We can take "four divided by the product of x and y" and express it as $\frac{4}{xy}$

So our two quantities are:
QUANTITY A: $\frac{4}{xy}$
QUANTITY B: $\frac{xy}{4}$

Since $x$ and $y$ are both positive, we can be certain that the product $xy$ is also positive, which means we can safely multiply both quantities by $xy$ to get:
QUANTITY A: $4$
QUANTITY B: $\frac{x^2y^2}{4}$

To eliminate the remaining fraction, we can multiply both quantities by $4$ to get:
QUANTITY A: $16$
QUANTITY B: $x^2y^2$

Since $x > 4$, we know that $x^2 > 16$
Similarly, since $y > 4$, we know that $y^2 > 16$

Since $x^2$ and $y^2$ are each greater than $16$, the product $x^2y^2$ is definitely greater than 16

Answer: B[/quote]
Can you explain why the answer can’t be D?

I used the choose numbers strategy.
I chose x = 1 and y = 2.

For Option A, I got 2 and for Option B, I got 1/2.

In another scenario, I chose x = 2 and y = 3.
For Option A, I got 4/6 and for Option B, I got 6/4.

Thank you

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