Question

Seven people, L, M, N, O, W, X and Y, are sitting in a row, facing north (but not necessarily in the same order). No one sits to the right of N. Only three people sit between N and X. Only two people sit between X and W. M sits third to the left of L. Y sits to the immediate right of L. How many people sit between O and W?

• A. Two
• B. Three
• C. One
• D. Four

Answer 1

Answer:

B. Three

Let’s build the arrangement step by step.

Position of N and X

• No one sits to the right of N ⇒ N is at the extreme right (position 7 if left to right is 1–7).

• Only three people sit between N and X ⇒ distance is 4 seats.

So X must be at position:

• N = 7 ⇒ X = 3

  Position of W

• Only two people sit between X and W ⇒ distance is 3 seats.

So W can be:

• X = 3 ⇒ W = 6 or W = 0 (invalid)

So:

• W = 6

  Place remaining seats

We now have:
1 2 3 X 4 5 6 W 7 N

Remaining: L, M, O, Y

Use L and Y condition

• Y sits immediate right of L (facing north, right = increasing position)

Try pairs:

• (L, Y) = (1,2) or (2,3) or (4,5) or (5,6)

But 3 is X, 6 is W → blocked pairs:

• (4,5) works best

So:

• L = 4

• Y = 5

  Remaining positions

Now:
1 2 3 X 4 L 5 Y 6 W 7 N

Remaining M and O go in 1 and 2.

• M is third to left of L (L=4 ⇒ M=1)

So:

• M = 1

• O = 2

  Final arrangement:

1 M
2 O
3 X
4 L
5 Y
6 W
7 N

Distance between O and W

• O = position 2

• W = position 6

People between them: 3, 4, 5 → 3 people

Final Answer:

$\boxed{3}$