UPSC Prelims 2021 · CSAT

Question 20: Logical Reasoning and Mental Ability

A woman runs 12 km towards her North, then 6 km towards her South and then 8 km towards her East. In which direction is she from her starting point ?

aAn angle less than 45° South of East

bAn angle less than 45° North of East

cAn angle more than 45° South of East

dAn angle more than 45° North of East

AnswerUPSC’s answer is (b).

Net north-south movement is 12 − 6 = 6 km north. She also went 8 km east. So she is 6 km north and 8 km east of the start. The angle north of east has tan θ = 6/8 = 0.75, which is less than 1, the value for 45°, so the angle is less than 45°, about 37°. She is at an angle less than 45° north of east. Remember: reduce the movements to a net (east, north) pair and compare the two numbers; equal means exactly 45°.

Why each option is right or wrong

(a) She is north of her start, not south: the net north-south movement is 6 km north.
(b) Right: 6 km north and 8 km east gives tan θ = 0.75, about 37° north of east.
(c) Wrong side, since she is north of the start, and the angle would also be too large.
(d) North is right, but the angle exceeds 45° only if she went further north than east; 6 is less than 8.

Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.

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Source: UPSC, Civil Services (Preliminary) Examination 2021, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.