CSAT Solved Papers/ 2024/Q57

2024 CSAT — Q57

Quant Logical & quantitative reasoning 2.5 marks Easy

A person walks $100$ m Westward, then turns left and walks $100$ m. He then takes $225^\circ$ turn clockwise. In which direction is he walking now?

A South-West
B South-East
C North-West
D North-East Answer

Worked rationale

This is a heading-only problem — the distances are decoys. Track the facing direction as a clockwise bearing (North $=0^\circ$ , East $=90^\circ$ , South $=180^\circ$ , West $=270^\circ$ ).

He walks West, so his heading is $270^\circ$ .
He turns left. Facing West, the left hand points South, so he is now facing South ( $180^\circ$ ).
He turns $225^\circ$ clockwise: $180^\circ + 225^\circ = 405^\circ \equiv 45^\circ \pmod{360^\circ}$ .

A bearing of $45^\circ$ is North-East.

Answer: (d) North-East.

Visual solution

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

Hand-drawn worked solution for UPSC 2024 CSAT Q57 — Logical & quantitative reasoning — Tap the drawing to open it full size for the fine detail.

Why the other options miss

A

solved the wrong question: treats the $225^\circ$ turn as anticlockwise, sending the heading to $180^\circ - 225^\circ \equiv -45^\circ \equiv 315^\circ$ (North-West direction) or mis-signs it into the South-West quadrant.
B

an arithmetic slip: adds only $135^\circ$ (the supplement of $225^\circ$ ) to South, reaching $315^\circ$ / $135^\circ$ and mislabelling it South-East.
C

takes the turn from the wrong reference heading: turns left correctly to South but then takes the turn from West ( $270^\circ$ ) instead of South, giving $270^\circ + 225^\circ = 135^\circ$ mis-read, or applies the $225^\circ$ to the wrong reference heading.

Specialist insight

The only two steps that carry marks are: (i) a left turn while facing West lands you facing South, and (ii) bearing arithmetic mod $360^\circ$ . Converting ” $225^\circ$ clockwise” into ” $+225^\circ$ on the bearing” removes every chance of a sign error — $180 + 225 = 405 \equiv 45^\circ$ . The $100$ m legs never enter the answer; recognising that early saves the time a candidate would waste drawing a scaled path.

The trap, in one line

Carry the facing direction as a clockwise bearing: West $\to$ left $=$ South $(180^\circ)$ , $+225^\circ = 405^\circ \equiv 45^\circ =$ North-East $(d)$ ; the distances are decoys.

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