Question #17d0e87d - SAT Suite Question Bank

ID: 17d0e87d

Modded SAT Question Bank by Abdullah Mallik

$\frac{14 x}{7 y} = 2 \sqrt{w + 19}$

The given equation relates the distinct positive real numbers $w$ , $x$ , and $y$ . Which equation correctly expresses $w$ in terms of $x$ and $y$ ?

$w = \sqrt{\frac{x}{y}} - 19$
$w = \sqrt{\frac{28 x}{14 y}} - 19$
$w = {(\frac{x}{y})}^{2} - 19$
$w = {(\frac{28 x}{14 y})}^{2} - 19$

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Correct Answer: C

Rationale

Choice C is correct. Dividing each side of the given equation by $2$ yields $\frac{14 x}{14 y} = \frac{2 \sqrt{w + 19}}{2}$ , or $\frac{x}{y} = \sqrt{w + 19}$ . Because it's given that each of the variables is positive, squaring each side of this equation yields the equivalent equation ${(\frac{x}{y})}^{2} = w + 19$ . Subtracting $19$ from each side of this equation yields ${(\frac{x}{y})}^{2} - 19 = w$ , or $w = {(\frac{x}{y})}^{2} - 19$ .

Choice A is incorrect. This equation isn't equivalent to the given equation.

Choice B is incorrect. This equation isn't equivalent to the given equation.

Choice D is incorrect. This equation isn't equivalent to the given equation.

Question Difficulty: Hard