1) The document provides directions for two sets of linear arrangement questions involving students ranked 1st to 5th and girls standing in a line. 2) For the first set, the document analyzes each clue and arrives at 3 possible arrangements of students by rank and shirt color. 3) For the second set, the document considers two cases based on one girl's position and analyzes the clues to modify a partial lineup of girls from left to right.

1. Some Solved examples (with step wise detailed solution)
We will show the complete solution for 2 set of questions on linear
arrangement for better understanding of solving the problems

2. Directions for set 3
• Directions for 11 to 15
• The top 5 students of a class (all are boys) are P, Q, R, S & T (not in any order). They are wearing
shirts of Red, White, Black, Green & Blue colours (not in any order).
• 1. R got better rank then Q who was wearing green shirt.
• 2. T got 1st rank & S got the 5th rank.
• 3. Neither Q nor R got the 2nd best rank among the 5 students.
• 4. The red shirt is worn by S.
• 5. The boy who was wearing black shirt got a rank which is better than at least 3 students.
• 6. At least 1 boy got the better rank than the rank obtained by the boy who is wearing white
shirt.
• 7. A smaller rank is better than larger rank.
• 11. What is the rank obtained by Q?
• (a) 2nd (b) 3rd (c) 4th (d) either 3rd or 4th (e) cannot be determined
• 12. Who is wearing white shirt?
• (a) P (b)R (c) T (d) either P or R (e) cannot be determined
• 13. If R is wearing the White shirt, then what is colour of shirt of T?
• (a) Black (b) Green (c) Blue (d) either Green or Blue (e) cannot be determined
• 14. If black shirt is worn by P, who is wearing blue shirt?
• (a) P (b) R (c) T (d) either P or T (e) cannot be determined
• 15. How many different arrangements are possible?
• (a) 1 (b) 2 (c) 3 (d) 4 (e) more than 4

3. • General Solution for 11 to 15
• P, Q, R, S & T are arranged in 1st to 5th ranks & wearing shirts of Red, White, Black,
Green & Blue colours. The arrangement must be linear as we will start with rank 1 and
will end with rank 5. This is how we can show the arrangement
Rank 1 2 3 4 5
Name
Colour

4. • Points 2, 3 and 4
• T got 1st rank & S got the 5th rank.
• Neither Q nor R got the 2nd best rank among the 5 students.
• We know T and S didn’t got 2nd rank. So, P got 2nd rank
• The red shirt is worn by S.
• Using it, the table is modified as-
Rank 1 2 3 4 5
Name
Colour

5. • Points 2, 3 and 4
• T got 1st rank & S got the 5th rank.
• Neither Q nor R got the 2nd best rank among the 5 students.
• We know T and S didn’t got 2nd rank. So, P got 2nd rank
• The red shirt is worn by S.
• Using it, the table is modified as-
• Using it, the table is modified as-
Rank 1 2 3 4 5
Name T P S
Colour Red

6. • Point 1 (points 2, 3 and 4 are used)
• R got better rank then Q who was wearing green shirt.
• So, R and Q got 3rd and 4th ranks, respectively. Q is wearing green shirt
• Using it, the table is modified as-
• Using it, the table is modified as-
Rank 1 2 3 4 5
Name T P S
Colour Red

7. • Point 1 (points 2, 3 and 4 are used)
• R got better rank then Q who was wearing green shirt.
• So, R and Q got 3rd and 4th ranks, respectively. Q is wearing green shirt
• Using it, the table is modified as-
Rank 1 2 3 4 5
Name T P R Q S
Colour Green Red

8. • Points 5 and 6 (points 2, 3, 4 and 1 are used)
• The boy who was wearing black shirt got a rank which is better than at least 3
students.
• so his rank is either 1st or 2nd. So, either T or P is wearing black shirt.
• At least 1 boy got the better rank than the rank obtained by the boy who is wearing
white shirt.
• So, T cannot be wearing the white shirt. So, either P or R is wearing black shirt
• Using it, the table is modified as-
Rank 1 2 3 4 5
Name T P R Q S
Colour Green Red

9. • Points 5 and 6 (points 2, 3, 4 and 1 are used)
• The boy who was wearing black shirt got a rank which is better than at least 3
students.
• so his rank is either 1st or 2nd. So, either T or P is wearing black shirt.
• At least 1 boy got the better rank than the rank obtained by the boy who is wearing
white shirt.
• So, T cannot be wearing the white shirt. So, either P or R is wearing black shirt
• Using it, the table is modified as-
Rank 1 2 3 4 5
Name T P R Q S
Colour Green Red

10. • Points 5 and 6 (points 2, 3, 4 and 1 are used)
• The boy who was wearing black shirt got a rank which is better than at least 3
students.
• so his rank is either 1st or 2nd. So, either T or P is wearing black shirt.
• At least 1 boy got the better rank than the rank obtained by the boy who is wearing
white shirt.
• So, T cannot be wearing the white shirt. So, either P or R is wearing black shirt
• Using it, the table is modified as-
Rank 1 2 3 4 5
Name T P R Q S
Colour Black/Blue Black/White/Blue White/Blue Green Red

