Source: https://es.scribd.com/document/236078447/Reasoning-Takshzila-Material
Timestamp: 2019-04-20 02:31:00+00:00

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otherwise, without the prior permission of the copyright owner.
there are three or four questions that have to be answered with the help of the data given.
about the relative placement of two or more objects, their placement with respect to the ends, etc.
We will take an example to help you ‘model’ the clues given.
A, B, C, D, E, F, G and H are sitting in a row facing north.
i. A is fourth to the right of E.
ii. H is fourth to the left of D.
iii. C and F, which are not at the ends, are neighbours of B and E respectively.
iv. H is next to the left of A and A is the neighbour of B.
Who are sitting at the extreme ends?
Now, one should read through all the clues again and try to ‘model’ the data given.
The above is the most common way that a student would read the clues.
Clue iv: H A B .
need to go through the clues all over again.
row of nine tents, each to a tent.
i. A, B and C do not want to live in a tent at the end of the row.
ii. D and A must not have anybody adjacent to their tents.
iii. There is only an empty tent between A and C.
iv. E is adjacent to both F and C.
v. B is in a cottage next to an end.
Who is in the ffth tent?
Who has empty tents on both sides?
There are nine tents and only six friends. So three places will be vacant.
Data is primarily about vacant tents and about neighbours.
be thought of as follows: × × D and × × A .
the earlier clue, A cannot be at any end. Thus both cottages to A’s side have to be vacant cottages.
two empty tent’s to his side is A.
to get a specifc answer.
to the right of B” implies that A could be anyplace to the right of B and need not be adjacent.
right of A; B is to the right of D. Which of the houses is in the middle?
of R and to the left of T. Who is standing in the middle?
who is sitting to the extreme left, and T is not sitting next to K. Who are sitting adjacent to S?
adjacent to Sulekha. Rashi is adjacent to Monika. Monika is seated in the middle of the row.
Then, amongst the following choices, to whom is Anuradha adjacent?
between C and E and D is between B and A. Find the person sitting right in the middle.
6. Five boys are standing in a row facing east. Mohan is standing between Umesh and Suresh.
of the row. Who is standing at the other end of the row?
when the photographed is viewed?
either P or D. K does not stand next to D. E stands between A and K.
9. Who occupies the extreme ends of the row?
is a mystery, one is a romantic novel, one is an autobiography and one is on business management.
management. The science fction has the autobiography and the mystery novel as it’s neighbour.
11. Counting from the left-end of the row, the romantic novel is at which place?
12. Which book is in the middle of the arrangement?
arrangement even if the clue was not given?
and do on. The following is known about their ranking or timings.
timing worse than B and better than E.
ii. F has a better timing than D. But A has a timing that is worse than D’s and E’s.
15. Who stood ffth in the race?
16. How many swimmers have their timings between that of A and F?
rows in such a way that a child in one row is exactly facing a child in the other row.
M is not at the end of any row and is to the right of J, who is facing C.
K is to the left of D, who is facing M.
19. Which of the following group of children is in the same row?
20. Who is to the immediate left of B?
Six persons A, B, C, D, E and F are sitting in two rows, three people in each row.
E is not at the end of any row.
D is second to the left of F.
C, the neighbor of E, is sitting diagonally opposite to D.
B is the neighbor of F.
21. Which of the following are sitting diagonally opposite to each other?
22. Who is facing B?
23. Which of the following are in the same row?
24. Which of the following are in one of the two rows?
25. After interchanging seats with E, who will be the neighbors of D in the new position?
Table-Tennis was played on the previous day of Cricket.
Football was not played either on Wednesday or Saturday.
No game was played on Thursday and Sunday.
Kho-Kho was played on Monday.
There was a gap of two days between Cricket and Football.
26. The sports week started with which game?
27. How many days gap is there between Hockey and Football?
28. Which pair of games was played on Wednesday?
29. Which game exactly precedes Kho-Kho?
30. Table-tennis follows which game?
1. Course should start with Psychology.
July, being Sunday, should be a holiday.
3. Science subject should be on the previous day of the Engineering Subject.
4. Course should end with Mechanics.
5. Philosophy should be immediately after holiday.
6. There should be a gap of one day between Economics and Engg.
7.There should be a gap of two days between Sociology and Economics.
31. Of the seven subjects, which is the subject taught in the middle of the course?
32. Which subject will be on Tuesday?
33. Which subject is preceded by Science?
34. Which subject precedes Mechanics?
35. How many days gap is there between Science and Philosophy?
schedule of plays is to be in accordance with the following information.
1. A must be staged a day before E.
2. C must not be staged on Tuesday.
3. B must be staged on the day following the day on which F is staged.
4. D must be staged on Friday only and should not be immediately preceded by B.
5. E must not be staged on the last day of the schedule.
36. Which of the following plays is staged immediately after E?
37. Which of the following plays is played on Monday?
38. Play D is between which of the following pair of plays?
forward in any other question.
spend time trying to arrive at a unique solution based on the data.
question to complete the arrangement.
given in a particular question.
1. Which of the following must be false ?
3. If A and B are together , then which of the following must be necessarily true ?
& Mrs. Deodhar are in neighbouring foors.
4. If the Agarwals live on foor 1, which of the following is true?
6. If the Bhandaris were on foor 1, on which foor could the Agarwals be?
numbered foor or both on an even-numbered foor.
A must be shown earlier than C.
B must be shown earlier than D.
E should NOT be the ffth flm shown.
9. Which among the following is an acceptable order for showing the educational flms ?
10. In case C is shown earlier than E, which among the following will hold true ?
(1) A is the frst flm shown. (2) B is the second flm shown.
(3) C is the third flm shown. (4) D is the ffth flm shown.
exactly one position from frst through ffth in which it can be scheduled to be shown ?
12. Which among the following is a pair of flms that CANNOT both be shown earlier than E?
(1) E is shown earlier than B. (2) B is shown earlier than C.
