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?

The correct option is 1.

Let's break down the step-by-step logical reasoning to find the answer:
We need to find the number of times the digit 5 appears in the given sequence such that:

1. It is immediately followed by 7.
2. It is not immediately preceded by 3.

The given sequence is:
1, 5, 7, 3, 5, 7, 4, 3, 5, 7

Let's identify all occurrences of the digit 5 in the sequence and analyze each one:

• First 5 (at index 2):
  The sequence around it is: 1, 5, 7
  - Is it immediately followed by 7? Yes (the next number is 7).
  - Is it immediately preceded by 3? No (the preceding number is 1).
  Since both conditions are met, this is a valid occurrence.


• Second 5 (at index 5):
  The sequence around it is: 3, 5, 7
  - Is it immediately followed by 7? Yes (the next number is 7).
  - Is it immediately preceded by 3? Yes (the preceding number is 3).
  Since it is preceded by 3, this occurrence is invalid.


• Third 5 (at index 9):
  The sequence around it is: 3, 5, 7
  - Is it immediately followed by 7? Yes (the next number is 7).
  - Is it immediately preceded by 3? Yes (the preceding number is 3).
  Since it is preceded by 3, this occurrence is also invalid.

Thus, there is only 1 such occurrence of the digit 5 that satisfies both given conditions.