https://www.gregmat.com/problems/quant?problem=the-angle-between-the-line
The problem says the angle increases by 30° while the starting position stays at the origin, but the endpoint changes to (c, d). The length isn’t stated to stay the same, so the answer depends on that.
Case 1: the length stays the same (call it r).
- A = a + b = r(cos 30° + sin 30°) = r(0.866 + 0.5) = 1.366r
- B = c + d = r(cos 60° + sin 60°) = r(0.5 + 0.866) = 1.366r
The two quantities are equal.
Case 2: the length changes.
The new segment could be any length. If it is much longer, B is larger. If it is much shorter, A is larger.
Since the problem never says the length is preserved, the relationship can’t be determined from the information given.
Answer: D (the relationship cannot be determined from the information given).
If the problem had said the segment is rotated, or that its length is unchanged, the answer would be C (equal), because cos 30° + sin 30° = cos 60° + sin 60°. The wording “the angle is increased” only describes the angle, not the length, which is the trap here.