LOGICAL Problems in TCS Solved Q's:
Question 1
For the IPL 5 cricket matches Mr. Bala Josiar has been predicting the winner of each match with amazing success. It is rumored that in a match between 2 teams X and Y, Bala Josiar picks X with the same probability as X's chances of winning. Let's assume such rumors to be true and that in a match between Rajasthan Royals and Chennai Super Kings, Chennai Super Kings the stronger team seems to have a probability of 3/4 of winning the game. What is the probability that Bala Josiar will correctly pick the winner of the Rajasthan Royals–Chennai Super Kings game?
a) 7/ 16 b) 9/16 c) 3/4 d) 10/16
Answer : d) 10/16
Solution :
Probability that CSK wins = 3/4
Probability that RR wins = 1 - Probability that CSK wins = 1 - 3/4 = 1/4
Probability of picking a winner = Probability of picking RR x Probability that RR wins + Probability of picking CSK x Probability that CSK wins
Bala Josiar picks with the same probability of a team’s chance of winning. This means, Probability of picking RR = Probability that RR wins and Probability of picking CSK = Probability that CSK wins
Therefore, Probability of picking a winner = (Probability that CSK wins)2 + (Probability that RR wins)2
= ( 3/4 )2 + (1/4)2
= 9/16 + 1/16
= (9 + 1) / 16
= 10/16
Question 2
Mr. Randor Guy, the famous astrologer staying at Anna Nagar, Chennai has been able to predict the winner of each Hockey match with amazing success. It is told in the sports circle that in a match between two teams A and B, Mr. Randor Guy picks A team with the same probability as A’s chances of winning. But he seems to be incapable of predicting a tie. Let us assume such rumors to be true and that in a match between Pakistan and India, India the stronger team has a probability of 2/3 of winning the game. Based on past data it is also estimated that the probability of match getting tied is 1/9. What is the probability that Randor Guy will correctly pick the winner of the Pakistan-India game?
a) 4/9 b) 2/3 c) 52/81 d) none of these.
Answer : c) 52/81
Solution :
This question is very similar to the previous question, except the fact that there is a probability of tie as well.
Probability of India winning = 2/3
Probability of Pakistan winning = 1 - Probability of India winning - Probability of Tie
= 1 - 2/3 - 1/9 = 1 - 5/9 = 4/9
So probability of picking a winner = probability of picking Pakistan* Probability of Pakistan winning + probability of picking India* Probability of India winning + probability of picking a tie x probability of tie ....(1)
Randor Guy picks with the same probability of a team’s chance of winning.
Therefore, Probability of picking Pakistan = Probability of Pakistan winning, Probability of picking India = Probability of India winning. Also we know that he is unable to predict a tie. Therefore, probability of picking a Tie = 0.
Applying above in eq (1) we get,
probability of picking a winner = (Probability of Pakistan winning )2+(Probability of India winning)2+ 0 x probability of tie
= ( 4/9 * 4/9) + ( 2/3* 2/3) + 0
= 16/81 + 4/9
= (16 + 36) / 81
= 52/81
Question 3
Om Navasakthi Astrologers , Chennai has been able to predict the winner of each football match with amazing success. It is told in the sports circle that in a match between two teams A and B, Om Navasakthi Astrologers picks A team with the same probability as B’s chances of winning and vice versa. Let us assume such rumors to be true and that in a match between Germany and Brazil, Brazil the stronger team has a probability of 4/7 of winning the game. What is the probability that Om Navasakthi Astrologers will correctly pick the winner of the Germany-Brazil game?
a) 24/49 b) 4/7 c) 18/49 d) none of these.
Answer : a) 24/49
Solution :
This is similar to earlier questions except the fact that Astrologers pick A team with the same probability as B’s chances of winning and pick B team with the same probability as A's chances of winning.
Probability of Brazil winning = 4/7.
