UPSC Prelims 2017 · CSAT
Question 75: Basic Numeracy
Two walls and a ceiling of a room meet at right angles at a point P. A fly is in the air 1 m from one wall, 8 m from the other wall and 9 m from the point P. How many meters is the fly from the ceiling?
AnswerUPSC’s answer is (a).
Treat the corner P, where two walls and the ceiling meet, as the origin of three perpendicular axes. The fly's distances from the three surfaces are its coordinates, and its distance from P is the square root of the sum of their squares: 1² + 8² + h² = 9². So 1 + 64 + h² = 81, h² = 16, and h = 4 m from the ceiling. This is the three-dimensional Pythagoras rule.
How you could have got this
No shortcut here: in a “how many” question, ruling out options doesn’t help. Every statement has to be judged.
Which options go is worked out from UPSC’s key and the options, not by a model.
Why each option is right or wrong
- (a) Correct: h² = 81 - 65 = 16, so h = 4.
- (b) 6 gives 1 + 64 + 36 = 101, not 81.
- (c) 12 gives a distance from P far above 9.
- (d) 15 gives a distance from P far above 9.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2017, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.