(3) C is shown earlier than E. (4) D is shown earlier than A.
and D, which among the following will hold true?
(1) B is the flm shown between A and C. (2) E is the frst flm shown.
(3) E is the flm shown between A and C. (4) D is the last flm shown.
II. Moral Science must be the frst lecture or the last lecture.
16. How many of the subjects can never be third in the sequence of lectures?
in the sequence of lectures, how many values can n assume?
only one person can work per day.
The painter can do his work only after the plumber and the carpenter have completed their jobs.
The interior decorator has to complete his job before that of the electrician.
The carpenter cannot work on Monday or Tuesday.
21. In case the painter works on Thursday, which among the following alternatives is possible?
(1) The electrician works on Tuesday.
(2) The electrician works on Friday.
(3) The interior decorator does his work after the painter.
(4) The plumber and the painter work on consecutive days.
22. In case the painter works on Friday, which among the following statements must be untrue?
(1) The carpenter may work on Wednesday.
(2) The carpenter and the electrician may work on consecutive days.
(3) In case the carpenter works on Thursday, the electrician has to work on the previous day i.e.
(4) The plumber may work before the electrician does.
23. Which arrangement among the following is possible?
(1) The electrician will work on Tuesday and the interior decorator on Friday.
(2) The painter will work on Wednesday and the plumber on Thursday.
(3) The carpenter will work on Tuesday and the painter on Friday.
(4) The carpenter will work on Wednesday and the plumber on Thursday.
V always fnishes somewhere ahead of P.
P always fnishes somewhere ahead of Q.
Either R fnishes frst and T fnishes last, or S fnishes frst and U or Q fnishes last.
24. If in a race V fnishes ffth, which of the following must be true?
26. If in a race S fnishes second, which of the following can be true ?
27. If in a race S fnishes sixth and Q fnishes ffth, which of the following can be true ?
28. If in a race R fnishes second and Q fnishes ffth, which of the following must be true ?
Flight 101 must depart at 9:00 a.m.
Flight 105 must depart later than fight 103, and also later than fight 102.
Flights 104, 106 and 107 must depart on consecutive hours in that order.
(1) 10:00 a.m. (2) 11:00 a.m. (3) 1:00 p.m. (4) 3:00 p.m.
(1) 9:00 a.m. (2) 10:00 a.m. (3) 1:00 p.m. (4) 2:00 p.m.
(1) 10:00 a.m. (2) 11:00 a.m. (3) 12 noon (4) 1:00 p.m.
32. What is the latest hour at which Flight 102 can be scheduled to depart ?
1. 10:00 a.m. (2) 11:00 a.m. (3) 12 noon (4) 2:00 p.m.
two players to speak in order were Radal and Regor.
33. Among the following which is not an appropriate order of speaking?
the following statements which would be false?
(1) Kovan spoke immediately after Albert.
(2 The order of the frst four speakers was Radal, Albert, Regor, Victor.
(3) Kovan’s coach was present at the dinner.
(4) Blake was the fourth speaker after Radal.
35. Among the following statements, which statement must be true?
(1) In case the second speaker was a player, the seventh speaker was a coach.
(2) In case the second speaker was a coach, the seventh speaker was a player.
(3) In case the third speaker was a coach, the seventh speaker was a player.
(4) In case the third speaker was a player, the seventh speaker was a coach.
present, which among the following statements must be true?
four, fve, and six respectively. The stops, in alphabetical order, are L, M, N, O, P, and Q.
P is the third stop.
M is the sixth stop.
The stop O is the stop immediately before Q.
N is the stop immediately before L.
39. In case N is the fourth stop, which among the following must be the stop immediately before P?
the following must be true?
(1) O is stop one. (2) Q is stop three. (3) P is stop four. (4) N is stop fve.
position in a circular arrangement, to begin with.
2. The right and left of a person, becomes anti-clockwise and clockwise directions.
Sanjay mutually exchange their positions, who is now sitting to the right of Manoj?
of Monika. Now Deepti and Kamini, Monika and Radhika mutually exchange their positions.
3. Who will be sitting opposite to Sonia?
4. Who will be sitting left of Kamini?
5. Who will be sitting left of Deepti?
opposite to Rita. Mita is also sitting at the table.
6. Who is the only person sitting between Gita and Sita?
(1) Rita and Nita (2) Lata and Gita (3) Mita and Lata (4) All of these.
(1) left of Mita (2) right of Rita (3) left of Rita (4) right of Nita.
10. Which of the following statements is not correct?
(1) Mita and Sita are exactly opposite to each other.
(2) Rita and Mita are at equal distance from Gita.
(4) Mita is on the immediate left of Lata.
A, B, C, D, E, F, G are playing cards sitting across a circular table and facing inwards.
i) F is second to the right of G.
ii) B is neighbour of F but not of E.
iii) E, the neighbour of C, is fourth to the right of G.
iv) D is immediately between E and A.
11. Who is fourth to the left of G?
12. Who is to the left of G?
13. Who are neighbours of F?
14. If the turn moves anticlockwise, who would play after B?
So far we had only two variables, a position and a person. Now there would be one more variable.
Chennai and also their professions, say Accountant, Engineer, Lawyer and Doctor.
and one for the professions.
Now read through each of the clue and try to populate the lower two rows.
Do not forgot to ‘tie-up’ the previously read clues with any new information read in successive clues.
In few of the sets, one of the variables could be the positions in a row or the days of a week.
will start from Monday and will end on Sunday. There will be a day of rest.
Chemistry will immediately follow Geology.
A, who is a mathematician, will demonstrate either on second or last day.
C will demonstrate on third day. Physics will be on the ffth day.
E, who is a zoologist, demonstrates on second day.
B has demonstrated on Monday and the rest day will be immediately after F’s demonstration day.
1. On which of the following days no demonstration will take place?
2. On which day Botany will be demonstrated?
3. Geology is immediately preceded by which of the following subjects?
5. Who among the following demonstrates just after B and just before C?
subjects – HRM, Business Strategy, Accounts, Financial management, Marketing and Taxation.
