DATA ARRANGEMENT and RANKINGS

DATA ARRANGEMENTS & RANKING

Note: Question numbers are numbers from the actual exam in the respective years mentioned below

Five people A, B, C, D and E are seated about a round table. Every chair is spaced equidistant from adjacent chairs. (2016)

(i) C is seated next to A

(ii) A is seated two seats from D

(iii) B is not seated next to A

On the basis of the above information, which of the following must be true?

D is seated next to B
E is seated next to A
D and C are separated by two seats

Select the correct answer using the code given below :

(a) 1 only

(b) 1 and 2 only

(d) Neither 1 nor 2 nor 3

Answer-b

We know that C is seated next to A, A is seated two seats from D, and B is not seated next to A. This means that D must be seated next to B and E must be seated next to A. D and C are not necessarily separated by two seats, as it is possible for E to be seated between them.

There are five hobby clubs in a college - photography, yachting, chess, electronics and gardening. The gardening group meets every second day, the electronics group meets every third day, the chess group meets every fourth day, the yachting group meets every fifth day and the photography group meets every sixth day. How many times do all the five groups meet on the same day within 180 days?(2016)

(a) 5

(b)18

(d) 3

Answer-d

The least common multiple of 2, 3, 4, 5, and 6 is 60. This means that all five groups will meet on the same day every 60 days. Within 180 days, there are 3 periods of 60 days, so all five groups will meet on the same day 3 times.

There are some nectar-filled flowers on a tree and some bees are hovering on it. If one bee lands on each. flower, one bee will be left out. If two bees land on each flower, one flower will be left out. The number of flowers and bees respectively are:(2016)

(a) 2 and 4

(b) 3 and 2

(d) 4 and 3

Answer-c

If one bee lands on each flower, one bee will be left out. This means that the number of bees is one more than the number of flowers. If two bees land on each flower, one flower will be left out. This means that the number of flowers is one more than the number of pairs of bees.

The only option that satisfies both of these conditions is (c), 3 flowers and 4 bees.

Directions for the following 5 (five) items: Consider the following information and

answer the five items that follow:(2016)

There are five people in a group - P, Q, R, S and T. The group has one doctor, one

lawyer and one artist. P and S are unmarried students. T is a man married to one

of the group members.

Q is the brother of P and is neither doctor nor artist. R is not a doctor.

Explanation:

P and S are unmarried students. It means that Q, R, and T are doctor, lawyer, and artist but not necessarily in the same order.

T is a man married to one of the group members. Implies, T is married to either Q or R because P and S are unmarried.

Q is the brother of P and is neither doctor nor an artist. As Q is a male, implies, R is the wife of T. Also, Q is a lawyer as he is neither an artist not a doctor.

R is not a doctor.

Now, that we know that Q is a lawyer. Thus, R and T are doctor and artist. Also, as R is not a doctor, implies, R is an artist and T is a doctor. Clearly, T is the doctor.

Who is the doctor?

(a) T

(b) P

(d) R

Answer -a

Who is the artist ?

(a) P

(b) Q

(d) I

Answer -c

Who is the spouse of R?

(a) P

(b) T

(d) S

Answer-b

Who is the lawyer?

(a) P

(b) Q

(d) S

Answer-b

Who of the following is definitely a man ?

(a) P

(b) S

(d) None of the above

Answer- c

Direction for the following 3 (three) items: Consider the given information and answer the three items that follow.(2016)

Six boxes A, B, C, D, E and F have been painted with six different colours viz., violet, indigo, blue, green, yellow and orange and arranged from left to right (not necessarily either kept or painted with the colours in the same order). Each box contains a ball of any one of the following six games: cricket, hockey, tennis, golf, football and volleyball (not necessarily in the same order). The golf ball is in the violet box and is not in the box D. The box A which contains the tennis ball is orange in colour and is at the extreme right. The hockey ball is neither in box D nor in box E. The box C having cricket ball is painted green. The hockey ball is neither in the box painted blue nor in the box painted yellow. The box C is fifth from right and next to Box B. The box B contains volleyball. The box containing the hockey ball is between the boxes containing the golf ball and volleyball.