Therefore, Probability of Germany winning = 1 - 4/7 = 3/7
So probability of picking a winner = probability of picking Brazil*Probability of Brazil winning + probability of picking Germany * Probability of Germany winning ....(1)
Astrologers pick A team with the same probability as B’s chances of winning and pick B team with the same probability as A's chances of winning.
Therefore, Probability of Brazil winning = probability of picking Germany and Probability of Germany winning = probability of picking Brazil
Applying this in eq (1) we get
probability of picking a winner = ( 3/7 * 4/7) + ( 4/7* 3/7)
= 12/49 + 12/49
= 24/49
Question 4
Sneha is engaged. Her Fiance is one amongst Abdul, John, King and Vimal. Sneha either speaks truth or lies. One of four men always speaks truth while others may or may not speak the truth. Now based on the below statements, can you find the Fiance ?
1) Abdul says "Sneha always speaks truth".
2) King says "Sneha always lies".
3) Vimal says "Sneha always speaks truth but only to him".
4) John says "The only truth speaking person amongst Vimal and John is Sneha's Fiance"
a) Abdul b) King c) Vimal d) John.
Answer : d) John
Solution :
From the question, we know clearly that Sneha can speak either Truth or Lies.
But as per statement (1) Abul says "Sneha always speaks truth". Hence this statement cannot be true. Hence our inference is that Abdul always lies.
As per statement (2) King says "Sneha always lies". Again this statement is false as Sneha can speak either Truth or Lies. Hence we can infer that King always lies.
On statement (3) Vimal says "Sneha always speaks truth but only to him". But there is no evidence / proof for this claim on data in question. Hence we can safely consider that Vimal also lies always.
In question it is clearly given that one of four men always speaks truth while others may or may not speak the truth. Since we have concluded Abdul, King and Vimal always lie, John should be the only truth speaking man.
According to statement (4) John says that "The only truth speaking person amongst Vimal and John is Sneha's Fiance". Since John is found to speak truth always, this particular statement from John should be absolutely True.
Also we have found earlier that Vimal always lies. Hence the truth speaking person John has to be the Fiance.
Question 5
Three men Ravi, Ram, Rahul and two women Rekha and Padma were seated next to each other (not in order given) in a meeting. The arrangement was that the person who speaks definitely the truth will occupy the first position and the person who speaks definite lie always will be the last. The middle three positions will be filled by people whose statements may be truth or may be false. Can you find the correct arrangement from the options based on the statements below :
1) Padma says the probability of her occupying the 4th place is lesser than the probability of her occupying 1st place.
2) Rahul says that "Padma lies always when calculating probability"
3) Rekha says "Ram is the tallest of the 5 people"
3) Ravi says "He will be leaving early provided Rahul is a truth speaking person"
4) Ram says "He does not know probability"
a) Rahul - Ravi - Rekha - Ram - Padma b) Ravi - Rahul - Rekha - Ram - Padma
c) Rekha - Rahul - Ravi - Padma - Ram d) Rahul - Ravi - Ram - Padma -Rekha
Answer : a) Rahul - Ravi - Rekha - Ram - Padma
Solution :
Though the question looks bit difficult it is actually a simple question provided you can quickly extract out only required data and ignore irrelevant details.
All the options have different combinations for 1st and last positions. This means, if you are smart enough to find the person who always speaks truth and the person who always speaks lies, it is more than enough to answer the question.
According to statement I, Padma says that the probability of her occupying the 4th place is lesser than the probability of her occupying 1st place. But this cannot be true. This is because probability of Padma to occupy any given position is 1/5 . (1/5 is the probability of Padma to occupy any given position be it 1st or 2nd or 3rd or 4th or 5th positions). Therefore we can safely conclude that Padma is definitely lying.
According to statement 2, Rahul says "Padma lies always when calculating probability". This is a definite truth based on our conclusion in previous paragraph. We can safely conclude that Rahul speaks definitely the truth.
From the above two paragraphs, we can say that 1st position will be occupied by Rahul (as he speaks definite truth) and the last position will be occupied by Padma (as she speaks definite lies). Only option that has this combination is option a) and hence the answer.
