UPSC Prelims 2018 · CSAT
Question 58: Basic Numeracy
There are 24 equally spaced points lying on the circumference of a circle. What is the maximum number of equilateral triangles that can be drawn by taking sets of three points as the vertices?
AnswerUPSC’s answer is (c).
On a circle with 24 equally spaced points, an equilateral triangle must have its vertices equally spaced, which means 24 ÷ 3 = 8 steps apart. Starting from any of the 24 points gives a triangle, but each triangle is reached from each of its three vertices, so it is counted three times. Number of triangles = 24 ÷ 3 = 8.
Why each option is right or wrong
- (a) 4 undercounts; starting points 1 to 8 already give 8 different triangles.
- (b) 6 undercounts in the same way.
- (c) Correct: 24 starting points, each triangle counted three times, gives 8.
- (d) 12 comes from dividing by 2, as if a triangle had two vertices.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2018, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.