How many numbers from $11$ to $50$ are there which are exactly divisible by $7$ but not by $3$?

There are $35$ students in a class. Suman ranks $3^{rd}$ among the girls in the class. Amit ranks $5^{th}$ among the boys in the class. Suman is one rank below Amit in the class. No two students hold the same rank in the class. What is Amit's rank in the class?

Manisha ranked sixteenth from the top and twenty-ninth from the bottom among those who passed an examination. Six boys did not participate in the competition and five failed in it. How many boys were there in the class?

Rahul ranked ninth from the top and thirty-eighth from the bottom in a class. How many students are there in the class?

Abhishek ranks thirteenth in a class of thirty-one students. What is his rank from the last (in $19^{th}$)?

How many numbers from $11$ to $50$ are there which are exactly divisible by $7$ but not by $3$?