11. • 11. Q obtained 4th rank. Hence option (c) is the answer
• 12. Either P or R is wearing white shirt. Hence option (d) is the answer
Rank 1 2 3 4 5
Name T P R Q S
Colour Black/Blue Black/White/Blue White/Blue Green Red

12. • 13. If R is wearing the White shirt, then the arrangement can be modified as-
• So, the colour of shirt which T is wearing is either Black or Blue. So, it cannot be
determined. Hence option (e) is the answer
Rank 1 2 3 4 5
Name T P R Q S
Colour Black/Blue Black/Blue White Green Red

13. • 14. If black shirt is worn by P, then the arrangement can be modified as-
• T is wearing blue shirt. Hence option (c) is the answer
Rank 1 2 3 4 5
Name T P R Q S
Colour Blue Black White Green Red

14. • 15. There are 3 possible arrangements
• Hence option (c) is the answer
Rank 1 2 3 4 5
Name T P R Q S
Colour-1 Black White Blue Green Red
Colour-2 Black Blue White Green Red
Colour-3 Blue Black White Green Red

15. Set 4
• Directions for 16 to 20:
• A, B, C, D, E, F, G and H are 8 girls who are standing in a straight line (facing north).
• Further it is known that-
• 1. Only one girl is sitting between E and G. It is also known that G is not standing at any of the extreme positions
• 2. C and F are not at adjacent positions
• 3. F is fourth to the right of A
• 4. Neither B nor E is standing in any of extreme positions. Further it is known that both are immediate
neighbours of each other
• 5. C is second to left of D
• 6. F is standing at either sixth position from the left or fourth position from the right.
• 16. What is the position of B with respect of A?
• (a) 5th to the left (b) Immediate neighbor (c) 2nd to the left (d) 3rd to the right (e) None of these
• 17. Who are standing at the extreme positions?
• (a) A and F (b) H and D (c) C and F (d) H and A (e) H and C
• 18. How many girls are standing between C and E?
• (a) 1 (b) 2 (c) 3 (d) 4 (e) None of these
• 19. If A is related to B is a way, and it is also known that D is relate in same way to E, then to whom F is related in
same way?
• (a) H (b) A (c) C (d) D (e) G
• 20. Who among the following is standing in exact middle of the girls who are at the 1st position from right &
2nd position from left?
• (a) F (b) B (c) E (d) D (e) A

16. • General solution - A, B, C, D, E, F, G and H are
8 girls who are standing in a straight line
(facing north). There are 8 positions which can
be shown from left to right.
• The tabular arrangement is as follows-
Position from left 1 2 3 4 5 6 7 8
Name

17. • Points 6, 3
• F is standing at either sixth position from the left or fourth position from the right
• So, we have 2 possible cases-
• Case 1- F is standing at 6th position from the left
• Case 2- F is standing at 4th position from the right
• We can check for both cases –
•
• Case 1- F is standing at 6th position from the left
• F is fourth to the right of A. So, A is at 2nd position.
Position from left 1 2 3 4 5 6 7 8
Name

18. • Points 6, 3
• F is standing at either sixth position from the left or fourth position from the right
• So, we have 2 possible cases-
• Case 1- F is standing at 6th position from the left
• Case 2- F is standing at 4th position from the right
• We can check for both cases –
•
• Case 1- F is standing at 6th position from the left
• F is fourth to the right of A.
• So, A is at 2nd position.
Position from left 1 2 3 4 5 6 7 8
Name A F

19. Approach 1
• Points 2,1,4,5 (points 6 and 3 are used)
• C and F are not at adjacent positions
• So, C is neither at 5th nor at 7th position
• Only one girl is sitting between E and G. It is also known that G is not standing at any of the extreme
positions
• Neither B nor E is standing in any of extreme positions. Further it is known that both are immediate
neighbours of each other
• C is second to left of D
• The linear arrangement of case 1 (by looking at all possibilities) can be modified as-
Position from left 1 2 3 4 5 6 7 8
Name A F

20. Approach 2
• Points 2,1 (points 6 and 3 are used)
• C and F are not at adjacent positions
• So, C is neither at 5th nor at 7th position
• Only one girl is sitting between E and G. It is also known that G is not standing at any of the extreme
positions
• Only one girl is sitting between E and G. So, the 3 consecutive positions are obtained by E,G and the girl
between E and G. It is like E/G – X – G/E (X is girl between E and G)
• The possibilities for these 3 consecutive positions are –
• 1. 1st , 2nd and 3rd (with A between E and G)
• 2. 3rd , 4th and 5th
• 3. 5th, 6th and 7th (with F between E and G)
• It is also known that G is not standing at any of the extreme positions.
• The linear arrangement of case 1 can be modified as-
Position from left 1 2 3 4 5 6 7 8
Name A F

