A number is larger than half of 100. It is more than 6 tens and less than 8 tens. The sum of its digits is 9. The tens digit is the double of the ones digit. What is the number ?

The correct option is 63.

Let's break down the clues step-by-step to find the required number:

Step 1: Analyze the range of the number
"Half of 100" is: $\frac{100}{2}=50$ The number is larger than 50.
It is "more than 6 tens and less than 8 tens", which means it lies between 60 and 80:
$60<\text{Number}<80$

Step 2: Check the tens and ones digits relationships
Let the tens digit be T and the ones digit be O.
We are given that "the tens digit is the double of the ones digit":
$T=2\times O$

Since the number is in the 60s or 70s, the tens digit T can only be 6 or 7:

• If $T=6$, then $O=\frac{6}{2}=3$. This gives the number 63.
• If $T=7$, 7 is not divisible by 2 to give a whole single digit.

Step 3: Verify the sum of the digits
We are told that "the sum of its digits is 9":
$6+3=9$
This perfectly satisfies all conditions specified in the problem.

Therefore, the number is 63.