Forget conventional ways of solving math questions. In DS, VA (Variable Approach) method is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution.

There are 3 variables and 0 equation. E is most likely to be the answer.

Condition 1) & 2)

Assume a = 1 and b = 2. Then, we have 1 + 4 +c^2 = 14 or c^2 = 9.

Thus, we have a solution a =1, b = 2 and c =3, since a, b and c are positive integers.

Assume a = 2 and b = 3. Then, we have 4 + 9 + c2 = 14 or c2 = 1.

However, c2 must be greater than 9.

Thus, we can realize that a = 1, b = 2 and c = 3 is a unique solution.

Condition 1)

Both of a = 1, b = 2, c = 3 and a = -1, b = 2, c = 3, are solutions.

Thus, we don’t have a unique solution.

This is not sufficient.

Condition 2)

Both of a = 1, b = 2, c = 3 and a = 1/2, b = 1, c = √51/2, are solutions.

Thus, we don’t have a unique solution.

This is not sufficient either.

Therefore, C is the answer.

For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both con 1) and con 2). Therefore, there is 80 % chance that E is the answer, while C has 15% chance and A, B or D has 5% chance. Then, E is most likely to be the answer using con 1) and con 2) together according to DS definition. Obviously, there may be cases where the answer is A, B, C or D. .

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