CSAT Solved Papers/ 2021/Q20

2021 CSAT — Q20

Quant Logical & quantitative reasoning 2.5 marks Medium

A woman runs 1212 km towards her North, then 66 km towards her South and then 88 km towards her East. In which direction is she from her starting point?

  1. A An angle less than 45° South of East
  2. B An angle less than 45° North of East Answer
  3. C An angle more than 45° South of East
  4. D An angle more than 45° North of East

Worked rationale

Net north–south: 1212 N −6- 6 S =6= 6 km North. Net east–west: 88 km East. So from the start she is at (East 8, North 6)(\text{East }8,\ \text{North }6) — in the North-East quadrant.

The bearing measured from the East axis satisfies

tan⁡θ=NorthEast=68=0.75,\tan\theta = \frac{\text{North}}{\text{East}} = \frac{6}{8} = 0.75,

so θ=arctan⁡(0.75)≈36.9∘\theta = \arctan(0.75)\approx 36.9^\circ. Since 6<86 < 8, the northward offset is smaller than the eastward one, hence θ<45∘\theta < 45^\circ, North of East.

Answer: (b) An angle less than 45° North of East.

Visual solution

The same solve, worked by hand — read it, then trace it.

Hand-drawn worked solution for UPSC 2021 CSAT Q20 — Logical & quantitative reasoning
Tap the drawing to open it full size for the fine detail.

Why the other options miss

  • A
    wrong hemisphere: gets the magnitude comparison right but ends North of the start, not South.
  • C
    wrong on both counts: wrong hemisphere and wrong angle comparison.
  • D
    ratio flipped: inverts the ratio (8/6>18/6 > 1) and concludes the angle exceeds 45∘45^\circ.

Specialist insight

You never need the actual arctangent — only whether the angle beats 45∘45^\circ, which is decided by comparing the two legs. East leg 8>8 > North leg 66, so the resultant hugs the East axis: less than 45∘45^\circ, and North because the net vertical is positive. Reducing a bearing question to “which leg is bigger, and which hemisphere” is the time-saver that dodges the calculator and the two-way hemisphere trap.

The trap, in one line

Net (8 E,6 N)(8\text{ E},6\text{ N}) with East >> North ⇒\Rightarrow less than 45∘45^\circ North of East ⇒\Rightarrow (b).

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