CA Foundation · Quantitative Aptitude · Direction Tests
Town X is 16 km west of town Y. Town Z is 12 km north of town Y. In which direction is X from Z, and what is the distance between X and Z?
X is south-west of Z, at a distance of 20 km. Relative to Z, town X is 12 km south and 16 km west. The straight-line distance is the square root of 144 plus 256, which equals 20 km.
- ASouth-west, 20 kmCorrect
- BSouth-east, 20 km
- CSouth-west, 28 km
- DNorth-west, 20 km
Explanation
Take Y as origin: X=(-16,0), Z=(0,12). From Z, X is 16 km west and 12 km south, so it lies south-west. Distance = sqrt(16^2+12^2) = sqrt(400) = 20 km. The 28 km option adds the legs instead of using Pythagoras.
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