Discussion
\(\oplus\) and \(\odot\) are two operators on numbers p and q such that
\(p \oplus q = \frac{p^{2} + q^{2}}{pq}\) and \(p \odot q = \frac{p^{2}}{q}\);
If \(x \oplus y = 2 \odot 2\), then x =
Answer: B
The answer is x = y.
First evaluate the right-hand side: \(2 \odot 2 = \frac{2^{2}}{2} = 2\). Then
\[ \begin{aligned} \frac{x^{2} + y^{2}}{xy} &= 2 \\ x^{2} - 2xy + y^{2} &= 0 \\ (x - y)^{2} &= 0 \end{aligned} \]
so x = y. Checking a distractor: with x = 2y the left side is (4 + 1)/2 = 2.5, and with x = y/2 it is also 2.5, not 2; x = 3y/2 gives 13/6. Only x = y makes the sum of squares equal to twice the product.
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