Question

Four hills H1, H2, H3, and H4 are present in an area. The following observations are made about them:

1. Neither H2 nor H3 is the easternmost hill.
2. Neither H2 nor H3 is the westernmost hill.
3. Neither the easternmost hill nor the westernmost hill is the southernmost hill.
4. Two hills are located to the west of H2.
5. The southernmost hill has at least two hills to its east.

The southernmost hill is .

• A. H1
• B. H2
• C. H3
• D. H4

Hint:

Use clues (i), (ii), and (iv) first to fix the east-west order of all four hills, then apply (iii) and (v) to pick the southernmost one.

Answer 1

The Correct Option is C

Step 1: Understanding the Question.
Four hills H1, H2, H3, H4 sit in an area, and we are told several things about their east-west order and about which one is the southernmost. We need to work out which hill is the southernmost.

Step 2: Key Formula or Approach.
Treat clues (i), (ii), (iv) as fixing the east-west line-up of the four hills, since they only talk about "easternmost", "westernmost", and "west of H2". Then use clue (iii) to rule out two candidates for southernmost, and clue (v) to choose between what remains.

Step 3: Detailed Explanation.
From clue (i), the easternmost hill is not H2 and not H3, so it must be H1 or H4.
From clue (ii), the westernmost hill is not H2 and not H3 either, so it must also be H1 or H4.
Since there is exactly one easternmost hill and one westernmost hill, and both slots can only be filled by H1 or H4, the pair {H1, H4} takes the two end positions, one east end and one west end, in some order.
That leaves H2 and H3 sitting in the two middle positions of the east-west line-up.
From clue (iv), two hills lie to the west of H2. In a line-up of 4 positions numbered 1 to 4 from west to east, the only position with exactly two hills to its west is position 3. So H2 sits at position 3.
Since H2 and H3 fill the two middle spots, positions 2 and 3, and H2 is at position 3, H3 must be at position 2.
So the west-to-east order is: (H1 or H4) at position 1, H3 at position 2, H2 at position 3, (H4 or H1) at position 4.
From clue (iii), the southernmost hill is neither the easternmost nor the westernmost hill, so it is not the hill at position 1 or position 4. That rules out H1 and H4, leaving H2 or H3 as the southernmost hill.
From clue (v), the southernmost hill has at least two hills to its east. If H2 (position 3) were southernmost, only 1 hill (position 4) lies to its east, which fails the at-least-two requirement. If H3 (position 2) is southernmost, positions 3 and 4 (H2 and the position-4 hill) both lie to its east, giving exactly two hills to the east, which satisfies clue (v).

Step 4: Final Answer.
The southernmost hill is H3, which is option (C).