UPSC Prelims 2023 · CSAT
Question 30: Basic Numeracy
ABCD is a square. One point on each of AB and CD; and two distinct points on each of BC and DA are chosen. How many distinct triangles can be drawn using any three points as vertices out of these six points ?
AnswerUPSC’s answer is (c).
There are 1 + 1 + 2 + 2 = 6 points. Any three of them form a triangle unless they are collinear. A straight line meets a square's boundary in at most two points unless it runs along a side, and no side holds more than two of the chosen points, so no three are collinear. Number of triangles = 6C3 = 20.
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) Wrong: 6C3 = 20 and nothing needs removing.
- (b) Wrong: 6C3 = 20 and nothing needs removing.
- (c) Right: 6C3 = 20 with no three points collinear.
- (d) Wrong: more than 6C3 = 20, the most possible.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2023, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.