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 $p=\frac{x^{a+b}}{x^b}$, what is the value of positive integer $p$?
(1) $x=5$
(2) $a=0$

• 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

Answer: (B)

Data in statement II alone is sufficient.

This question isn't really about $p$. It's about the expression $\frac{x^{a+b}}{x^b}$,which can be simplified by subtracting the exponent in the denominator from the exponent in the numerator:

$\frac{x^{a+b}}{x^b}=x^{a+b-\left(b\right)}=x^a$

So, this question may be rephrased as simply. What is $x^a$?

Be careful though-sufficiency in this case does not necessarily mean that you to know $x$ and $a$ individually. (As just one example, if $x$ is $1$, then $a$ is not needed, because $1$ to any power is still $1$.

(1) INSUFFICIENT: knowing that $x$ is $5$ is not sufficient without knowing $a$

(2)SUFFICIENT: Anything to the $0$ power is $1$. The only exception to the rule is $0$, because $0^0$ is undefined. How ever, you have been told that $p$ is a positive integer, so you know that $x$ cannot equal $0$

The correct answer is (B)