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Any 3 digit number can be expressed in the form of:
Where represent any natural number from 0 to 9.
We are told the hundreds number (this means in the expression above) is equal to the value of 40 tens, 40 tens is 400. Then, we know the digit in the tens is greater then 6, this means
in the expression above.
So, there are multiple numbers the room number could be, namely:
where can be 7, 8, or 9; and
can be 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. So, there's 30 possible room numbers Lydia may be.