2017 CSAT, all questions
UPSC Prelims 2017 · CSAT
Question 38: Basic Numeracy
There are 4 horizontal and 4 vertical lines, parallel and equidistant to one another on a board. What is the maximum number of rectangles and squares that can be formed?
a16
b24
c36
d42
AnswerUPSC’s answer is (c).
Four horizontal and four vertical lines form a 3 x 3 grid of small squares. Any rectangle, a square included, is fixed by choosing 2 of the 4 horizontal lines and 2 of the 4 vertical lines. That is C(4,2) x C(4,2) = 6 x 6 = 36. Remember the shortcut: with m lines one way and n lines the other, the count is C(m,2) x C(n,2).
Why each option is right or wrong
- (a) 16 is only 4 x 4, the number of intersection points.
- (b) 24 does not arise from choosing lines.
- (c) Correct: 6 pairs of horizontal lines x 6 pairs of vertical lines = 36.
- (d) 42 is more than the 36 possible rectangles.
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.