21. • Points 2,1 (points 6 and 3 are used)
• C and F are not at adjacent positions
• So, C is neither at 5th nor at 7th position
• Only one girl is sitting between E and G. It is also known that G is not standing at any of the extreme
positions
• Only one girl is sitting between E and G. So, the 3 consecutive positions are obtained by E,G and the girl
between E and G. It is like E/G – X – G/E (X is girl between E and G)
• The possibilities for these 3 consecutive positions are –
• 1. 1st , 2nd and 3rd (with A between E and G)
• 2. 3rd , 4th and 5th
• 3. 5th, 6th and 7th (with F between E and G)
• It is also known that G is not standing at any of the extreme positions.
• The linear arrangement of case 1 can be modified as-
Position from left 1 2 3 4 5 6 7 8
Name xG A xC F xC xG

22. • Point 4 [points 6, 3, 2 and 1(partially) are used]
• Neither B nor E is standing in any of extreme positions. Further it is known that both are immediate
neighbours of each other
• Neither B nor E is standing in any of extreme positions
B and E are immediate neighbours of each other.
The possibilities for E are-
1. E at position 3 (with B ang G at positions 4 and 5 respectively)
2. E at position 5 (with B ang G at positions 4 and 3/7 respectively)
(E cannot be at position 4 or 7. Why?)
So, B is at potion 4 and E is either at 3rd or 5th position
The linear arrangement of case 1 can be modified as-
Position from left 1 2 3 4 5 6 7 8
Name xG A xC F xC xG

23. • Point 4 [points 6, 3, 2 and 1(partially) are used]
• Neither B nor E is standing in any of extreme positions. Further it is known that both are immediate
neighbours of each other
• Neither B nor E is standing in any of extreme positions
B and E are immediate neighbours of each other.
The possibilities for E are-
1. E at position 3 (with B ang G at positions 4 and 5 respectively)
2. E at position 5 (with B ang G at positions 4 and 3/7 respectively)
(E cannot be at position 4 or 7. Why?)
So, B is at potion 4 and E is either at 3rd or 5th position
The linear arrangement of case 1 can be modified as-
Position from left 1 2 3 4 5 6 7 8
Name xG
xB
xE
A B xC F xC xG
xB
xE

24. • Point 5 [points 6, 3, 2, 4 and 1(partially) are used]
C is second to left of D
The only possibility for C and D is -C at position 1 and D at 3 (with E at 5 and G at 7)
(why cant be C at 3?)
Position from left 1 2 3 4 5 6 7 8
Name xG
xB
xE
A B xC F xC xG
xB
xE

25. • Point 5 [points 6, 3, 2, 4 and 1 are used]
C is second to left of D
The only possibility for C and D is -C at position 1 and D at 3 (with E at 5 and G at 7)
(why can't be C at 3?)
Position from left 1 2 3 4 5 6 7 8
Name C A D B E F G H

26. • Case 2- F is standing at 4th position from the right
• F is fourth to the right of A. So, A is at 1st position.
Position from left 1 2 3 4 5 6 7 8
Name A F

27. • Now, B, E and G are not at extreme position. So, B, E or G is not at 8th position. So, we have
now 3 options for 8th position- C, D & H. C is second to left of D. So, C cannot be at 8th
position. If D is at 8th position, C will be at 6th position. But, C and F are not adjacent. So, D is
not at 8th position. So, H must be at 8th position.
• C and F are not at adjacent positions
• The linear arrangement in case 2 can be modified as-
Position from left 1 2 3 4 5 6 7 8
Name A xC F xC H

28. • C is second to left of D
• So, there are 2 possibilities-
• 1. C and D at positions 2 and 4 respectively
• 2. C and D at positions 4 and 6 respectively. But it is not possible.
• So, C and D are at 2nd and 4th positions respectively.
• The linear arrangement in case 2 can be modified as-
Position from left 1 2 3 4 5 6 7 8
Name A C D F xC H

29. • Only one girl is sitting between E and G. So, there must be gap of 1 position between
positions of E and G. But, there Is no such possibility in linear arrangement in case 2
• So, this is not feasible arrangement
Position from left 1 2 3 4 5 6 7 8
Name A C D F xC H

30. So, the final arrangement is as we obtained in case 1 which is shown below-
• 16. B is 2nd to the right of A. Hence option (e) is the answer
• 17. C and H are standing at the extreme positions. Hence option (e) is the answer
• 18. Three girls are standing between C and E. Hence option (c) is the answer
• 19. A is 2nd to the left of B and D is 2nd to the left of E. In a similar way F is 2nd to the left of H.
Hence option (a) is the answer
• 20. E is standing in exact middle of the girls who are at the 1st position from right & 2nd position
from left. Hence option (c) is the answer
Position from left 1 2 3 4 5 6 7 8
Name C A D B E F G H