The size of a proper subgroup of a finite group G is given as 31. We need to find the smallest possible size of group G.

To solve this problem, let's consider the definition of a subgroup. A subgroup of a group G is a subset of G that is itself a group with respect to the same operation as G.

We know that the order of a subgroup must divide the order of the original group. In other words, if the order of the group G is n, then the order of any subgroup of G must divide n.

Now, let's consider the size of the subgroup given in the question, which is 31. Since 31 is a prime number, the only possible divisors of 31 are 1 and 31 itself.

This means that the order of the group G must be either 1 or 31. However, since the question asks for the smallest possible size of G, we can exclude the case where the order of G is 31, as it would not be the smallest.

Therefore, the order of G must be 1. In other words, G is the trivial group, which consists of only the identity element.

The size of the trivial group is defined as 1, as it contains only the identity element. Therefore, the smallest possible size of group G is 1.

However, it is important to note that the trivial group is not a proper subgroup, as it is the group itself. Therefore, the smallest possible proper subgroup of any finite group is 31.

Hence, the correct answer is 62, as it is the double of the smallest possible proper subgroup size of 31.