They have graduated from one of the 6 B-schools – Wharton, Harvard, Stanford, Sloan, Kellogg, AIM.
i) None of the IIM professors are from Sloan.
iii) B and C teach Business Strategy and HRM respectively.
iv) D and E teach at XLRI and FMS respectively, but do not teach Accounts.
vi) Marketing is taught by D.
I. The movie starring Shah Rukh is produced by Ramsay Brothers.
II. The romantic movie is produced by Red-Chillies.
11. The movie produced by Adlabs falls in which genre?
13. Aamir stars in movie of which production house?
interest and one hobby concerned with fne arts.
Arun is not a painter nor does he play Hockey.
Bharat and Dharma do not play Cricket.
15. Who among the following plays Cricket and is a painter?
16. Who among the following is a singer?
17. Which pair shows the correct relationship of the game and hobby of Dharma?
Ahmedabad, Bangalore, Kolkata, Delhi, Ernakulam and Indore.
i. The football player is married to an Engineer, but does not belong to either Kolkata or Delhi.
ii. The Doctor and Athlete do not stay in Indore and Ernakulam respectively.
iii. The Hockey player is not married to either Doctor or CA, and his wife is not a housewife either.
iv. One of the Engineers stays in Delhi.
vi. The lady, who stays in Ernakulam, is a housewife.
18. Who is married to the Hockey player?
19. In which city does the Doctor stay?
20. Who is married to the Athlete?
21. The CA stays in which city?
i. Mr. Agarwal goes to Mahabaleshwar but not by fight or bus.
ii. Mr. Sharma travels by bus but does not travel in Feb or May.
iii. Neither Mishra nor Dubey family go to Shimla or Mussorie.
iv. Kodaikanal was visited in April.
v. Families going to Kullu and Shimla go by bus and rail respectively.
vi. Mr. Joshi goes to Nainital in Mar by air and Mishra does not travel in April.
22. Who of the following visit Shimla?
A, B, C, D, E and F are six members of a family.
Out of six members, three are male members.
There are two married couples among them.
C is the father of A and F and E is the mother of C.
A is the granddaughter of B.
According to the above given information, let’s try and make the family tree.
Now the only member left is D and since A and F are siblings, C and D must be the second couple.
Now we have the complete family tree. Let us now try some questions based on this.
1. Which of the following pairs is one of the married couples?
From the diagram, we see that married couples are BE and CD. So answer is (3).
2. Who is the husband of E?
Again, from the diagram its apparent that husband of E is B.
3. How is B related to F?
father.” How is the woman related to that person?
the woman’s husband related to the man in the photograph?
how is Bina, who is the sister of Rani related to Mohan?
How is the man related to Sally?
grandmother.” Whom did Raj defeat?
Few of the members of a big family are M, N, O and P.
M is the daughter of N.
O is the father of P.
7. Among the following statements, which is true?
(1) O is the uncle of M.
(3) M is the daughter of P.
(4) If B is the daughter of N, then M and B are sisters.
8. Which among the following statements is contradictory to the above premises?
(1) P is the father of M. (2) O has three children.
(3) M has one brother. (4) M is the granddaughter of O.
I. M is the sister of D. II. D and N are brothers.
P is the grandmother of M and mother of N.
R is the granddaughter of Q.
O is the wife of N and mother of R.
10. How is O related to M?
11. How many male members are there in the family?
12. Which of the following is true?
13. Who among the following is one of the couples?
is the brother of N.
14. How many male members are there in the family?
15. Who is the mother of N?
16. How many children does M have?
17. Who is the wife of Q?
18. Which of the following is a pair of females?
19. How is Q related to P?
happy with Q’s wife. But P and his father support Q’s wife, S.
20. Who is the daughter of T?
21. What is the relation of P with S?
22. How is T related to Q?
23. Who is the wife of Q?
24. How is P related to T?
(i) Y is married to U who is a professor.
(ii) X, who is a housewife, is the mother of U.
(iii) V is the grandfather of W who is a doctor.
(iv) Y, who is the father of the doctor, is not a banker.
(v) Z is the granddaughter of X and is a manager.
25. Which of the family members is the banker?
26. What is the profession of Y?
27. How many female members are there in the family?
28. Who is the husband of the housewife?
29. How is W related to Z?
Five people A, B, C, D, E are related to each other.
Four of them make one true statement each as follows.
Statement 1: B is my father’s brother.
Statement 2: E is my mother-in-law.
Statement 4: A is my brother’s wife.
30. Who made statement 1?
31. Who made statement 2?
32. Who made statement 3?
33. Who made statement 4?
34. Who did not make any statement?
If A is selected, then C is selected.
If D is selected, then F is not selected.
the focus is on placing the variables into a workable group.
In analyzing Grouping questions we use a system similar to the one for linear arrangements.
three have to be selected.
students are divided into two four-person study groups.
The number of variables to be selected is not equal to the overall number of available spaces.
Unbalanced questions are either Overloaded or Underfunded.
number of candidates than selection spaces).
order for another event to occur.
If this is the case then via the contrapositive, it is the case that when D is selected, C is not selected.
1. When working with diagrams that have vertical components.
I. Either K or S or both must be selected.
II. Either O or V must be selected, but neither V nor S can be selected with O.
According to the conditions, K or S can occupy the third place if it hasn’t already been selected.
Some other object can also occupy the third place.
1. Which of the following is an acceptable selection of objects?
objects. One of O and V is a must but option ((2) has neither.
Option (3) is acceptable since it satisfes all conditions.
2. Which of the following pairs of objects cannot be both among the objects selected?
two places must be occupied by one of K and S and one of O and V.
3. If S is selected, which of the following must also be among the objects selected?
selected hence V must be selected.
4. If V is not selected, which pair of objects must be among those selected?
If V is not selected, O must be selected. If O is selected, S cannot be selected so K must be selected.
