UPSC Prelims 2014 · CSAT
Question 22: Basic Numeracy
A straight line segment is 36 cm long. Points are to be marked on the line from both the end points. From each end, the first point is at a distance of 1 cm from the end, the second point is at a distance of 2 cm from the first point and the third point is at a distance of 3 cm from the second point and so on. If the points on the ends are not counted and the common points are counted as one, what is the number of points ?
AnswerUPSC’s answer is (b).
From the left end the marked points are at 1, 3, 6, 10, 15, 21 and 28 cm (gaps of 1, 2, 3 and so on). The next, 36 cm, is the far end, which is not counted. From the right end the points are at 35, 33, 30, 26, 21, 15 and 8 cm. Positions 15 and 21 appear in both lists. So the count is 7 + 7 - 2 = 12.
Why each option is right or wrong
- (a) 10 undercounts: each end gives 7 points and only 2 are shared.
- (b) Right. 7 + 7 - 2 shared points = 12.
- (c) 14 forgets that the points at 15 cm and 21 cm are common to both sets.
- (d) 16 overcounts; the end points are excluded and shared points count once.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2014, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.