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 $x$ and $y$ are integers, what is $x+y$?
(1) $3^x=81$
(2) $5^x=\frac{25}{5^y}$

• 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 B Data in statement II alone is sufficient.

(B): The question asks for the combo $x+y$ and specifies that $x$ and $y$ are integers.

(1) INSUFFICIENT : $3^x=81$

You could solve for the value of $x$, but the statement does not provide any information about the value of $y$, so this statement is not sufficient. Don't solve for $x$ now; check statement (2) first.

(2) SUFFICIENT:

$5^x=\frac{25}{5^y}$

$\left(5^x\right)\left(5^y\right)=25$

$5^{x+y}=5^2$

$x+y=2$