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

Instead of building the full order first, check each option (each hill as a candidate for southernmost) against all five clues and see which one survives.

1. H1 as southernmost: from clues (i) and (ii), only H1 and H4 can be the easternmost or the westernmost hill. If H1 were the southernmost hill, clue (iii) says the southernmost hill cannot be the easternmost or the westernmost hill. But H1 is forced to be one of those two extremes, since H2 and H3 are barred from both ends, so H1 cannot be the southernmost hill. Ruled out.
2. H2 as southernmost: clue (iv) tells us two hills sit west of H2, which places H2 third in the west-to-east line of four hills, one spot before the easternmost end. If H2 is the southernmost hill, clue (v) needs at least two hills east of it, but only one position, the fourth easternmost slot, lies east of position 3. That is only one hill, not two. Ruled out.
3. H3 as southernmost: since H1 and H4 occupy the two extreme positions and H2 sits at position 3 (from clue iv), H3 is pushed into position 2. Clue (iii) is fine since H3 is not an extreme hill. Clue (v) needs at least two hills to the east of H3, and positions 3 and 4 (H2 and the extreme hill there) both lie east of position 2, that is two hills. This fits every clue.
4. H4 as southernmost: the same reasoning as H1 applies. H4 is forced into one of the two extreme positions, since H2 and H3 cannot occupy the extremes, so clue (iii) directly rules H4 out as the southernmost hill.

Only the H3 case satisfies clues (i) through (v) together, without any contradiction.

Let's summarize:

• Clues (i) and (ii) force H1 and H4 into the two extreme, easternmost and westernmost, spots, leaving H2 and H3 in the middle.
• Clue (iv) fixes H2 at the third position from the west, which pushes H3 to the second position.
• Clue (v) then singles out H3, since H2 in that spot would leave only one hill to its east instead of the required two.

The southernmost hill is H3, option (C).