Hence K and O must be selected.
and then focus on the possibility of the remaining ones.
I. Each table has at least two sponsors seated at it, and each sponsor is seated at exactly one table.
II. Any sponsor receiving honors is seated at table 1 or table 2.
III. L is seated at the same table as V.
1. Which one of the following is an acceptable assignment of sponsors to tables?
sponsors assigned to table 3 ?
3. If K is assigned to a different table than M, which one of the following must be true?
(1) K is seated at the same table as L. (2) L is seated at the same table as Q.
(3) Exactly 2 sponsors are seated at table 1. (4) Exactly 2 sponsors are seated at table 3.
true of the seating assignment?
(1) K is seated at the same table as L. (2) K is seated at the same table as Q.
(3) M is seated at the same table as V. (4) M is seated at the same table as Z.
of the following could be the list of sponsors assigned to table 1?
I. If both G and S are reduced, W is also reduced.
II. If N is reduced, neither R nor S is reduced.
III. If P is reduced, L is not reduced.
IV. Of the three areas L, M, and R, exactly two are reduced.
other areas of expenditure to be reduced?
both of which are reduced?
11. If R is not reduced, which one of the following must be true?
(1) G is reduced. (2) N is not reduced.
(3) P is reduced. (4) S is reduced.
of which could be reduced?
13. Which one of the following areas must be reduced?
A soloist will play six different guitar concertos, exactly one each Sunday for six consecutive weeks.
I. If N is selected, then J is also selected.
II. If M is selected, then neither J nor O can be selected.
III. If X is selected, then neither Z nor P can be selected.
IV. If both J and O are selected, then J is played at some time before O.
the frst through the sixth Sunday in the given order?
Sunday, then which one of the following concertos CANNOT be played on the second Sunday?
one of the following is a concerto that CANNOT be played on the ffth Sunday?
18. Which one of the following is a concerto that must be selected?
19. Which one of the following is a concerto that CANNOT be selected together with N?
I. Day 2 is the only day for which Oils can be scheduled.
II. Neither Sculpture nor Watercolors can be scheduled for the afternoon.
III. Neither Oils nor Pastels can be scheduled for the same day as Lithography.
following Pastels must be Fresco and History, not necessarily in that order.
which one of the following is a lecture that could be scheduled for the afternoon of day 1?
which one of the following lectures could be scheduled for the morning of day 1?
one of the following CANNOT be scheduled for any day?
in that order, which one of the following could be true?
(1) Lithography is scheduled for day 3. (2) Naturalism is scheduled for day 2.
(3) Fresco is scheduled the same day as Naturalism.
don’t function well together. The following guidelines were established to set up the new offce.
III. D and G have not been on speaking terms and should not be sent to the new place together.
IV. Since D and F have been competing for a promotion, both of them should not be sent together.
30. If D goes to the new offce, which of the following is/are true?
Fiza and Kavita, and fve men: Ram, Shyam, David, Peter and Rahim.
i. Ram would not like to be in the group if Shyam is also selected.
ii. Shyam and Rahim want to be selected together in the group.
iii. Kavita would like to be in the group only if David is also there.
iv. David, if selected, would not like Peter in the group.
v. Ram would like to be in the group only if Peter is also there.
vi. David insists that Fiza be selected in case he is there in the group.
31. Which of the following is a feasible group of three ?
32. Which of the following is a feasible group of four ?
33. Which of the following statements is true ?
Seven friends T, N, P, M, R, F and K have to travel by car. Two cars are available.
I. T must travel in the same car as R.
II. F cannot be in the same car as P unless M is also in the car.
III. Not more than 4 people can travel in a car.
IV. Neither N nor P can be assigned to the same car as K.
34. If N travels in the same car as R and T, then who can be the fourth person in the car?
35. If F and P travel in the same car, then who else of the following could be in the same car?
36. Which of the following can be the combination of passengers in any one car?
38. If F and P are in the same car, how many passengers can be present in that car?
(3) either 3 or 4 (4) F & P cannot be in same car.
write down the letter of the region which represents the given statement.
Study the diagram given below and answer the following questions.
comply with all the rules listed below.
twice as that of L.
iii. A single perfume should never contain N as well as O.
iv. O and P should not be used together.
17. Among the following which is an agreeable formula for a perfume?
18. Adding more amount of essence N will make which of the following perfumes agreeable?
containing two parts N and one part P agreeable?
containing two or more essences?
all of one essence ?
i. In case only switch A is the switch on in the initial setting , then turn on switch B.
ii. In case switches A and B are the only switches on in the initial setting, then turn on switch C.
iii. In case all the three switches are on initially setting, then turn off the switch C.
could be the second setting?
(1) A on, B on, C on. (2) A on, B off, C on. (3) A on, B off, C off. (4) A off, B on, C off.
23. In case switch B is the only switch on in the initial setting, what must be the second setting?
(1) A on, B on, C on. (2) A on, B on, C off. (3) A on, B off, C on. (4) A off, B off, C on.
have been the initial setting?
(1) A on, B on, C on. (2) A on, B on, C off. (3) A on, B off, C on. (4) A on, B off, C off.
(1) A on, B on, C on. (2) A on, B off, C on. (3) A off, B on, C off. (4) A off, B off, C on.
(1) A on, B on, C off. (2) A on, B off, C on. (3) A off, B on, C on. (4) A off, B on, C off.
Read the following statements carefully and answer the questions that follow.
i. Mohan and Ram play hockey and football. ii. Edward and Ram play football and cricket.
iii. Mohan and Rafq play tennis and hockey. iv. Rafq and Edward play cricket and tennis.
28. Name the boy who plays hockey, football and tennis.
29. Name the boy who plays hockey, football and cricket.
30. Name the boy who plays hockey, cricket and tennis.
three equal segments of 1 inch each resulting in cubes of side 1 inch being formed.