Explanation:

Let's start by listing the information we have about the boxes and their contents:

Box A is orange and contains a tennis ball.
Box B is next to box A and contains a volleyball.
Box C is green and contains a cricket ball.
Box D is not violet and does not contain a hockey ball.
Box E is between the boxes containing the golf ball and volleyball.
Box F is not violet and does not contain a golf ball.

We can use this information to eliminate some of the possible arrangements of the boxes. For example, we know that box A is orange and contains a tennis ball. This means that it cannot be next to box B, which is green and contains a cricket ball. Therefore, box A must be on the leftmost end, followed by box B, followed by box C.

We can also use the information about the hockey ball to eliminate some of the possible arrangements. We know that the hockey ball is neither in box D nor in box E. This means that it must be in either box A, box B, or box C. However, we also know that box A contains a tennis ball, and box B contains a volleyball. This means that the hockey ball must be in box C.

Now that we know that the hockey ball is in box C, we can use the information about the golf ball to determine which box contains the golf ball. We know that the golf ball is in a violet box and is not in box D. This means that the golf ball must be in box E, which is violet.

33.Which of the following statements is/are correct?

(a) D is painted yellow

(b) F is painted indigo

(d) All of the above

Answer - b

Which one of the following boxes contains the golf ball?

(a) F

(b) E

(d) None of the above

Answer - b

The football is in the box of which colour?

(a) Yellow

(b) Indigo

(d) Blue

Answer- c

The information given in the question is not sufficient to determine the colour of the box containing the football. We know that the football is in box D, but we do not know the colour of box D. The only information we have about the colour of box D is that it is not violet. This means that the football could be in a box of any colour other than violet.

Direction for the following 3 (three) items: Consider the given information and answer the three items that follow.

When three friends A, B and C met, it was found that each of them wore an outer garment of a different colour.

In random order, the garments are: jacket, sweater and tie;

and the colours are: blue, white and black. Their surnames in random order are: Ribeiro, Kumar and Singh.

Further, we know that:

neither B nor Ribeiro wore a white sweater
C wore a tie
Singh's garment was not white
Kumar does not wear a jacket
Ribeiro does not like to wear the black colour
Each of the friends wore only one outer garment of only one colour

What is C's surname?

(a) Ribeiro

(b) Kumar

(d) Cannot be determined

Answer - a

We can eliminate options (b) and (c) immediately because Singh's garment was not white and Kumar does not wear a jacket.

We can also eliminate option (d) because we know that each of the friends wore only one outer garment of only one colour.

Therefore, C must be Ribeiro because he is the only one who meets all of the criteria.

Here is a step-by-step solution:

Neither B nor Ribeiro wore a white sweater. This means that A must be wearing the white sweater.

C wore a tie. This means that B must be wearing the jacket.

Singh's garment was not white. This means that Singh must be wearing the black jacket.

Kumar does not wear a jacket. This means that Kumar must be wearing the white sweater.

Ribeiro does not like to wear the black colour. This means that Ribeiro must be wearing the tie.

Therefore, C must be Ribeiro.

What is the colour of the tie?

(a) Black

(b) Blue

(d) Cannot be determined,

Answer -b

We know that Ribeiro wore the tie, and that Ribeiro does not like to wear the black colour. This means that the tie cannot be black.

We also know that Singh's garment was not white, and that Kumar wore the white sweater. This means that the tie cannot be white.

Therefore, the tie must be blue.

Here is a step-by-step solution:

Ribeiro wore the tie.

Ribeiro does not like to wear the black colour.

Singh's garment was not white.

Kumar wore the white sweater.

Therefore, the tie must be blue.

Who wore the sweater ?