Question 1
For the IPL 5 cricket matches Mr. Bala Josiar has been predicting the winner of each match with amazing success. It is rumored that in a match between 2 teams X and Y, Bala Josiar picks X with the same probability as X's chances of winning. Let's assume such rumors to be true and that in a match between Rajasthan Royals and Chennai Super Kings, Chennai Super Kings the stronger team seems to have a probability of 3/4 of winning the game. What is the probability that Bala Josiar will correctly pick the winner of the Rajasthan Royals–Chennai Super Kings game?
a) 7/ 16 b) 9/16 c) 3/4 d) 10/16
Answer : d) 10/16
Solution :
Probability that CSK wins = 3/4
Probability that RR wins = 1 - Probability that CSK wins = 1 - 3/4 = 1/4
Probability of picking a winner = Probability of picking RR x Probability that RR wins + Probability of picking CSK x Probability that CSK wins
Bala Josiar picks with the same probability of a team’s chance of winning. This means, Probability of picking RR = Probability that RR wins and Probability of picking CSK = Probability that CSK wins
Therefore, Probability of picking a winner = (Probability that CSK wins)2 + (Probability that RR wins)2
= ( 3/4 )2 + (1/4)2
= 9/16 + 1/16
= (9 + 1) / 16
= 10/16
Question 2
Mr. Randor Guy, the famous astrologer staying at Anna Nagar, Chennai has been able to predict the winner of each Hockey match with amazing success. It is told in the sports circle that in a match between two teams A and B, Mr. Randor Guy picks A team with the same probability as A’s chances of winning. But he seems to be incapable of predicting a tie. Let us assume such rumors to be true and that in a match between Pakistan and India, India the stronger team has a probability of 2/3 of winning the game. Based on past data it is also estimated that the probability of match getting tied is 1/9. What is the probability that Randor Guy will correctly pick the winner of the Pakistan-India game?
a) 4/9 b) 2/3 c) 52/81 d) none of these.
Answer : c) 52/81
Solution :
This question is very similar to the previous question, except the fact that there is a probability of tie as well.
Probability of India winning = 2/3
Probability of Pakistan winning = 1 - Probability of India winning - Probability of Tie
= 1 - 2/3 - 1/9 = 1 - 5/9 = 4/9
So probability of picking a winner = probability of picking Pakistan* Probability of Pakistan winning + probability of picking India* Probability of India winning + probability of picking a tie x probability of tie ....(1)
Randor Guy picks with the same probability of a team’s chance of winning.
Therefore, Probability of picking Pakistan = Probability of Pakistan winning, Probability of picking India = Probability of India winning. Also we know that he is unable to predict a tie. Therefore, probability of picking a Tie = 0.
Applying above in eq (1) we get,
probability of picking a winner = (Probability of Pakistan winning )2+(Probability of India winning)2+ 0 x probability of tie
= ( 4/9 * 4/9) + ( 2/3* 2/3) + 0
= 16/81 + 4/9
= (16 + 36) / 81
= 52/81
Question 3
Om Navasakthi Astrologers , Chennai has been able to predict the winner of each football match with amazing success. It is told in the sports circle that in a match between two teams A and B, Om Navasakthi Astrologers picks A team with the same probability as B’s chances of winning and vice versa. Let us assume such rumors to be true and that in a match between Germany and Brazil, Brazil the stronger team has a probability of 4/7 of winning the game. What is the probability that Om Navasakthi Astrologers will correctly pick the winner of the Germany-Brazil game?
a) 24/49 b) 4/7 c) 18/49 d) none of these.
Answer : a) 24/49
Solution :
This is similar to earlier questions except the fact that Astrologers pick A team with the same probability as B’s chances of winning and pick B team with the same probability as A's chances of winning.
Probability of Brazil winning = 4/7.
