M1, M2, M3, M4 and M5 are five men sitting in a line facing towards the south. L1, L2, L3, L4 and L5 are five women sitting in a second line, parallel to the first line, facing towards the north. M2, who is to the immediate left of M4, is opposite L5. M3 and L2 are diagonally opposite each other. M5 is opposite L3, who is to the immediate right of L1. L4, who is to the immediate right of L3, is opposite M4. L1 is at one end of the line. Which of the following pair is diagonally opposite each other?
Seating Arrangement Setup
There are two parallel lines of five people each. Five men (M1-M5) face South, and five women (L1-L5) face North. We need to determine the arrangement based on the given clues to find a diagonally opposite pair.
Step-by-Step Deduction
Let's denote the positions in each line from 1 to 5, from left to right for the North-facing line.
- Clue 1: $L1$ is at one end. Assume $L1$ is at Position 1 (North).
- Clue 2: $L3$ is to the immediate right of $L1$ (facing North). So, $L3$ is at North, Position 2.
- Clue 3: $M5$ is opposite $L3$. So, $M5$ is at South, Position 2.
- Clue 4: $L4$ is to the immediate right of $L3$ (facing North). So, $L4$ is at North, Position 3.
- Clue 5: $M4$ is opposite $L4$. So, $M4$ is at South, Position 3.
- Clue 6: $M2$ is to the immediate left of $M4$ (facing South). Facing South, left is towards the higher position number. So, $M2$ is at South, Position 4.
- Clue 7: $L5$ is opposite $M2$. So, $L5$ is at North, Position 4.
- Clue 8: $M3$ and $L2$ are diagonally opposite each other. The remaining North position is 5, so $L2$ is at North, Position 5. For $M3$ to be diagonally opposite $L2$ (North, Pos 5), $M3$ must be at South, Pos 1 (considering opposite corners).
- The remaining person $M1$ must be at the last South position, South, Position 5.
Final Seating Arrangement
The arrangement based on the deductions is:
| Position | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| North Line (Facing North) | L1 | L3 | L4 | L5 | L2 |
| South Line (Facing South) | M3 | M5 | M4 | M2 | M1 |
Identifying Diagonally Opposite Pairs
Opposite pairs (same column): (L1, M3), (L3, M5), (L4, M4), (L5, M2), (L2, M1).
Diagonally opposite pairs are typically formed by connecting corners or adjacent positions across rows. Based on the arrangement and the clue "$M3$ and $L2$ are diagonally opposite":
- $L2$ is at North, Position 5.
- $M3$ is at South, Position 1.
- These are diagonally opposite (corner positions).
- Similarly, $L1$ is at North, Position 1 and $M1$ is at South, Position 5. They are also diagonally opposite (corner positions).
Let's check the options:
- M5 and L3 are opposite.
- M1 and L2 are opposite.
- M3 and L1 are opposite.
- M1 and L1 are diagonally opposite.
Therefore, the pair $M1$ and $L1$ is diagonally opposite each other.
Important Questions from Double Lineup
A, B, C, D, E, F and G are seven coaches. Each one among them is a coach of a different game. The games are Hockey, Cricket, Badminton, Tennis, Volleyball, Basketball and Football (not necessarily in the same order). Each of them trains on one of the seven days of the week from Monday to Sunday (not necessarily in the same order). No two coaches train on the same day of the week. C trains Badminton on Friday. B teaches Volleyball on the previous day of the day on which a coach trains Hockey. G trains on Sunday but does not train Cricket or Tennis. D trains Basketball on the previous day of the day on which F trains. A trains Football on Tuesday. E does not train Tennis. On which day does F train?
Five students A, B, C, D and E attend five different schools S1, S2, S3, S4 and S5 (not necessarily in the same order). Each also likes a different subject namely D1, D2, D3, D4 and D5 (not necessarily in the same order). A goes to S5 but does not like D3. C likes D4. The one who goes to S1 likes D5. D goes to S3. E does not like D5. The one who goes to S2 likes D1.
Which of the following statement is correct?
I. B likes D5.
II. C goes to S4.
P, Q, R, S, T, V and W are seven members of the family. There are three female members. Each of them has a difference profession-Lawyer, Chartered Accountant (CA), Engineer, Teacher, Doctor, Architect and Pharmacist. No Lady is either a pharmacist or a chartered Accountant. Each of them has a different monthly income. The chartered accountant earns the most. S, the engineer, earns less than V, the doctor. R, the teacher, earns more than P and less than S. W’s wife earns the least. T is an unmarried lady Lawyer and she earns less than P and more than only Q. The pharmacist’s income is not the lowest
Who earns the least?
Which colour does the Teacher like?
A. Blue
B. Brown
C. Purple
D. Green
Who is the Principal?
A. Daisy
B. Andy
C. Mary
D. Lily
