UPSC Prelims 2016 · CSAT
Question 50: Basic Numeracy
An agricultural field is in the form of a rectangle having length X1 meters and breadth X2 meters (X1 and X2 are variable). If X1 + X2 = 40 meters, then the area of the agricultural field will not exceed which one of the following values ?
AnswerUPSC’s answer is (a).
With X1 + X2 = 40, the area X1 x X2 is largest when the two are equal: 20 x 20 = 400 sq m. In general, for a fixed sum the product is at most the square of half the sum (AM-GM): (40 / 2)^2 = 400. So the area never exceeds 400 sq m; each lower value is exceeded by the 20 x 20 field.
Why each option is right or wrong
- (a) Right: the maximum area is 20 x 20 = 400.
- (b) 300 is exceeded, for example by 20 x 20.
- (c) 200 is exceeded.
- (d) 80 is exceeded.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2016, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.