Hint- This question can be solved by writing all composite numbers on the higher side i.e. from $90$ onwards.
In order to write seven consecutive composite numbers between $1$ and $100$ we have to consider the numbers of the higher side in counting because if we take smaller numbers there is more probability of prime numbers.
For example: If we start from first prime number i.e.
$2$ and $3$ are prime numbers followed by $5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97$.
When we see these numbers we get, composite numbers
On seeing these numbers we find that we are not able to get $5$ consecutive composite numbers from $4$ to $88$ . And when we start from $90$ to $96$ we get seven consecutive composite numbers.
Note- Whenever we face such types of questions the key concept is that we have to locate composite numbers in the top series i.e. $90$ onwards . Like we did in this question. We can’t find consecutive seven composite numbers from $4$ to $88$.