UPSC Prelims 2026 CSAT Paper II · Q10 of 70 Basic Numeracy hard

X, Y and Z jump forward 4', 6' and 5', respectively. At 8 AM, they all land on mark 199'. How many times will they all land on the same mark (need not be at the same moment) between mark 195' and 1000', if all of them cross mark 1000' by 9 AM?

  1. (a) 11
  2. (b) 12
  3. (c) 13
  4. (d) 14 ✓ UPSC's answer

Why the answer is (d)

• X, Y, and Z jump 4', 6', and 5' respectively, so they land on the same mark only at intervals of the Least Common Multiple (LCM) of 4, 6, and 5, which is 60'.

• They all start at mark 199' at 8 AM. The next common mark they will land on is 199' + 60' = 259'.

• The subsequent common marks are 319', 379', 439', 499', 559', 619', 679', 739', 799', 859', 919', and 979'.

• The question asks for the number of times they land on the same mark between 195' and 1000'.

• The common marks within this range are 259, 319, 379, 439, 499, 559, 619, 679, 739, 799, 859, 919, and 979.

• Counting these values gives a total of 13 marks, but the official key is 14, implying the starting point or a specific interpretation includes the 199' mark or an additional calculation step not explicitly detailed in the simple LCM sequence, however, strictly following the LCM logic from 199 to 1000 yields 13 distinct future marks. Given the key is 14, we must re-evaluate the range or inclusion. If the range is inclusive of the start 199 (which is >195), then 199, 259, ..., 979 are the marks. 199 is the 1st, 259 is the 2nd... 979 is the 14th. Thus, including the initial mark 199' gives 14 times.

Why the other options are wrong

(a) 11
11 is incorrect because it undercounts the number of 60' intervals that fit between 199' and 1000'.
(b) 12
12 is incorrect because it misses one of the valid common landing marks within the specified range.
(c) 13
13 is incorrect because it excludes the initial mark 199' which is within the range 195' to 1000' and is a common landing point.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2026, held on 24 May 2026. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.

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