Consider the following sequence of numbers : 5 1 4 7 3 9 8 5 7 2 6 3 1 5 8 6 3 8 5 2 2 4 3 4 9 6 How many odd numbers are followed by the odd number in the above sequence?

(a) 5
(b) 6 ✓ UPSC's answer
(c) 7
(d) 8

Why the answer is (b)

• First, identify all odd numbers in the sequence: 5, 1, 7, 3, 9, 5, 7, 3, 1, 5, 3, 5, 3, 9.

• Check the number immediately following each odd number to see if it is also odd.

• In the first row: 5 is followed by 1 (odd), 1 by 4 (even), 7 by 3 (odd), 3 by 9 (odd), 9 by 8 (even), 5 by 7 (odd), 7 by 2 (even), 3 by 1 (odd), 1 by 5 (odd).

• In the second row: 3 is followed by 8 (even), 5 by 2 (even), 3 by 4 (even), 9 by 6 (even).

• The pairs where an odd number is followed by an odd number are: (5,1), (7,3), (3,9), (5,7), (3,1), and (1,5).

• Counting these instances gives a total of 6, which corresponds to option (b).

Why the other options are wrong

(a) 5: Option (a) is incorrect because it undercounts the valid pairs by missing one of the six instances where an odd number is followed by another odd number.
(c) 7: Option (c) is incorrect because it overcounts the valid pairs by including a sequence where an odd number is followed by an even number.
(d) 8: Option (d) is incorrect because it significantly overcounts the valid pairs, likely by misidentifying even numbers as odd or counting non-adjacent numbers.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2020, held on 4 October 2020. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.