(a) A

(b) B

(d) Cannot be determined

Answer - a

We can eliminate options (b) and (c) immediately because we know that C wore a tie and B wore a jacket.

We can also eliminate option (d) because we know that each of the friends wore only one outer garment of only one colour.

Therefore, A must have worn the sweater.

Here is a step-by-step solution:

C wore a tie.

B wore a jacket.

Each of the friends wore only one outer garment of only one colour.

Therefore, A must have worn the sweater.

Four-digit numbers are to be formed using the digits 1, 2, 3 and 4; and none of these four digits are repeated in any manner.(2016)

Further,

2 and 3 are not to immediately follow each other
1 is not to be immediately followed by 3
4 is not to appear at the last place
1 is not to appear at the first place

How many different numbers can be formed ?

(a) 6

(b) 8

(d) None of the above

Answer - a

The following are the possible numbers that can be formed:

2134
2413
3124
3412
4123
4312

The numbers 1234 and 1324 are not possible because 1 is not allowed to be followed by 3. The numbers 2314 and 3214 are not possible because 2 and 3 are not allowed to be next to each other. The number 4132 is not possible because 4 is not allowed to be in the last place.

In a class of 60 students, where the number of girls is twice that of boys, Kamal, a. boy, ranked seventeenth from the top. If there are 9 girls ahead of. Kamal, the number of boys in rank after him is(2016)

(a) 13

(b) 12

(d) 3

Answer - b

There are 60 students in the class, and the number of girls is twice that of boys. This means that there are 20 boys and 40 girls in the class.

Kamal is ranked 17th from the top, and there are 9 girls ahead of him. This means that there are 7 boys ahead of Kamal.

There are 43 students ranked after Kamal, and 31 of them are girls. This means that there are 12 boys ranked after Kamal.

Four tests-Physics, Chemistry, Mathematics and Biology are to be conducted on four consecutive days, not necessarily in the same order. The Physics test is held before the test which is conducted after Biology. Chemistry is conducted exactly after two tests are held. Which is the last test held?(2017)

(a) Physics

(b) Biology

(d) Chemistry

Answer - c

We know that the tests are held on four consecutive days, and that Chemistry is held exactly after two tests are held. This means that Chemistry cannot be held on the first or last day.

We also know that Physics is held before the test which is conducted after Biology. This means that Physics cannot be held on the last day, and Biology cannot be held on the first day.

This leaves us with two possibilities for the order of the tests:

Day 1: Biology
Day 2: Chemistry
Day 3: Physics
Day 4: Mathematics

Day 1: Chemistry
Day 2: Biology
Day 3: Physics
Day 4: Mathematics

In either case, the last test held is Mathematics.

15 students failed in a class of 52. After removing the names of failed students, a merit order list has been prepared in which the position of Ramesh is 22nd from the top. What is his position from the bottom?(2017)

(a) 18th

(b) 17th

(d) 15^th

Answer - c

There are 52 students in the class, and 15 of them failed. This means that there are 37 students who passed.

Ramesh is ranked 22nd from the top, which means that there are 21 students ranked above him. This means that there are 16 students ranked below him.

Therefore, Ramesh's position from the bottom is 16th.

In a group of six women, there are four tennis players, four postgraduates in Sociology, one postgraduate in Commerce and three bank employees. Vimala and Kamla are the bank employees while Amala and Komala are unemployed. Komala and Nirmala are among the tennis players. Amala, Kamla, Komala and Nirmala are postgraduates in Sociology of whom two are bank employees. If Shyamala is a postgraduate in Commerce, who among the following is both a tennis player and a bank employee?(2017)

(a) Amala

(b) Komala

(d) Shyamala

Answer - c

We know that there are four tennis players, four postgraduates in Sociology, one postgraduate in Commerce and three bank employees. We also know that Vimala and Kamla are the bank employees, Amala and Komala are unemployed, and Komala and Nirmala are among the tennis players.

