Logical Reasoning

Arrangements

Hard

A, B, C, D, L, M, N and O live on eight different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it, number 2 and so on till the topmost floor is numbered 8.

L lives on the fourth floor. Sum of floor numbers of L and C is more than 10. The sum of floor numbers of D and O is 8. O does not live on an odd numbered floor. M lives on an odd numbered floor. The sum of floor numbers of M and D is more than 12. More than three people live between M and N. The sum of floor numbers of N and A is more than 5.

Which of the following is NOT TRUE based on the given information?

A lives on a floor immediately above L

Only four people live between M and O

C lives on the topmost floor

B lives on floor number 5

✅ Correct Option: 4

Step 1: Analyze Fixed Information & Basic Constraints

L is on floor 4.
O is on an even floor ( $2, 6, 8$ ).
M is on an odd floor ( $1, 3, 5, 7$ ).

Step 2: Determine positions of D, O, and M

Constraint: Sum of floors of $D + O = 8$ $D + O = 8$ .
- Since O is even ( $2, 6, 8$ ) and L is already on 4:
- If $O=8$ , then $D=0$ (Impossible).
- If $O=6$ , then $D=2$ .
- If $O=2$ , then $D=6$ .
Constraint: Sum of floors of $M + D > 12$ $M + D > 12$ .
- If $D=2$ , then $M + 2 > 12 \Rightarrow M > 10$ (Impossible).
- Therefore, D must be 6 and O must be 2.
- With $D=6$ , $M + 6 > 12 \Rightarrow M > 6$ . Since M is odd, M is on floor 7.

Step 3: Determine positions of C and N

Constraint: Sum of floors of $L + C > 10$ $L + C > 10$ .
- $L=4$ , so $4 + C > 10 \Rightarrow C > 6$ .
- Floors $>6$ are 7 and 8. Since M is on 7, C is on floor 8.
Constraint: More than 3 people live between M and N.
- M is on 7. The gap must be at least 4 floors ( $6, 5, 4, 3$ ).
- This forces N to be below floor 3. Floor 2 is O, so N is on floor 1.

Step 4: Determine positions of A and B

Constraint: Sum of floors of $N + A > 5$ $N + A > 5$ .
- $N=1$ , so $1 + A > 5 \Rightarrow A > 4$ .
- Available floors are 3 and 5. Since A must be $>4$ , A is on floor 5.
Remaining: The only empty spot is floor 3, so B is on floor 3.

Final Arrangement Table

Floor	Person
8	C
7	M
6	D
5	A
4	L
3	B
2	O
1	N

Verifying the Options

A) A lives on a floor immediately above L: True ( $5$ is above $4$ ).
B) Only four people live between M and O: True (Floors 6, 5, 4, 3 are between 7 and 2).
C) C lives on the topmost floor: True (Floor 8).
D) B lives on floor number 5: FALSE. (B lives on floor 3; A lives on floor 5).

Correct Answer: Option D

2025: Sample Paper

Ten people are sitting in two parallel rows containing 5 people each in such a way that there is equal distance between adjacent persons.

In row 1 – A, B, C, D and E are seated and all of them are facing south.

In row 2 – P, Q, R, S, and T are seated and all of them are facing north.

Thus, each person faces another person from the other row.

C sits third to the left of E. An immediate neighbour of C faces T. C sits to the right of B.
R sits third to the left of the person facing B. Only one person sits between R and P.
A faces one of the immediate neighbours of Q. Q does not sit at any of the extreme ends.
S does not sit at any position to the right of T.

Which of the following is true based on the above information?

2025: Sample Paper

Each of P, Q, R, S, T, U and V has an exam on a different day of a week starting from Monday and ending on Sunday of the same week.

Only four people have exams between T and V. V has an exam on one of the days before T.

R does not have an exam on Friday. More than two people have exams between V and R. S has an exam immediately before U and immediately after P. More than one person has an exam between Q and S.

Which of the following when substituted in the same sequence would make the sentence correct based on the given arguments?

S has an exam on ______ while P and U have their exams on ____ and ____.

2025: Actual Paper

Ten people are sitting in two parallel rows containing 5 people each in such a way that there is equal distance between adjacent persons.

In row 1 – A, B, C, D and E are seated and all of them are facing south.

In row 2 – P,Q, R, S and T are seated and all of them are facing north.

Thus each person faces another person from the other row.

C sits at an extreme end of the row. Only two people sit between B and C. The person facing B sits to the immediate left of Q. Only one person sits between Q and P. A faces P. A sits to the immediate left of the person facing S. E sits second to the right of the person facing T.

Who faces B?

2025: Actual Paper

A, B, C, D, E, F and G each scored a different marks in an exam and all marks were integers. Only three people scored more than F. Only G scored less than B. More than three people scored between G and D. C scored less than E and no one scored between C and E. If E scored 90, F scored 84 and the second lowest score was 71, which of the following may be the possible score of A?

2025: Actual Paper

Each of P, Q, R, S, T, U and V has an exam on a different day of a week starting from Monday and ending on Sunday of the same week.

U has an exam on Thursday. Only one person has exam between P and U. T has an exam immediately after P. As many people have an exam before T as after S. Q has an exam immediately after V but not on Sunday.

How many people have an exam between R and V?

Solution

Step 1: Analyze Fixed Information & Basic Constraints

Step 2: Determine positions of D, O, and M

Step 3: Determine positions of C and N

Step 4: Determine positions of A and B

Final Arrangement Table

Verifying the Options

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