Therefore, Probability of Germany winning = 1 - 4/7 = 3/7
So probability of picking a winner = probability of picking Brazil*Probability of Brazil winning + probability of picking Germany * Probability of Germany winning ....(1)
Astrologers pick A team with the same probability as B’s chances of winning and pick B team with the same probability as A's chances of winning.
Therefore, Probability of Brazil winning = probability of picking Germany and Probability of Germany winning = probability of picking Brazil
Applying this in eq (1) we get
probability of picking a winner = ( 3/7 * 4/7) + ( 4/7* 3/7)
= 12/49 + 12/49
= 24/49
Question 4
Sneha is engaged. Her Fiance is one amongst Abdul, John, King and Vimal. Sneha either speaks truth or lies. One of four men always speaks truth while others may or may not speak the truth. Now based on the below statements, can you find the Fiance ?
1) Abdul says "Sneha always speaks truth".
2) King says "Sneha always lies".
3) Vimal says "Sneha always speaks truth but only to him".
4) John says "The only truth speaking person amongst Vimal and John is Sneha's Fiance"
a) Abdul b) King c) Vimal d) John.
Answer : d) John
Solution :
From the question, we know clearly that Sneha can speak either Truth or Lies.
But as per statement (1) Abul says "Sneha always speaks truth". Hence this statement cannot be true. Hence our inference is that Abdul always lies.
As per statement (2) King says "Sneha always lies". Again this statement is false as Sneha can speak either Truth or Lies. Hence we can infer that King always lies.
On statement (3) Vimal says "Sneha always speaks truth but only to him". But there is no evidence / proof for this claim on data in question. Hence we can safely consider that Vimal also lies always.
In question it is clearly given that one of four men always speaks truth while others may or may not speak the truth. Since we have concluded Abdul, King and Vimal always lie, John should be the only truth speaking man.
According to statement (4) John says that "The only truth speaking person amongst Vimal and John is Sneha's Fiance". Since John is found to speak truth always, this particular statement from John should be absolutely True.
Also we have found earlier that Vimal always lies. Hence the truth speaking person John has to be the Fiance.
Question 5
Three men Ravi, Ram, Rahul and two women Rekha and Padma were seated next to each other (not in order given) in a meeting. The arrangement was that the person who speaks definitely the truth will occupy the first position and the person who speaks definite lie always will be the last. The middle three positions will be filled by people whose statements may be truth or may be false. Can you find the correct arrangement from the options based on the statements below :
1) Padma says the probability of her occupying the 4th place is lesser than the probability of her occupying 1st place.
2) Rahul says that "Padma lies always when calculating probability"
3) Rekha says "Ram is the tallest of the 5 people"
3) Ravi says "He will be leaving early provided Rahul is a truth speaking person"
4) Ram says "He does not know probability"
a) Rahul - Ravi - Rekha - Ram - Padma b) Ravi - Rahul - Rekha - Ram - Padma
c) Rekha - Rahul - Ravi - Padma - Ram d) Rahul - Ravi - Ram - Padma -Rekha
Answer : a) Rahul - Ravi - Rekha - Ram - Padma
Solution :
Though the question looks bit difficult it is actually a simple question provided you can quickly extract out only required data and ignore irrelevant details.
All the options have different combinations for 1st and last positions. This means, if you are smart enough to find the person who always speaks truth and the person who always speaks lies, it is more than enough to answer the question.
According to statement I, Padma says that the probability of her occupying the 4th place is lesser than the probability of her occupying 1st place. But this cannot be true. This is because probability of Padma to occupy any given position is 1/5 . (1/5 is the probability of Padma to occupy any given position be it 1st or 2nd or 3rd or 4th or 5th positions). Therefore we can safely conclude that Padma is definitely lying.
According to statement 2, Rahul says "Padma lies always when calculating probability". This is a definite truth based on our conclusion in previous paragraph. We can safely conclude that Rahul speaks definitely the truth.
From the above two paragraphs, we can say that 1st position will be occupied by Rahul (as he speaks definite truth) and the last position will be occupied by Padma (as she speaks definite lies). Only option that has this combination is option a) and hence the answer.
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