This means that Amala, Kamla, Komala and Nirmala are postgraduates in Sociology, and two of them are bank employees. We also know that Shyamala is a postgraduate in Commerce.

This leaves us with two possibilities for the bank employees: Vimala and Kamla, or Vimala and Nirmala.

If the bank employees are Vimala and Kamla, then Nirmala is the only person who is both a tennis player and a postgraduate in Sociology.

If the bank employees are Vimala and Nirmala, then Nirmala is the only person who is both a tennis player and a bank employee.

Therefore, Nirmala is the only person who is both a tennis player and a bank employee.

In a test, Randhir obtained more marks than the total marks obtained by Kunal and Debu. The total marks obtained by Kunal and Shankar are more than those of Randhir. Sonal obtained more marks than Shankar. Neha obtained more marks than Randhir. Who amongst them obtained highest marks?(2017)

(a) Randhir

b) Ncha

(d) Data are inadequate

Answer - d

We know that Randhir obtained more marks than the total marks obtained by Kunal and Debu. This means that Randhir obtained more marks than Kunal and Debu combined.

We also know that the total marks obtained by Kunal and Shankar are more than those of Randhir. This means that Kunal and Shankar combined obtained more marks than Randhir.

We also know that Sonal obtained more marks than Shankar, and Neha obtained more marks than Randhir.

However, we do not know how many marks each person obtained. It is possible that Randhir obtained the highest marks, but it is also possible that Neha or Sonal obtained the highest marks.

Therefore, the data are inadequate to determine who obtained the highest marks.

If 2 boys and 2 girls are to be arranged in a row so that the girls are not next to each other, how many possible arrangements are there?(2017)

(a) 3

(b) 6

(d) 24

Answer- c

There are 24 possible arrangements of 2 boys and 2 girls. However, in half of these arrangements, the girls will be next to each other. This leaves 12 possible arrangements in which the girls are not next to each other.

One way to see this is to consider the following four arrangements:

Boy, Girl, Boy, Girl
Girl, Boy, Girl, Boy
Boy, Boy, Girl, Girl
Girl, Girl, Boy, Boy

In each of these arrangements, the girls are next to each other. If we swap the positions of the boys and girls, we get the following four arrangements:

Girl, Boy, Boy, Girl
Boy, Girl, Girl, Boy
Girl, Girl, Boy, Boy
Boy, Boy, Girl, Girl

In each of these arrangements, the girls are still next to each other. This means that there are 8 possible arrangements in which the girls are next to each other.

There are 24 possible arrangements of 2 boys and 2 girls, so there are 12 possible arrangements in which the girls are not next to each other.

Consider the following :(2017)

A, B, C, D, E, F, G and H are standing in a row facing North.

B is not a neighbour of G.

F is to the immediate right of G and neighbour of E.

G is not at the extreme end.

A is sixth to the left of E.

H is sixth to the right of C.

Which one of the following is correct in respect of the above?

(a) C is to the immediate left of A.

(b) D is an immediate neighbour of B and F.

(d) A and E are at the extreme ends.

Answer - c

We know that A is sixth to the left of E, so we can write:

A E

We also know that H is sixth to the right of C, so we can write:

C H

Since F is to the immediate right of G and neighbor of E, we can write:

E F G

Since G is not at the extreme end, we know that F cannot be at the extreme left end. This means that A must be to the left of E, and C must be to the right of H.

We also know that B is not a neighbor of G, so B cannot be to the immediate left or right of G. This means that D must be to the immediate left or right of G.

Since F is to the immediate right of G, D cannot be to the immediate right of G. This means that D must be to the immediate left of G.

Therefore, the final order is:

A C B D G F E H

This means that G is to the immediate right of D.

