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?

The correct answer is 6 (which corresponds to Option 6).

Step-by-Step Explanation:

We are given 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

We need to count how many odd numbers are immediately followed by another odd number in this sequence (i.e., patterns of the form: Odd → Odd).

Let's examine the sequence step-by-step and check each pair of adjacent numbers:

1. 5 → 1: Both 5 and 1 are odd. This is an odd number followed by an odd number. (Count = 1)

2. 1 → 4: 4 is even (Not applicable).

3. 4 → 7: 4 is even (Not applicable).

4. 7 → 3: Both 7 and 3 are odd. (Count = 2)

5. 3 → 9: Both 3 and 9 are odd. (Count = 3)

6. 9 → 8: 8 is even (Not applicable).

7. 8 → 5: 8 is even (Not applicable).

8. 5 → 7: Both 5 and 7 are odd. (Count = 4)

9. 7 → 2: 2 is even (Not applicable).

10. 2 → 6: 2 is even (Not applicable).

11. 6 → 3: 6 is even (Not applicable).

12. 3 → 1: Both 3 and 1 are odd. (Count = 5)

13. 1 → 5: Both 1 and 5 are odd. (Count = 6)

14. 5 → 8: 8 is even (Not applicable).

15. 8 → 6: 8 is even (Not applicable).

16. 6 → 3: 6 is even (Not applicable).

17. 3 → 8: 8 is even (Not applicable).

18. 8 → 5: 8 is even (Not applicable).

19. 5 → 2: 2 is even (Not applicable).

20. 2 → 2: Even numbers (Not applicable).

21. 2 → 4: Even numbers (Not applicable).

22. 4 → 3: 4 is even (Not applicable).

23. 3 → 4: 4 is even (Not applicable).

24. 4 → 9: 4 is even (Not applicable).

25. 9 → 6: 6 is even (Not applicable).

The pairs of odd numbers followed by an odd number are:

1. (5, 1)
2. (7, 3)
3. (3, 9)
4. (5, 7)
5. (3, 1)
6. (1, 5)

Thus, there are total 6 odd numbers followed by another odd number in the sequence.