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 ?
- (a) 10
- (b) 12 ✓ UPSC's answer
- (c) 14
- (d) 16
Why the answer is (b)
• From the left end, the marked interior points are at 1, 3, 6, 10, 15, 21 and 28 cm, giving 7 points.
• From the right end, the marked interior points are at 35, 33, 30, 26, 21, 15 and 8 cm, giving 7 points.
• The common points are at 15 cm and 21 cm, so they must be counted only once.
• Therefore the total number of distinct points is 7 + 7 - 2 = 12, which is option (b).
Why the other options are wrong
- (a) 10
- 10 is wrong because the two sets have 7 interior points each and only 2 common points, so the total is 12, not 10.
- (c) 14
- 14 is wrong because it adds the 7 left-end points and 7 right-end points without subtracting the 2 common points at 15 cm and 21 cm.
- (d) 16
- 16 is wrong because it uses 8 points from each end, but the end points are not counted and the 2 common points must be counted once.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2014, held on 24 August 2014. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.