Consider the given information and answer the three items that follow.(2017)

A, B, C, D, E, F and G are Lecturers from different cities Hyderabad, Delhi, Shillong, Kanpur, Chennai, Mumbai and Srinagar (not necessarily in the same order) who participated in a conference. Each one of them is specialized in a different subject, viz., Economics, Commerce, History, Sociology, Geography, Mathematics and Statistics (not necessarily in the same order).

Further

Lecturer from Kanpur is specialized in Geography
Lecturer D is from Shillong
Lecturer C from Delhi is specialized in Sociology
Lecturer B is specialized in neither History nor Mathematics
Lecturer A who is specialized in Economics does not belong to Hyderabad
Lecturer F who is specialized in Commerce belongs to Srinagar
Lecturer G who is specialized in Statistics belongs to Chennai

Explanation:

Here is a table that summarizes the information given in the problem:

Lecturer City Subject

A Mumbai Economics

B Kanpur Geography

C Delhi Sociology

D Shillong History/Mathematics

E Hyderabad History/Mathematics

F Srinagar Commerce

G Chennai Statistics

Who is specialized in Geography?

(a) B

(b) D

(d) Cannot be determined as data are inadequate

Answer - a

To which city does the Lecturer specialized in Economics belong?

(a) Hyderabad

(b) Mumbai

(d) Cannot be determined as data are inadequate

Answer - b

Who of the following belongs to Hyderabad?

(a) B

(b) E

(d) Cannot be determined as data are inadequate

In a school, there are five teachers A, B, C, D and E. A and B teach Hindi and English. C and B teach English and Geography. D and A teach Mathematics and Hindi. E and B teach History and French. Who teaches the maximum number of subjects?(2017)

(a) A

(b) B

(d) E

Answer - b

Here's the breakdown of subjects each teacher teaches:

A: Hindi, English

B: Hindi, English, Geography, History, French

C: English, Geography

D: Mathematics, Hindi

E: History, French

Therefore, B teaches the maximum number of subjects.

Directions for the following 3 (three) items:(2017)

Consider the given information and answer the three items that follow.

Eight railway stations A, B, C, D, E, F, G and H are connected either by two-way passages or one-way passages. One-way passages are from C to A, E to G, B to F, D to H, G to C, E to C and H to G. Two-way passages are between A and E, G and B, F and D, and E and D.

While travelling from C to H, which one of the following stations must be passed through?

(a) G

(b) E

(d) F

Answer - b

To travel from C to H, we must pass through either station A or station E.

However, the one-way passage from C to A is only in the direction of A, so we cannot travel from C to A.

Therefore, we must travel from C to E, then from E to H.

In how many different ways can a train travel from F to A without passing through any station more than once?

(a) 1

(b) 2

(d) 4

Answer - d

There are 4 ways through which a train can travel from F to A without passing through any station more than once.

F to D to E to A
F to D to H to G to C to A
F to D to H to G to B to E to A
F to D to H to G to C to E to A

Therefore, the correct answer is (d).

If the route between G and C is closed, which one of the following stations need not be passed through while travelling from H to C?

(a) E

(b) D

(d) B

Answer - c

If the route between G and C is closed, then tjhe possible route for travelling from H to C,

H → G → B → F → D → E → C

Station A is not on this route.

Directions for the following 2 (two) items:(2018)

Read the following information and answer the two items that follow.

The plan of an office block for six officers A, B, C, D, E and F is as follows : Both B and C occupy offices to the right of the corridor (as one enters the office block) and A occupies on the left of the corridor. E and F occupy offices on opposite sides of the corridor but their offices do not face each other. The offices of C and D face each other. E does not have a corner office. F's office is further down the corridor than A's, but on the same side.

If E sits in his office and faces the corridor, whose office is to his left?

(a) A

(b) B

(c) C

(d) D

Answer - c

Given that E and F occupy offices on opposite sides of the corridor but their offices do not face each other, this means that E's office is on the left side of the corridor and F's office is on the right side of the corridor.

Since E does not have a corner office, this means that C's office is to E's left.

