UPSC Prelims 2018 · CSAT
Question 4: Basic Numeracy
How many diagonals can be drawn by joining the vertices of an octagon?
AnswerUPSC’s answer is (a).
An n-sided polygon has n(n - 3) ÷ 2 diagonals. For an octagon that is 8 × 5 ÷ 2 = 20. The same result comes from counting all lines between pairs of vertices, C(8,2) = 28, and removing the 8 sides, leaving 20. Each vertex can be joined to 5 non-neighbouring vertices, and halving avoids counting each diagonal twice.
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: 28 vertex pairs minus 8 sides = 20.
- (b) 24 comes from 8 × 3, which is not the formula.
- (c) 28 counts every pair of vertices, including the 8 sides.
- (d) 64 is 8 × 8, ignoring both the halving and the sides.
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.