Question

This data sufficiency problem consists of a question and two statements labelled (1) and (2), which contain certain data. Using these data and your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), decide whether the data given are sufficient for answering the question and then indicate one of the following answer choices:

If $xy\ne 0$ and $\sqrt{\frac{xy}{3}}=x$, what is $y$?
(1) $\frac{x}{y}=\frac{1}{3}$
(2) $x=3$

• A. Data in statement I alone is sufficient.
• B. Data in statement II alone is sufficient.
• C. Data in both statements together is sufficient.
• D. Data in both statements together is not sufficient.
• E. Either of the statements I or II is sufficient.

Answer 1

Answer: (E)

Either of the statements I or II is sufficient.

The question asks for the value of $y$, so isolate $y$ in the given equation:

$\sqrt{\frac{xy}{3}}=x$

$\frac{xy}{3}=x^2$

$xy=3x^2$

$y=3x$ It's okay to divide by $x$ since you know that $x$ is not $0$

In other words, if you can find the value of $x$, then you can also find the value of $y$.

(1) SUFFICIENT: statement (1) provides the value of $\frac{x}{y}$ but does not provide the value of $x$ and $y$ individually. For example, $x$ could be $1$ and $y$ could be $3$ or $x$ could be $2$ and $y$ could be $6$. Ironically, the combo is not helpful here since this same combo is given in teh stem.

(2) SUFFICIENT: With $x$, you can find $y$ using the rephrased equation from the question stem.

This problem is a reminder that sometimes what appears to be a combo question might just involve "school" algebra of solving for a single variable.