerce, not necessarily in the same order. No person got the same rank in any of two subjects. Each of them knows the following:

P – M is 4^th ranker in chemistry. S is the 4^th ranker in physics. N is the 1^st ranker in math.
N – He is the first ranker in commerce. S is the first ranker in chemistry. M is the third ranker in physics.
M – He is the first ranker in commerce. S is the 4^th ranker in Chemistry. P is the first ranker in physics.
S – P is the 3^rd ranker in commerce. He is himself the 4^th ranker in math. N is the 2^nd ranker in physics.

Each of them knows a true and a false statement alternatively and in total they know equal number of true and false statements.

Who is the third ranker in chemistry?

Question 5

Directions: Read the following information carefully and answer the questions based on it.

4 persons, P, N, M and S are the top four rankers of the subject Math, Physics, Chemistry and commerce, not necessarily in the same order. No person got the same rank in any of two subjects. Each of them knows the following:

P – M is 4^th ranker in chemistry. S is the 4^th ranker in physics. N is the 1^st ranker in math.
N – He is the first ranker in commerce. S is the first ranker in chemistry. M is the third ranker in physics.
M – He is the first ranker in commerce. S is the 4^th ranker in Chemistry. P is the first ranker in physics.
S – P is the 3^rd ranker in commerce. He is himself the 4^th ranker in math. N is the 2^nd ranker in physics.

Each of them knows a true and a false statement alternatively and in total they know equal number of true and false statements.

What is S’s rank in Physics?

Question 6

Directions: Read the following information carefully and answer the questions based on it.

4 persons, P, N, M and S are the top four rankers of the subject Math, Physics, Chemistry and commerce, not necessarily in the same order. No person got the same rank in any of two subjects. Each of them knows the following:

P – M is 4^th ranker in chemistry. S is the 4^th ranker in physics. N is the 1^st ranker in math.
N – He is the first ranker in commerce. S is the first ranker in chemistry. M is the third ranker in physics.
M – He is the first ranker in commerce. S is the 4^th ranker in Chemistry. P is the first ranker in physics.
S – P is the 3^rd ranker in commerce. He is himself the 4^th ranker in math. N is the 2^nd ranker in physics.

Each of them knows a true and a false statement alternatively and in total they know equal number of true and false statements.

In which subject did N get a better rank than P but a worse rank than M?

Question 7

Directions: Read the following information carefully and answer the questions based on it.

4 persons, P, N, M and S are the top four rankers of the subject Math, Physics, Chemistry and commerce, not necessarily in the same order. No person got the same rank in any of two subjects. Each of them knows the following:

P – M is 4^th ranker in chemistry. S is the 4^th ranker in physics. N is the 1^st ranker in math.
N – He is the first ranker in commerce. S is the first ranker in chemistry. M is the third ranker in physics.
M – He is the first ranker in commerce. S is the 4^th ranker in Chemistry. P is the first ranker in physics.
S – P is the 3^rd ranker in commerce. He is himself the 4^th ranker in math. N is the 2^nd ranker in physics.

Each of them knows a true and a false statement alternatively and in total they know equal number of true and false statements.

What is N’s rank in commerce?

Question 8

Direction: The following table represents addition of two six-digit numbers given in the first and the second rows, while the sum is given in the third row. In the representation, each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 has been coded with one letter among A, B, C, D, E, F, G, H, J, K, with distinct letters representing distinct digits.

Which digit does the letter A represent?

Question 9

Direction: The following table represents addition of two six-digit numbers given in the first and the second rows, while the sum is given in the third row. In the representation, each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 has been coded with one letter among A, B, C, D, E, F, G, H, J, K, with distinct letters representing distinct digits.

Which digit does the letter B represent?

Question 10

Direction: The following table represents addition of two six-digit numbers given in the first and the second rows, while the sum is given in the third row. In the representation, each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 has been coded with one letter among A, B, C, D, E, F, G, H, J, K, with distinct letters representing distinct digits.

Which among the digits 3, 4, 6 and 7 cannot be represented by the letter D?