Question

Seven people, G, H, I, J, K, L and M, are sitting in a row, facing north(but not necessarily in the same order). No one sits to the right of M. Only three people sit between M and K. Only two people sit between K and H. G sits third to the left of L. J sits to the immediate right of L. How many people sit between I and H?

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

Answer 1

Answer:

C. Three

Let's solve this step by step carefully.

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Step 1: List of people

People: G, H, I, J, K, L, M
They are sitting in a row facing north.

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Step 2: Analyze clues

1. No one sits to the right of M → M sits at the extreme right.

   • Row (left → right): _ _ _ _ _ _ M

2. Only three people sit between M and K

   • So K is 4th from the right.

   • Row positions (from left to right, 7 positions): _ _ K _ _ _ M

3. Only two people sit between K and H

   • So H is either 2 seats to the left or 2 seats to the right of K

   • K is 3rd position from left (if M is 7th), positions: 1 2 3 4 5 6 7

     • Let's assign positions: M = 7, K = 3 (since 3 people between K and M: positions 3 and 7 → 4 people? Let's calculate carefully).

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Step 3: Find K's position

• 3 people sit between M and K → There are 3 seats between them.

• M = 7 (rightmost) → 3 people between M and K → K = 3

Check:
Positions between K (3) and M (7) → positions 4,5,6 → 3 people Correct.

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Step 4: H's position

• 2 people sit between K and H

• K = 3 → H can be:

  • Left: position 0 (no seat)

  • Right: position 6

• So H = 6

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Step 5: G, L, J clues

• G sits third to the left of L → G = L − 3

• J sits immediate right of L → J = L + 1

We have positions 1 2 3 4 5 6 7 filled as:

• 3 → K

• 6 → H

• 7 → M

Positions left: 1,2,4,5

• We need L, G, J, I for these positions

• Let’s try possibilities:

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Step 6: Place L, G, J

• G = L − 3 → So L must be position ≥ 4 (otherwise G would be negative)

• Positions available: 1,2,4,5

• Test L = 4 → G = 1

• Then J = L +1 = 5

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Step 7: Remaining person I

• Remaining position: 2 → I = 2

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Step 8: Final arrangement

Position (left → right)	1	2	3	4	5	6	7
Person	G	I	K	L	J	H	M

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Step 9: Find how many people sit between I and H

• I = 2

• H = 6

• People between positions 2 and 6 → positions 3,4,5 → K, L, J → 3 people

3 people sit between I and H.