# Question Bank - Logical Reasoning

• Q25) Pool A of the European Cup qualifying matches has eight countries – Austria, Bulgaria, Czech Republic, Denmark, England, France, Germany and Spain. In the first round, each of these countries plays a match with every other country. In every match, the winning country is awarded 10 points, the losing country is awarded 0 points and in case of a draw, each of the countries is awarded 5 points. The top three countries, in terms of points, will advance to the next round. After the first round, it was observed that:

The number of matches won by Austria was a perfect square, while exactly two of her matches ended in a draw.
Bulgaria won exactly two of her matches and lost her matches against Austria and Spain.
France lost exactly three of her matches. Each country lost at least one match and six matches ended in a draw.
The sum of points won by Austria and twice the points won by the Czech Republic equal four times the points won by Bulgaria.
The difference between the points won by Austria and England equals the difference between the points won by Bulgaria and Denmark.
The sum of the points won by Spain and five times the points won by France equals the sum of points won by Denmark and six times the points won by Germany.
The sum of points won by Bulgaria and twice the points won by the Czech Republic equals twice the points won by Austria.
Six times the points won by Germany equals seven times the points won by Spain.

How many points did England score?

• A: 50(4W - 2D - 1L)
B: 30(2W - 2D - 3L)
C: 35
D: 20
E: 280 - 240 = 40 (Total matches=28, Total points = 280)
F: 40(4W - 0D - 3L)
G: 35
S: 30

• Q26) In a group of ten students – A, B, C, D, E, F, G, H, I and J – each pursuing Phd, every student has chosen two subjects – one as a compulsory subject from among History, Chemistry, English and Politics and the other as an optional subject from among Economics, History, Geography and Sociology. Each of the compulsory subjects was chosen by a different number of students, which is at least one, and the same is true for the optional subjects. Further it is also known that:

1. Three students have chosen History as their compulsory subject and each of these students has chosen a different optional subject but none of them has chosen Sociology. I has chosen History as both of his/her subjects.
2. Both D and H have chosen English as their compulsory subject and this is the only pair of students in which both the students have chosen the same compulsory subject as well as same optional subjects, which is different from the compulsory subject. A has chosen the same optional subject which has been chosen by both D and H as their optional subject.
3. Maximum number of students have chosen History as their optional subject. No two students who have chosen History as their optional subject have the same compulsory subject.
4. E has chosen English as his/her compulsory subject and Economics as the optional subject.
5. No one has chosen the same optional subject which B has chosen as optional subject. B and C have chosen the same compulsory subjects while G and A have chosen different compulsory subjects.
6. C and F have chosen different compulsory subjects as well as optional subjects. C has chosen Economics as his/her optional subject.
7. F and G have chosen different compulsory subjects but the same optional subjects. G has chosen Politics as his compulsory subject.

How many students have chosen Geography as the optional subject?

• Q27) Four friends – F1, F2, F3 and F4 – visited the New Delhi World Book Fair 2012. Each of them bought a different book among Magic Island, Fragmented Frames, Unlikely Hero and Eternal Romantic. They unanimously decided that each of them would read all the four books in the next four weeks such that each person would read exactly one book in a week, and they would meet at the end of each of the first three weeks to redistribute the books. It is also known that:

(i) F3 was the first one to read Fragmented Frames, and F1 was not the last one to read the same.
(ii) The first book read by each of the four friends was not the one which he/she had bought.
(iii) The 2nd and the 3rd books read by F2 were Eternal Romantic and Fragmented Frames respectively.
(iv) The 3rd book read by F4 was Unlikely Hero. The last book read by F3 was Eternal Romantic.
(v) The last person who read Magic Island was not F2.

1. Who among the following did certainly not buy Magic Island?
(a) F1
(b) F4
(c) F2
(d) F3

2. Which was the first book read by F1?
(a) Unlikely Hero
(b) Magic Island
(c) Eternal Romantic
(d) Fragmented Frames

• Q28) Each of the eight players – CG, VK, ST, RP, MSD, VS, AF and GG –represented a different team among RCB, HS, MI, DD, CSK, PW, KKR and RR (not necessarily in that order) in a cricket tournament called PPL. Each of them got to play exactly one match in the tournament. The number of runs scored by each of the eight players in the tournament was distinct. The same was true for the number of balls faced by them.

It is also known that :
(i) The player from DD who scored 28 runs off 33 balls was neither VK nor ST.
(ii) AF, who scored 22 runs, represented neither RCB nor HS.
(iii) The player who represented MI scored 23 runs off 19 balls.
(iv) VS, who represented PW, faced 7 balls.
(v) The number of balls faced by MSD was equal to the average number of runs scored by VK and RP. (
vi) GG, who represented RR, scored 17 runs.
(vii) CG represented RCB.
(viii) VK did not represent MI.
(ix) MSD scored more than 50 runs.