1. How many small cubes of 1 inch sides are formed?
2. How many of these small 1 inch cubes have three of their faces painted?
3. How many of these small 1 inch cubes have two of their faces painted?
4. How many of these small 1 inch cubes have one of their faces painted?
5. How many of these small 1 inch cubes have none of their faces painted?
person who drinks both coffee and tea is counted only once and not twice.
For the case of three sets, use of venn diagram is preferred.
Filmfare, 40 subscribe Filmfare and Femina and 20 subscribe Outlook and Femina.
12. The fowers in a basket become double every minute. In one hour, the basket becomes full.
After how many minutes, the basket would be half flled?
many seconds will he be able to touch the top of the tree?
does it tick at 12′o clock?
thick candle was twice as long as the thin one. For how long did Vipul study in candle light?
people are sad but not mad?
clear mornings and 20 clear evenings, how long was our vacation?
how many days did we do neither?
scored by opponents against the team.
23. How many goals were scored by team A?
other two told one true statement and one lie.
ALBERT: Clive drove the car. Bruce created the diversion.
BRUCE: Albert drove the car. I created the diversion.
CLIVE: I took the goods out of the shop. Bruce drove the car.
24. Who spoke both the true statements?
25. Who took the goods out of the shop?
only in the afternoon and lies in the morning. One out of A and B is Shahrukh and other is Salman.
A says that B is Shahrukh.
26. What time of the day is the statement made?
the third game. After the three games it was found that all of them had the same amount.
28. What amount did A start with?
29. What amount did B start with?
30. What amount did C start with?
32. What is the number of weights that he has?
33. If he has to measure 100 kgs, how many weights does he have to use?
weights in both of the pans if required.
34. What is the number of weights that he has?
35. If he has to measure 100 kgs, how many weights does he have to use?
want to open any bags.
36. What is the least number of bags that will be needed?
37. If I have to tender Rs. 80, how many bags would I have to give?
Directions for 38 to 40: Answer each question independently.
needed to identify the faulty coin?
is the minimum number of weighing needed to identify the faulty coin?
Quite often both the above are techniques are used.
changed. These types are easier to decode.
E.g.: If ACROPOLIS is coded as RACOOPSLI, what would ACROBATIC be coded as?
code is in re-arranging the alphabets.
1. Writing the word backwards.
This is the most easiest way. Thus, ACROPOLIS will be coded as SILOPORCA.
rightmost letter is moved to the start.
3. Changing the order among pairs of alphabets.
Instead of inter-changing pairs of words, groups of three alphabets could also be re-arranged.
both the word and code are A, C & R and similar is the case with the last three letter i.e. L, I & S.
result in R A C O O P S L I.
and hence these types are not popular in exams.
operation among the numbers that denote the position of the alphabet in the alphabetical listing.
E.g. If NAME is coded as 33, what will GIRL be coded as?
linking 33 with 14, 1, 5 and 13 will immediately lead to the fact that 33 = 14 + 1 + 5 + 13.
Thus, GIRL will be coded as 7 + 9 + 18 + 12 = 46.
This is most common in exams.
of changing the order, in addition to substituting the alphabets.
2. A pair of alphabets substituted for each other.
substituted with the other one.
12. If 18514 stands for AHEAD, what does 31385 stand for?
that language would mean ‘gives’?
and ‘lee ree mee’ means ‘he is intelligent’, which word in the language means ‘sweet’?
goes’ and ‘bsi nro zpi’ means ‘died down he’, what word of the language would mean ‘goes’?
Which number would replace the ? in the following series: 5, 6, 8, 11, 15, 20, ?
1. Check if the numbers are increasing or decreasing slowly or by a large magnitude?
suddenly increase by a large magnitude.
usually be addition or subtraction.
2. Check the differences between consecutive numbers.
numbers are increasing/decreasing at a slower pace.
E.g. The frst series with which the chapter was introduced: 5, 6, 8, 11, 15, 20, ?
5 6 8 11 15 20 ?
be 6 and the required answer will be 20 + 6 = 26.
50 52 55 60 67 78 91 ?
2 3 5 7 11 13 ?
difference will be 17 and the required number will be 91 + 17 = 108.
E.g. : Looking at the other series with slowly decreasing numbers, 50, 46, 38, 28, 16, ?
50 46 38 26 10 ?
4 8 12 16 ?
in the numbers of the series starts becoming larger and larger.
Now, let us look at the series where the numbers increase more rapidly.
E.g. : 2, 6, 30, 260, ?
differences between terms. Hence one should think of powers of natural numbers.
2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 and 3, 9, 27, 81, 243, 729.
E.g. : 2, 5, 10, 50, 500, ?
Occasionally the series given will be a very long series and would have a seemingly error in them i.e.
the series will not move smoothly (sometimes increase, sometimes decrease, or random behaviour).
could also be made up of two or more intervening series.
E.g. 3, 10, 7, 8, 11, 6, 15, 4, ?
Since the ? belongs to the frst of these two series, the answer would be 19.
Thus, the series could be a mixture of two or even three different/independent series.
Directions: Find the number that should replace the ? in the following series.
1. 21, 25, 33, 49, 81 ?
2. 12, 32, 72, 152, ?
3. 3, 6, 5, 20, 7, 42, 9, ?
4. 1, 3, 4, 8, 15, 27, ?
5. 2, 15, 41, 80, ?
6. 1, 2, 5, 12, 27, 58, 121, ?
7. 0.5, 0.55, 0.65, 0.8, ?
11 , 12 , 14 , 16 , ?
11. 3, 4, 7, 7, 13, 13, 21, 22, 31, 44, ?
12. 4, 23, 60, 121, ?
13. 2, 1, 2, 4, 4, 5, 6, 7, 8, 8, 10, 11, ?
14. 4, 8, 28, 80, 244, ?
15. 563, 647, 479, 815, ?
One of the most common themes of questions in Data Interpretation is that of fnding the growth rate.
Growth rate is just a percentage increase (or a percentage decrease).