Who is/are F's immediate neighbour/ neighbours?

(a) A only

(b) A and D

(d) B and C

Answer- a

F's immediate neighbor is A only.

Given that F's office is further down the corridor than A's, but on the same side, this means that F's office is next to A's. Since E does not have a corner office, this means that F's office is on the other side of A's office from C's office. Therefore, F's immediate neighbor is A only.

Directions for the following 6 (six) items:2018

Read the information given below and answer the six items that follow.

A, B, C and D are students. They are studying in four different cities, viz., P, Q, R and S (not necessarily in that order). They are studying in Science college, Arts college, Commerce college and Engineering college (not necessarily in that order), which are situated in four different States, viz., Gujarat, Rajasthan, Assam and Kerala (not necessarily in that order).

Further, it is given that-

(i) D is studying in Assam

(ii) Arts college is located in city S which is in Rajasthan

(iii) A is studying in Commerce college

(iv) B is studying in city Q

(v) Science college is located in Kerala

Explanation:

Here is a table that summarizes the information:

Student City College State

A P/R Commerce Gujarat

B Q Science Kerala

C S Arts Rajasthan

D P/R Engineering Assam

A is studying in

(a) Rajasthan

(b) Gujarat

(d) Kerala

Answer- b

Science college is located in

(a) city Q

(b) city S

(d) city P

Answer- a

C is studying in

(a) Science college

(b) Rajasthan

(d) city Q

Answer - b

Which one of the following statements is correct?

(a) D is not studying in city S.

(b) A is studying in Science college.

(d) Engineering college is located in Gujarat.

Answer- a

Which one of the following statements is correct regarding Engineering college?

(a) C is studying there.

(b) B is studying there.

(d) D is studying there.

Answer -d

Which one of the following statements is correct?

(a) Engineering college is located in Assam.

(b) City Q is situated in Assam.

(d) B is studying in Gujarat.

Answer - a

Lakshmi, her brother, her daughter and her son are badminton players. A game of doubles is about to begin:(2018)

(I) Lakshmi's brother is directly across the net from her daughter.

(ii) Her son is diagonally across the net from the worst player's sibling.

(iii) The best player and the worst player are on the same side of the net.

Who is the best player?

(a) Her brother

(b) Her daughter

(d) Lakshmi

Answer - a

Based on the given information:

Lakshmi's brother is directly across the net from her daughter.
Her son is diagonally across the net from the worst player's sibling.
The best player and the worst player are on the same side of the net.

From this information, we can deduce the following:

Lakshmi's brother and her daughter are in opposite teams and directly across the net.

Lakshmi's son and the worst player's sibling are in opposite teams and diagonally across the net.

Lakshmi and her brother are on the same side of the net.

Therefore, the worst player is Lakshmi, and her brother is the best player.

Hence, the best player is (a) her brother.

Directions for the following 3 (three) items:(2019)

Read the following information and answer the three items that follow :

Six students A, B, C, D, E and F appeared in several tests. Either C or F scores the highest. Whenever C scores the highest, then E scores the least. Whenever F scores the highest, B scores the least. In all the tests they got different marks; D scores higher than A, but they are close competitors; A scores higher than B; C scores higher than A.

If F stands second in the ranking, then the position of B is

(a) Third

(b) Fourth

(d) Sixth

Answer -c

The answer is (c), Fifth.

We know that either C or F scores the highest. If F stands second in the ranking, then C must have scored the highest. We also know that whenever C scores the highest, then E scores the least. This means that E must be in last place. We also know that whenever F scores the highest, B scores the least. However, we know that F did not score the highest, because C did. This means that B cannot be in last place. However, we do know that B scores lower than A, who scores lower than C. This means that B must be in fifth place.

If B scores the least, the rank of C will be

(a) Second

(b) Third

(d) Second or third

Answer - d

We know that whenever B scores the least, C scores the highest. This means that C must be in first or second place. However, we do not know which of these two places C is in.

