UPSC Prelims 2020 · CSAT
Question 73: Basic Numeracy
Consider the following statements :
- 1.The minimum number of points of intersection of a square and a circle is 2.
- 2.The maximum number of points of intersection of a square and a circle is 8.
Which of the above statements is/are correct?
AnswerUPSC’s answer is (b).
Statement 1 is wrong: a circle can sit wholly inside a square or wholly outside it, touching nothing, so the minimum number of intersection points is 0. Statement 2 is right: a circle can cross each of the four sides twice, giving 4 × 2 = 8 points, and a line meets a circle in at most 2 points.
- 1. A circle inside or outside the square meets it at no point.
- 2. Each of the four sides can meet the circle at two points, giving eight.
How you could have got this
- If you were sure statement 1 is not correct, (a) and (c) go: each of them includes 1.
What you needed to know: A circle inside or outside the square meets it at no point.
- Then, if you were sure statement 2 is correct, (d) goes: it leaves 2 out.
What you needed to know: Each of the four sides can meet the circle at two points, giving eight.
Only (b) is left. This one needs every statement.
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) 1 is false: the minimum is 0, not 2.
- (b) Right: only 2 is correct.
- (c) 1 is false, so both cannot be correct.
- (d) 2 is true: eight crossings are possible.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2020, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.