E.g. Sales of a company increased from Rs. 150,000 to Rs. 200,000. Find the growth rate of sales.
Would the growth rate in this case be the negative of the earlier answer i.e. –33.33%?
is less than 200,000 i.e.
With such a data, different growth rates could be defned …..
What was the growth rate of sales of cars in the year 2006?
compared to the previous year.
By what percentage did sales grow over the years 2002 – 2005?
In the year 2002, the sales were 150 and it grew to 250 in the year 2005.
What was the average annual growth rate of population over the years 1991-2001?
total growth rate over the years 1991-2001 divided by the number of years elapsed from 1991-2001.
to 2001 is 10 (91-92; 92-93; ……; 2000-01 are 10 annual time periods).
requires you to fnd the growth rate in a relatively simpler data structure.
and insurance, has shown the least percentage growth in their exports?
services lesser than the total export of travel services?
Thus, least percentage growth has been shown by the sector of insurance.
evident that exports of travel services more than doubled and exports of labour services have tripled.
have to do just two calculations that for transportation and insurance.
larger base, 2.0. Thus, growth rate would obviously be less for Insurance.
to be think, if you have to add across the columns or across the rows.
In Q. 2 we would need to add all values in the row of Feb and that in row of Apr.
to the total of all the relevant players in the sector/geographical area.
market, 100% – 20% – 30% = 50% has to be the market share of the third player.
Fill in all the six blank cells in the following table.
would have 100 – 16.5 – 15 – 12.5 = 56%.
is called Volume sales. Alternately we could also have said that the total value of all cars sold is Rs.
we are talking about volume or value, the market share could also be Volume share or Value Share.
representing the individual share of the players.
of the market or share of the volume of the market.
Number of cars × Price per car = Value of cars sold.
being sold at different prices.
simple exercise that captures all of this.
intentionally left blank. Your task is to fll in all the blank cells in the table.
Number of students with Topper’s Academy = 9.375% × 8000 i.e.
of 8000 i.e. 75 × 10 = 750.
250. And its market share will be 250/8000 = 3.125%.
market share = 1000/8000 = 12.5%.
20 × 6 = Rs. 120 mn.
Sales (in Rs. mn) of Scholar will be 30% × 120 mn = 36.
Market share of Topper’s will be 9/120 = 7.5%. Market share of Others = 3/120 = 2.5%.
Now the only cells left are that for Others which can be found by subtracting from the total.
Product price can be found by dividing sales (in Rs. mn) by the number of students.
Comcept 4: Measures using Ratio: Yield, Productivity, Density, etc.
less than) and hence these ratios do not pose any diffculty.
A few of these would be exactly similar to the earlier ratios i.e. would be a percentage value e.g.
However there are other ratios that may not be a percent value and will also have some unit to them.
will be measured in tons/hectare or kgs/acre or similar units.
and one needs to fnd the capacity.
and then you can practice these types of questions in the 5 sets given for practice.
For the following solved example, try out the above questions and then read the solutions that follow.
See if you have approached the question in the most effcient manner.
cultivation is expressed in millions of hectares.
crop and is expressed in tons/hectare.
1. In 2006, what was the yield of Maize in Brazil?
2. Which country, among the ones given, had the highest yield of Wheat in the year 2006?
3. In Brazil, which of the four crops require the least area to produce 1 ton of the crop?
groundnuts in Pakistan and those in USA?
0.4, thus, the required ratio will be just less than 3.4. This is enough to identify the option choice.
In this question we have to compare the yields.
rough the approximations are, atleast one or two options will be ruled out.
India: Finding orally what multiple of 26 is nearer to 69.
mark, 2.5, to compare other yields with. Remember we want to fnd the highest yield.
USA: First check to do is to fnd if the yield is more than the earlier bench-mark, 2.5.
is 2.5 + 0.33 i.e. 2.83.
slightly. So the yield will not be as much as that of USA.
the yield will be very very marginally more than 2.5, but not as much as that of USA.
have to be compared and the highest has to be found.
As learnt in above question, don’t write all four yields, just make an estimate frst.
Paddy: 11.5 is how many times of 3? Almost 4 times, but lesser than 4.
Wheat: 29.5 is how many times 11.3? Between 2 and 3 times, closer to 3. So this option is ruled out.
is also not as great as Paddy and is eliminated.
Groundnut: 0.24 is just 2.4 times 0.1. So this option is also ruled out.
Thus, again without need of detailed calculation, the answer can be found.
thrice of 44. Now, one can do more precise calculations with the decimal values. 3 × 43.7 = 131.1.
the ratio can be found as 3.1 very easily.
i.e. just less than 25%.
production will also increase by 10%.
increase it will be 0.77.
times old yield. Thus, the yield increases by 1/44 i.e. 9.0909/4% i.e. 2.272%.
that follow. All values are in Rs. bn.
1. In which year did the exports to China show the largest percentage growth?
2. In which year did the imports from Germany show the largest percentage increase?
5. In the year 2004-05, which country had the highest ratio of exports to imports?
the graph carefully and then answer the questions that follow. All values in the graph are in lacs.
8. In which year did commercial vehicles register the largest growth rate?
9. In the year 2006-07, which category of vehicles registered the least growth rate?
the year 2008-09 over those sold in the year 2006-07?
12. By what percent did the sales of the three categories of vehicles grow from 2007-08 to 2008-09?
the basis of only the information given in the graph.
13. How many more cars were sold by GM in 2009 as compared to 2008?
14. In 2008, how many more cars were sold by Hyundai as compared to GM?
16. What is the ratio of the number of cars sold by GM in the year 2008 to those sold in 2009?
18. From 2008 to 2009, which company showed the largest increase in the number of cars sold?
19. Which company showed a decrease in the number of cars sold in 2009 as compared to 2008?
the angle subtended by sector depicting sales by Honda in 2009?
a. 12 degrees b. 10.8 degrees c. 7.2 degrees d. 3 degrees.
