In the sequence 1, 5, 7, 3, 5, 7, 4, 3, 5, 7, how many such 5s are there which are not immediately preceded by 3 but are immediately followed by 7?

Correct Option (1)

The problem requires identifying the number of times the digit '5' appears in the given sequence under two specific conditions:

• The digit '5' must not be immediately preceded by '3'.
• The digit '5' must be immediately followed by '7'.

Let's analyze the sequence: 1, 5, 7, 3, 5, 7, 4, 3, 5, 7.

• The first occurrence of '5' is in the segment '1, 5, 7'. Here, '5' is preceded by '1' (not '3') and followed by '7'. This instance satisfies both conditions.
• The second occurrence of '5' is in the segment '3, 5, 7'. Here, '5' is preceded by '3'. This fails the first condition (must not be immediately preceded by '3'), even though it is followed by '7'.
• The third occurrence of '5' is in the segment '3, 5, 7'. Here, '5' is preceded by '3'. This also fails the first condition, despite being followed by '7'.

Based on this analysis, only one instance of '5' in the sequence meets both specified criteria.

Incorrect Options:

Options 2, 3, and 4 are incorrect. A thorough examination of the sequence reveals that only one '5' fulfills both conditions of not being immediately preceded by '3' and being immediately followed by '7'. The other instances of '5' that are followed by '7' are also immediately preceded by '3', thereby violating one of the stated requirements.