## Linear Arrangement

In a linear seating arrangement, persons are sitting in a straight line, on chair, in rooms in a row facing north or south direction. Here also given a set of information about positioning of different elements with respect to other elements. From the given set of information systematically to find the actual arrangement of the elements.

Left & Right: We can use Left and Right as per Information that generally is given and its interpretation is as follows:

Left & Right: We can use Left and Right as per our convenience. Generally we will use as follow:

 Left End Right End

Facing North

Facing South

A is 2 places right of B: Generally students used to get confuse that how many gaps are there between A and B. Here in this case there is only 1 gap between A and B. As it is explained in the diagram below.

A is 3 places left of B: Here in this case there is only 2 gaps between A and B. As it is explained in the diagram below. If B is at 1st place then A is at 4th place.

A stays 2 places away of B: Here in this case it is not given who is in right and who is in left so we have two different cases:

A stays 2 places away of B who is 3 place left of C: In this case, we can assume that B is at 3rd place then C is at 6th place,

Example- Six friends A, B, C, D, E and F are sitting in a row facing towards North. C is sitting between A and E. D is not at the end. B is sitting immediate right to E. F is not at the right end.

Q1. Who is on the extreme right? (a) B (b) E (c) F (d) G (e) none of these
Q2. Who is exactly in between F and A? (a) A (b) C (c) E (d) D (e) none of these
Solution: B is to the immediate right of E i.e E, B. C is between A and E i.e A, C, E, B. as, D is not at the ends and f is not in right end, so sequence in the row becomes:

1. So, extreme right is B, option (a)

2. So, exactly in between F and A, is D, option (d).

Example- A,B,C,D,E,F and G are sitting on a wall and all of them are facing east. C is on the immediate right of D. B is at an extreme end and has E as his neighbor. G is between E and F. D is sitting third from the south end.
Q.1. Who is sitting to the right of E? (a) A (b) C (c) D (d) F (e) none of these
Q.2. Which of the following pairs are sitting at the extreme ends? (a) AB (b) AE (c) CB (d) FB (e) cannot be determine
Solution: The arrangement is:

1. Option (e). G is right of E

2. Option (a) AB

Direction: Study the following information carefully and answer the questions given below:
(i) A, B, C, D, E, F, G and H are eight students, each having a different height.
(ii) D is shorter than A but taller than G
(iii) E is taller than H but shorter than C
(iv) B is shorter than D but taller than F
(v) C is shorter than G
(vi) G is not as tall as F

1.Which of the following is definitely false?
(a) G is shorter than F
(b) C is shorter than F
(c) F is taller than c
(d) B is taller than E
(e) All are true
Solution:- Correct Option (e)
A > D > G
C > E > H
D > B > F
G > C
F > G
Combining these , we get A > D > B > F > G > C > E > H

2. If another student J, who is taller than E but shorter than G, is added to the group, which of the following will be definitely true?
(a) C and J are of the same height
(b) J is shorter than D
(c) J is shorter than H
(d) J is taller than A
(e) None of these
Solution:- Correct Option (b)
A > D > G
C > E > H
D > B > F
G > C
F > G
Combining these , we get A > D > B > F > G > C > E > H
is the correct answer; A > D > B > F > G > C, J > E > H

3. Which of the following will definitely be the third from top when the eight student are arranged in descending order of height?
(a) B
(b) F
(c) G
(d) B or G
(e) Cannot be determined
Solution:- Correct Option (a)
A > D > G
C > E > H
D > B > F
G > C
F > G
Combining these , we get A > D > B > F > G > C > E > H

4. How many of them are definitely shorter than F?
(a) Three
(b) Four
(c) Five
( e) None of these
Solution:- Correct Option (b)
A > D > G
C > E > H
D > B > F
G > C
F > G
Combining these , we get A > D > B > F > G > C > E > H
is the correct answer; G, C, E and H

5. Which of the following is redundant to answer all the above questions?
(a) (ii) only
(b) (ii) and (iii) only
(c) (iii) and (iv) only
(d) (ii) and (v) only
(e) All are necessary to answer the above questions
Solution:- Correct Option (e)
A > D > G
C > E > H
D > B > F
G > C
F > G
Combining these , we get A > D > B > F > G > C > E > H