21. If Toyota accounts for 25% of Others in 2009, fnd the market share of Toyota in 2009?
increase in the number of cars sold by Audi in 2009.
total number of laptops sold by all the seven players.
which model will occupy the middle position?
average price at which Apple sells its laptops?
25. Which of the following is larger?
at an average price that is higher than the average price of Acer?
27. If the Average Market Price of a laptop is Rs. 54,000, fnd the average price of HP laptop.
The following table gives the details of production of 4 crops in India in the years 2006 to 2009.
are produced in both the seasons and the break-up across the two seasons is also given in the table.
the production of the crop per hectare of area under cultivation.
Production fgures are in million tonnes and the Yield is in tons/hectare.
34. The area under cultivation of which crop was the highest in the Kharif season of 2007?
35. The area under cultivation of Jowar in the Kharif season was the least for which year?
cars of Maruti, a car manufacturer, across the various models that it sells.
36. How many M-800 were sold in the year 2004?
38. Find the ratio of the number of Alto sold to the number of Ford sold in the year 2004.
Maruti. Find the number of increase in the Swift sold.
half years. First half of a fnancial year is Apr to Sep and second half is Oct to Mar.
the company in the frst half year to that in the second half year.
ratios most closely represent the ratio of the Interest paid by the company in the two half years.
Additional directions for questions 44 to 45: Income of the company in the frst half year i.e.
Apr ’09 – Sep ’09 is Rs. 120 cr and the income in the second half year i.e. Oct ’09 to Mar ’10 is Rs.
the entire year Apr ‘09 – Mar ‘10.
paid in the second half of the year?
applied in any one of the four categories – Chemical, Medicine, Electrical and Mechanical.
46. In which year was the maximum percentage of patents applied in the feld of Medicine granted?
percentage, as compared to the previous year?
First of all it’s not rocket science.
And it’s made up of two words: Deductive and Logic.
at (a fact or a conclusion) by reasoning.
justifable by reason; (the logic of) the course of action following as a necessary consequence of.
So Deductive Logic is the process by which we arrive at a conclusion with the help of reasoning.
which is a dog”. If it is given, then you have to accept it in the context of the given question.
Logic is not about content. It is about form. We don’t have to question the given premises.
We have to say – If the premises were true, would the conclusion follow.
taken to be true, the conclusion has to follow.
“If you use Brand X detergent your clothes will not get clean. But our detergent works much better.
has a strong argument that you should be infuenced by.
the conclusion to be false.
does not follow from the given premises, the argument is invalid.
arguments, whose major premises are based on observations or experiences.
Practice: Which of the following is an example of a deductive argument?
CDs in my bookcase. Therefore, there are 39 CDs in my bookcase.
b. Topeka is either in Kansas or Honduras. If Topeka is in Kansas, then Topeka is in North America.
If Topeka is in Honduras, then Topeka is in Central America. Therefore, Topeka is in Kansas.
test today, and get an A.
does not follow from them. Choices c and d have conclusions that do not follow the premises.
that make up a deductive argument.
What do you think the phrase means?
those elements that are A as well as B.
You might ask – how is this possible? The statement says “some”, and not “all”.
is – Some A are B. Rest we don’t know.
So the best inference that I can draw from the statement is this: At least one A is a B and vice-versa.
A note on the above fgure.
region marked with the ? are populated or not.
If there are some A which are not B but all B are A, the fgure becomes same as fg 2.
If there are some B which are not A but all A are B, the fgure becomes same as fg 3.
One more scenario is when the set of A and B are identical i.e. the two circles overlap.
Does it also mean Some B are not A?
If your answer was – No, then you’re right; cause A and B could be equal.
Directions for questions 1 to 5: In the given questions, which of the following are valid arguments?
1. A. Some printers are fast. No fast is slow. No printer is slow.
B. No poet is a thinker. Some thinkers are leaders. No leader is a poet.
C. No poet is a thinker. Some thinkers are leaders. Some leaders are not poets.
D. Only cats are dogs. No cat is a pig. No dog is a pig.
2. A. All music is good. All good is great. All music is great.
B. All men are wise. All wise are leaders. All leaders are men.
C. All men are wise. All wise are leaders. Some men are leaders.
D. All boys are men. Some men are smart. Some boys are smart.
3. A. I go out only on Sundays. Today is a Sunday. I am out.
B. I go out only on Sundays. Today is not a Sunday. I am not out.
C. I go out only on Sundays. I am out. Today is a Sunday.
D. I go out only on Sundays. I am not out. It is not a Sunday.
4. A. All princes have moles. Raj has a mole. Raj is a prince.
B. All princes have moles. Raj is a prince. Raj has a mole.
C. Only princes have moles. Raj is a prince. Raj has a mole.
D. No princes have moles. Raj is not a prince. Raj does not have a mole.
5. A. Raj has a mole. Raj is a prince. All princes have moles.
B. All kings are men. All men are weak. Some weak are kings.
C. All kings are men. All men are weak. All king are weak.
D. All kings are men. All men are weak. All weak are kings.
6. Statements: 1. All cars are cats. 2. All fans are cats.
Conclusions: 1. All cars are fans. 2. Some fans are cars.
7. Statements: 1. Some scooters are trucks. 2. All trucks are trains.
Conclusions: 1. Some scooters are trains. 2. No truck is a scooter.
8. Statements: 1. All pencils are pens. 2. No pen is a book.
Conclusions: 1. No pencil is a book. 2. Some pencils are books.
9. Statements: 1. Some rats are rabbits. 2. All rats are mosquitoes.
Conclusions: 1. Some mosquitoes are rabbits. 2. No rabbit is a mosquito.
10. Statements: 1. All fans are cups. 2. All cups are pillows.
Conclusions: 1. All fans are pillows. 2. All pillows are fans.
conclusion based on the frst two.