1. Who among the following could represent HS?
a) AF
b) RP
c) VK
d) ST

2. If VK scored 24 runs, what was the number of balls faced by MSD?
a) 26
b) 23
c) 20
d) Cannot be determined

3. If MSD represented KKR, for how many other players is it possible to find out the team which they represented?
a) 4
b) 5
c) 6
d) 7

• Q29) A machine recognises inputs only in the form of a string of bits to produce the products. It reads the string of bits from left to right. A bit could be only of two forms 0 or 1.

1. An input of 0 starts the machine if it is in the stop state and stops the machine if it is in the start state. Input of 1 is given to produce the product, only when the machine is in the start state. Otherwise, 1 is rejected by the machine. At the end of the day, machine should be stopped. If machine was in stop state initially, which of the following input strings is not valid for the day?
(1) 011100100111111001110
(2) 00011110101111101010
(3) 00110111100101010101010
(4) 0110110110110110110110

2. An input of 0 starts the machine if it is in the stop state and stops the machine if it is in the start state. Input of 1 is given to produce the product, only when the machine is in the start state, otherwise machine would not accept the input. If the machine was in stop state initially, in which of the following
options, the machine does not accept atleast one input?
(1) 011100110011100101110010
(2) 01100111100100100111100
(3) 01001001110010000001001
(4) 00010010011001110010010

3. There was a demand of products of two different kinds – product A and product B. To achieve this objective, the machine was configured to read two bits at a time. An input of 00 starts the machine, input of 01 produces a unit of product A, input of 10 produces a unit of product B and input of 11 stops the machine. The machine can produce the products only in its start state. Otherwise, it would just discard the input. It would also discard the input for stop or start if it is already in that state. Out of the following, the inputs that would produce more units of product A than product B are:
I. 00101010101010101010111101100110000101010101
II. 00110101001000010010010000011000001111101010
III. 00111000010101000101100100010010110011101100
(1) I and III only
(2) I and II only
(3) I only
(4) III only

4. With increasing demand in variety, the management decides to produce 1800 different kinds of products with the same machine. A unique input should specify the production of each of the products, apart from two different unique inputs asking machine to start and stop respectively. The machine should be configured to read at least how many bits at a time to achieve this objective?
(1) 10
(2) 11
(3) 901
(4) None of these

• Q30) On a particular day, exactly six persons – Amar, Bhanu, Chetan, Dinesh, Gaurav and Jitesh – visited a doctor for consultation, not necessarily in the same order. Each person paid a different amount to the doctor as consultation fee and each person consulted the doctor at a different time. At the end of the day, the doctor noticed that, except for the first two persons, the rest of the persons paid a consultation fee, which was equal to the average of the consultation fees paid by the previous two persons.

The following information is known about the fees paid and the order in which they consulted the doctor:

The consultation fee paid by each person (in Rs.) was not necessarily an integer and no person paid more than Rs.2500.
Bhanu paid Rs.1000, which was the lowest among all the six persons, and she consulted the doctor immediately before Gaurav, who did not pay the highest amount.
Amar paid Rs.100 more than Dinesh, who consulted the doctor before both Amar and Jitesh.

1. What is the highest amount (in Rs.) paid for consultation by any of the six persons?

2. Who was the last person to consult the doctor?

3. What is the total amount paid by all the six persons combined?

4. Who among the six persons paid the second lowest amount for consultation?

• @venkateshp A-5S+T
C-4S
B-3+2T
D-2S
OR
A-5S+3T
B-4S
C-3S
D-2
OR
A-5S+2T

``                        B-4S+T                                                         C-3S                                                         D-2     ``

PLS TELL HOW IS C BEING FIXED AT 3.

• @venkateshp

Solution:
To understand the answer,we need to reduce this problem to only 2 pirates. So what happens if there are only 2 pirates. Pirate 2 can easily propose that he gets all the 100 gold coins. Since he constitutes 50% of the pirates, the proposal has to be accepted leaving Pirate 1 with nothing.

Now let’s look at 3 pirates situation, Pirate 3 knows that if his proposal does not get accepted, then pirate 2 will get all the gold and pirate 1 will get nothing. So he decides to bribe pirate 1 with one gold coin. Pirate 1 knows that one gold coin is better than nothing so he has to back pirate 3. Pirate 3 proposes {pirate 1, pirate 2, pirate 3} {1, 0, 99}. Since pirate 1 and 3 will vote for it, it will be accepted.

If there are 4 pirates, pirate 4 needs to get one more pirate to vote for his proposal. Pirate 4 realizes that if he dies, pirate 2 will get nothing (according to the proposal with 3 pirates) so he can easily bribe pirate 2 with one gold coin to get his vote. So the distribution will be {0, 1, 0, 99}.

Smart right? Now can you figure out the distribution with 5 pirates? Let’s see. Pirate 5 needs 2 votes and he knows that if he dies, pirate 1 and 3 will get nothing. He can easily bribe pirates 1 and 3 with one gold coin each to get their vote. In the end, he proposes {1, 0, 1, 0, 98}. This proposal will get accepted and provide the maximum amount of gold to pirate 5.

copied

• @venkateshp

1. Rs. 1800
2. Jitesh
3. Rs. 7950
4. Gaurav

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