UPSC Prelims 2018 · CSAT
Question 60: Basic Numeracy
Twelve equal squares are placed to fit in a rectangle of diagonal 5 cm. There are three rows containing four squares each. No gaps are left between adjacent squares. What is the area of each square?
AnswerUPSC’s answer is (c).
Three rows of four squares form a rectangle four squares long and three squares high. If each square has side s, the rectangle is 4s by 3s, and its diagonal is √(16s² + 9s²) = 5s. The diagonal is 5 cm, so s = 1 cm and each square has an area of 1 sq cm. The 3-4-5 right triangle is the shortcut to recognise.
Why each option is right or wrong
- (a) Diagonal² = 25s², and with s² = 5/7 it is 125/7, not 25.
- (b) With s² = 7/5, the diagonal² would be 35, not 25.
- (c) Correct: 5s = 5 gives s = 1 and area 1 sq cm.
- (d) With s² = 25/12, the diagonal² would be 625/12, not 25.
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.