11. A. All green is blue. B. All green is white.
C. All green is black. D. All black is white.
E. All blue is yellow. F. All blue is white.
12. A. All copper is metal. B. All bronze is non metal.
C. Some metal is silver. D. Some metal is not silver.
E. No copper is bronze. F. Some silver is not metal.
13. A. All beaters cheat. B. All teachers cheat.
C. Some teachers teach. D. Some teachers beat.
E. Some teachers beat and cheat. F. Some beaters cheat.
14. A. Some communists are socialists. B. All socialists are Leninists.
C. Some socialists are Leninists. D. Marxists are not capitalists.
E. All Leninists are communists. F. All communists are socialists.
15. A. All Sitas lie. B. Some Sitas are girls.
C. All girls are Sitas. D. Some girls lie.
E. All girls lie. F. All liars are girls.
Directions for questions 16 to 30: In the given questions, which of the following are valid arguments?
16. A. Some workers are stupid. Some stupid are great. Some workers are great.
B. Some men are dancers. All dancers are poets. Some men are poets.
C. Some boys are not studious. All studious are men. Some boys are men.
D. Either Ram or Shyam attends college. Ram has gone to college. Shyam has gone for a movie.
17. A. All apples are oranges. Some oranges are mangoes. Some apples are mangoes.
C. All carrots are edible. All edible contain vitamin. Vitamin is present in carrot.
D. No car is a cart. No cart is a cycle. No cycle is a car.
18. A. All big stars are yellow. Sun is a star. Sun is yellow.
B. All men are educated. All Educated are wise. All men are wise.
C. All frocks are tubs. Some tubs are beds. Some frocks are beds.
D. All pranksters are funny. Clark is a prankster . Clark is funny.
19. A. All locks are books. No book is green. No lock is green.
B. All ghosts are scary. All scary are non funny. All non funny are ghosts.
C. A is part of Z. B is part of Z. A is part of B.
20. A. Verma is a coward. All models are coward. Verma is a model.
B. Some nets are monkeys. Rudolph is a monkey. Rudolph is a net.
C. Some snakes are poisonous. Some poisonous are secrets. Some secrets are snakes.
D. All guns are wrenches. All wrenches are wicked. All guns are wicked.
21. A. All teas are coffee. This is coffee. This is tea.
B. Some pets are peons. No peon is handsome. Some pets are handsome.
C. Some ponds are deep. Some lakes are deep. Some ponds are lakes.
D. All roads are poles. All poles are lamps. Some lamps are roads.
22. A. All poets are wrestlers. Some wrestlers are mad. Some poets are mad.
B. All practice is theory. All surgery is practice. All surgery is theory.
C. All men are tall. All tall are boors. All men are boors.
23. A. Some cars are blue. Some apples are blue. All blue are either cars or apples.
B. Some As are Bs. All Cs are As. Most Cs are Bs.
C. All birds lay eggs. Mammal is a bird. Mammal lays eggs.
D. All A need B. All C are A. All C need B.
24. A. No M is P. All R is M. All R is P.
B. All A are wrong. No A is C. No C is wrong.
C. Some C are A. Most C are right. Most A are right.
D. No M is P. All R is M. No R is P.
25. A. Some S is not P. Some X is S. Some X is not P.
B. Some S is not P. All X is P. No X is P.
C. No A is C. All C are B. No B is A.
26. A. All roses are red. Some roses are pink. Some pink are red.
B. Some roses are red. All Pink are red. Some roses are pink.
D. All zens are marutis. Some cars are not marutis. Some marutis are not cars.
B. There can be no photograph without a camera. There is no photograph. There is no camera.
D. There can be no photograph without a camera. There is a camera. There is no photograph.
28. A. Only soldiers carry guns. Sam is a soldier. Sam is carrying a gun.
B. Only soldiers carry guns. Sam is carrying a gun. Sam is a soldier.
C. All soldiers carry guns. Sam is carrying a gun. Sam is a soldier.
D. All soldiers carry guns. Sam is a soldier. Sam is carrying a gun.
29. A. Some toys are mad. Some mad are crazy. No toys are crazy.
B. Some clubs are hip. Some hip are cool. Some clubs are cool.
C. Some men are wise. Some wise are radioactive. Some men are radioactive.
D. All women are pretty. Some pretty are cool. Some women are cool.
30. A. No pig is a dog. Only dogs are cats. Some cats are pigs.
B. Some Apples are bad. All apples are handsome. Some handsome are bad.
D. All offcers are corrupt. All corrupt are smart. All smart are offcers.
31. Statements: 1. Some players are singers. 2. All singers are tall.
Conclusions: 1. Some players are tall. 2. All players are tall.
32. Statements: 1. Some hats are caps. 2. Some caps are mats.
Conclusions: 1. Some caps are hats. 2. Some mats are caps.
33. Statements: 1. Some vegetables are fruit. 2. No fruit is black.
Conclusions: 1. Some blacks are vegetables. 2. No vegetable is black.
34. Statements: 1. Some fools are intelligent. 2. Some intelligent are great.
Conclusions: 1. Some fools are great. 2. All great are intelligent.
35. Statements: 1. All stones are water. 2. Some waters are clean.
Conclusions: 1. Some stones are clean. 2. No stone is clean.
36. Statements: 1. All keys are locks. 2. All locks are screws.
Conclusions: 1. All screws are keys. 2. Some screws are not keys.
37. Statements: 1. Some books are pen. 2. No pen is pencil.
Conclusions: 1. Some books are pencils. 2. No book is a pencil.
38. Statements: 1. All dogs are monkeys. 2. No monkey is a cat.
Conclusions: 1. No dog is a cat. 2. No cat is a dog.
39. Statements: 1. Some phones are watches. 2. All watches are guns.
Conclusions: 1. All guns are watches. 2. Some guns are phones.
40. Statements: 1. All umbrellas are airplanes. 2. Some airplanes are birds.
Conclusions: 1. Some umbrellas are birds. 2. Some birds are umbrellas.

References: v. 

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