If E is ranked third, then which one of the following is correct?

(a) E gets more marks than C

(b) C gets more marks than E

(d) D is ranked fifth

Answer- b

We know that whenever C scores the highest, then E scores the least. This means that C must have scored higher than E.

A is 16th from the left end in a row of boys and V is 18th from the right end. G is 11th from A towards the right and 3rd from V towards the right end. How many boys are there in the row?(2020)

(a) 40

(b) 41

(d) Cannot be determined due to insufficient data

Answer - b

A is 16th from the left, so there are 15 boys to the left of A. G is 11th from A to the right, so there are 10 boys between A and G, including A and G. V is 3rd to the right of G, so there are 2 boys between G and V, including G and V. There are 18 boys to the right of V, so there are 14 boys to the right of G, not including G.

Therefore, there are 15 + 10 + 2 + 14 = 41 boys in the row.

Seven books P, Q, R, S, T, U and V are placed side by side. R, Q and T have blue covers and other books have red covers. Only S and U are new books and the rest are old. P, R and S are law reports; the rest are Gazetteers. Books of old Gazetteers with blue covers are(2021)

(a) Q and R

(b) Q and U

(d) T and U

Answer - c

We know that R, Q, and T have blue covers, and that P, R, and S are law reports. This means that Q and T are the only books that are both blue and gazetteers. We also know that only S and U are new books, so Q and T must be old. Therefore, the books of old gazetteers with blue covers are Q and T.

Consider two Statements and a Question:(2021)

Statement-1: Priya is 4 ranks below Seema and is 31st from the bottom.

Statement-2: Ena is 2 ranks above Seema and is 37th from the bottom.

Question: What is Seema's rank from the top in the class of 40 students?

Which one of the following is correct in respect of the Statements and the Question?

(a) Statement-1 alone is not sufficient to answer the Question

(b) Statement-2 alone is not sufficient to answer the Question

(d) Both Statement-1 and Statement-2 are required to answer the Question

Answer - c

Statement-1 alone is sufficient to answer the question. Priya is 31st from the bottom, which means she is 9th from the top. Seema is 4 ranks above Priya, which means she is 13th from the top.

Statement-2 alone is also sufficient to answer the question. Ena is 37th from the bottom, which means she is 3rd from the top. Seema is 2 ranks above Ena, which means she is 5th from the top.

Therefore, either Statement-1 alone or Statement-2 alone is sufficient to answer the question.

There are 6 persons arranged in a row. Another person has to shake hands with 3 of them so that he should not shake hands with two consecutive persons. In how many distinct possible combinations can the handshakes take place ?(2021)

(a) 3

(b) 4

(d) 6

Answer- b

There are 6 persons arranged in a row. Another person has to shake hands with 3 of them so that he should not shake hands with two consecutive persons. This means that the person can shake hands with any of the 6 persons, but he cannot shake hands with two consecutive persons.

There are 4 possible combinations of handshakes that can take place:

The person can shake hands with the first, third, and fifth persons.
The person can shake hands with the second, fourth, and sixth persons.
The person can shake hands with the first, fourth, and sixth persons.
The person can shake hands with the second, third, and fifth persons.

Therefore, there are 4 distinct possible combinations of handshakes that can take place.

Three persons A, B and C are standing in a queue not necessarily in the same order. There are 4 persons between A and B, and 7 persons between B and C. If there are 11 persons ahead of C and 13 behind A what could be the minimum number of persons in the queue?(2022)

(a) 22

(b) 28

(d) 38

Answer - a

We know that there are 11 persons ahead of C and 13 behind A. This means that there are at least 24 persons in the queue. We also know that there are 4 persons between A and B, and 7 persons between B and C. This means that there are at least 11 persons between A and C. However, we do not know the order of A, B, and C. Therefore, the minimum number of persons in the queue is 22.

