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 $A=\frac{\frac{x}{3}}{\frac{2}{y}}$, what is $A$?
(1) $xy=8$
(2) $\frac{x}{y}=2$

• 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.
  

Answer 1

The correct option is A Data in statement I alone is sufficient.

This question is a combo problem in disguise. the question asks for $A$, but the value of $A$ is dependent upon $x$ and $y$. before diving into the statements, simplify the given equation:

$A=\frac{\frac{x}{3}}{\frac{2}{y}}$

$A=\frac{x}{3}\times \frac{y}{2}$

$A=\frac{xy}{6}$

If you can find the value of $xy$, you will have enough information to answer the question.

(1) SUFFICIENT: Statement (1) matches the rephrased question, so it is sufficient to answer the question.

(2) INSUFFICIENT: It is not possible to find the value for $xy$ from the value for $\frac{x}{y}$. for example $x$ could be $2$ and $y$ could be $1$, in which case $xy$ is $2$. Alternatively, $x$ could be $4$ and $y$ could b4 $2$, in which case $xy$ is $8$. Put differently, the quotient combo and the product combo are not one in the same.