Question:
Four hills H1, H2, H3, and H4 are present in an area. The following observations are made about them:
i. Neither H2 nor H3 is the easternmost hill.
ii. Neither H2 nor H3 is the westernmost hill.
iii. Neither the easternmost hill nor the westernmost hill is the southernmost hill.
iv. Two hills are located to the west of H2.
v. The southernmost hill has at least two hills to its east.
The southernmost hill is .
Four hills H1, H2, H3, and H4 are present in an area. The following observations are made about them:
i. Neither H2 nor H3 is the easternmost hill.
ii. Neither H2 nor H3 is the westernmost hill.
iii. Neither the easternmost hill nor the westernmost hill is the southernmost hill.
iv. Two hills are located to the west of H2.
v. The southernmost hill has at least two hills to its east.
The southernmost hill is .
i. Neither H2 nor H3 is the easternmost hill.
ii. Neither H2 nor H3 is the westernmost hill.
iii. Neither the easternmost hill nor the westernmost hill is the southernmost hill.
iv. Two hills are located to the west of H2.
v. The southernmost hill has at least two hills to its east.
The southernmost hill is .
Show Hint
First fix the east-west order using clues (i), (ii) and (iv) alone, which pins H2 to the third position and H3 to the second; then use clue (v) to see which of the two middle hills can have at least two hills to its east.
Updated On: Aug 10, 2026
- H1
- H2
- H3
- H4
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Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Fix the east-west order using clues (i), (ii) and (iv).
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 also not H2 and not H3, so it must also be H1 or H4. Since one hill cannot be both extremes, H1 and H4 occupy the two extreme positions between themselves, leaving H2 and H3 to occupy the two middle positions.
Step 2: Pin down H2 and H3.
Clue (iv) says two hills are located to the west of H2, which fixes H2 exactly at the third position counting from the west. Since the two middle positions belong to H2 and H3, and H2 occupies the third position, H3 must occupy the second position from the west.
Step 3: Write the full order.
West to east: (H1 or H4) - H3 - H2 - (the other of H1 or H4).
Step 4: Apply clue (iii).
The southernmost hill cannot be whichever hill is easternmost or westernmost, so it must be H2 or H3.
Step 5: Apply clue (v).
The southernmost hill needs at least two hills to its east. If H2, at the third position, were southernmost, only the single easternmost hill would lie to its east, just one hill, failing clue (v). If H3, at the second position, is southernmost, then both H2 and the easternmost hill lie to its east, exactly two hills, satisfying clue (v).
Step 6: Conclude.
Only H3 satisfies every clue simultaneously.\[ \boxed{\text{H3}} \]
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 also not H2 and not H3, so it must also be H1 or H4. Since one hill cannot be both extremes, H1 and H4 occupy the two extreme positions between themselves, leaving H2 and H3 to occupy the two middle positions.
Step 2: Pin down H2 and H3.
Clue (iv) says two hills are located to the west of H2, which fixes H2 exactly at the third position counting from the west. Since the two middle positions belong to H2 and H3, and H2 occupies the third position, H3 must occupy the second position from the west.
Step 3: Write the full order.
West to east: (H1 or H4) - H3 - H2 - (the other of H1 or H4).
Step 4: Apply clue (iii).
The southernmost hill cannot be whichever hill is easternmost or westernmost, so it must be H2 or H3.
Step 5: Apply clue (v).
The southernmost hill needs at least two hills to its east. If H2, at the third position, were southernmost, only the single easternmost hill would lie to its east, just one hill, failing clue (v). If H3, at the second position, is southernmost, then both H2 and the easternmost hill lie to its east, exactly two hills, satisfying clue (v).
Step 6: Conclude.
Only H3 satisfies every clue simultaneously.\[ \boxed{\text{H3}} \]
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