Eight students A, B, C, D, E, F, G and H sit around a circular table, equidistant from each other, facing the centre of the table, not necessarily in the same order. B and D sit neither adjacent to C nor opposite to C. A sits in between E and D, and F sits in between B and H. Which one of the following is definitely correct?(2022)

(a) B sits in between A and G

(b) C sits opposite to G

(d) None of the above

Answer- b

Given the information:

B and D sit neither adjacent to C nor opposite to C.

A sits in between E and D.

F sits in between B and H.

From the given information, we can deduce the following:

Since B and D cannot be adjacent to C or opposite to C, the only possible seating arrangement for B and D is B-C-D.

A sits in between E and D. Since A is already between B and D, it means E cannot be adjacent to A. Therefore, E cannot sit next to A.

F sits in between B and H. Since A is already between B and D, it means F cannot be adjacent to A either. Therefore, F cannot sit next to A.

From the remaining students, G is the only one left. Since E cannot be adjacent to A and F cannot be adjacent to A, the only position left for G is to be opposite to C. Therefore, C sits opposite to G.

Hence, the correct statement is (b) C sits opposite to G.

Six persons A, B, C, D, E and F are sitting equidistant from each other around a circular table (facing the centre of the table)

Consider the Question and two Statements given below :(2022)

Question: Who is sitting on the immediate left of A?

Statement-1: B is sitting opposite to C and D is sitting opposite to E.

Statement-2: F is sitting on the immediate left of B.

Which one of the following is correct in respect of the Question and the Statements?

(a) Statement-1 alone is sufficient to answer the Question

(b) Statement-2 alone is sufficient to answer the Question

(d) Both Statement-1 and Statement-2 are not sufficient to answer the Question

Answer - d

The answer is (d) Both Statement-1 and Statement-2 are not sufficient to answer the Question.

Statement-1 gives us the information that B is sitting opposite to C and D is sitting opposite to E. This information does not tell us anything about the relative positions of A, B, C, D, E, and F. For example, the following are all possible arrangements of the six people around the table, given Statement-1:

A B C D E F
A C B D E F
A E B C D F
A F B C D E

Statement-2 gives us the information that F is sitting on the immediate left of B. This information does not tell us anything about the relative positions of A, B, C, D, E, and F, either. For example, the following are all possible arrangements of the six people around the table, given Statement-2:

A B F C D E
A C B F D E
A E B F C D
A F B E C D

In order to answer the question, we need more information than is given in either Statement-1 or Statement-2.

There are 9 cups placed on a table arranged in equal number of rows and columns out of which 6 cups contain coffee and 3 cups contain tea. In how many ways can they be arranged so that each row should contain at least one cup of coffee?(2022)

(a) 18

(b) 27

(d) 81

Answer - d

There are 9 cups placed on a table arranged in equal number of rows and columns out of which 6 cups contain coffee and 3 cups contain tea. In how many ways can they be arranged so that each row should contain at least one cup of coffee?

There are two cases here:

One row has 3 coffee cups. In such a case, one of the rows will have 2 cups of coffee and the other will have 1 cup of coffee.

Each row has 2 cups of coffee and 1 cup of tea.

Case 1:

There are 3! ways to arrange the rows. For the row with 3 coffee cups, there is only 1 way to arrange them. For the row with 2 coffee cups, there are 3 ways to arrange them. For the row with 1 coffee cup, there are 3 ways to arrange them.

Therefore, the total number of arrangements for case 1 is 3! × 1 × 3 × 3 = 54.

Case 2:

Each row has 2 coffee cups and 1 cup of tea. There are 3! ways to arrange the rows. For each row, there are 3 ways to arrange the 2 coffee cups and 1 way to arrange the tea cup.

Therefore, the total number of arrangements for case 2 is 3! = 3 × 3 × 3 = 27

The total number of arrangements for both cases is 54 +27 =81.

Therefore, the answer is (d)81.

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