How many such 5's are there in the following number sequence, each of which is immediately preceded by 3 or 4 but not immediately followed by 8 or 9?

3 5 9 5 4 5 5 3 5 8 4 5 6 7 3 5 7 5 5 4 5 2 3 5 1 0

Five

The correct answer is Option (3) → Five

We examine each 5 in the sequence and apply the conditions:

Condition:

• Immediately preceded by 3 or 4, and
• Not immediately followed by 8 or 9

Sequence:
3 5 9 5 4 5 5 3 5 8 4 5 6 7 3 5 7 5 5 4 5 2 3 5 1 0

Valid 5’s:

• 4 5 5 → preceded by 4, followed by 5
• 4 5 6 → preceded by 4, followed by 6
• 3 5 7 → preceded by 3, followed by 7
• 4 5 2 → preceded by 4, followed by 2
• 3 5 1 → preceded by 3, followed by 1

Invalid cases:

• 3 5 9 → followed by 9
• 3 5 8 → followed by 8
• Other 5’s not preceded by 3 or 4

Total valid 5’s = 5