p,q can be 1,1 as well as 4,1/4
So, it should be C and not A.
I think the solution is incorrect

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
2 % 4 = 4p + 16q = 4 ( p + 4q ) = 4( p* 1^2 + q*2^2 ) = 4(1%2)
Thus, condition 1) is sufficient.

Condition 2)
Now, 1%1 = p + q = 2.
If p = 1 and q = 1, then 2 % 4 = 1*2^2 + 1*4^2 = 20.
If p = 3 and q = -1, then 2 % 4 = 3*2^2 + (-1)*4^2 = 12 - 16 = -4.
Since we don't have a unique solution, condition 2) is not sufficient.

Therefore, A is the answer.
Answer: A

Max@Math Revolution wrote:[GMAT math practice question]

If the operation % is defined by x % y = px^2 + qy^2 (p and q are constants), what is the value of 2 % 4?

1) 1 % 2 = 5
2) 1 % 1 = 2

We are given that the operation % is defined by x % y = px^2 + qy^2 (p and q are constants) and we need to determine the value of 2 % 4.

We see that 2 % 4 = p(2)^2 + q(4)^2 = 4p + 16q = 4(p + 4q). Therefore, if we can know both the values of p and q, or if we know the value of the sum (p + 4q), then we can determine the value of 2 % 4.

Statement One Alone:

1 % 2 = 5

This means p(1)^2 + q(2)^2 = 5, i.e., p + 4q = 5. Since 2 % 4 = 4(p + 4q), 2 % 4 = 4(5) = 20.

Statement one alone is sufficient.

Statement Two Alone:

1 % 1 = 2

That means p(1)^2 + q(1)^2 = 2, i.e., p + q = 2. Since we don't know the value of either p or q, nor do we know the sum (p + 4q), statement two alone is not sufficient.

Answer: A