Is \(x\) positive or negative? (1) \(x y>0\) (2) \(y<0\) A. 1 alone, not 2 alone B. 2 alone, not 1 alone C. 1 and 2 together (need both) D. 1 alone or 2 alone E. 1 and 2 together are not sufficient

Algebra is a branch of mathematics that deals with symbols and the rules for manipulating those symbols.
In this problem, we're dealing with variables and equations involving these variables. Our main variables here are **x** and **y**. We use these symbols to represent unknowns in the problem.
We look at how these variables interact, particularly when multiplied together, such as in the term **xy**. In algebra, understanding how variables relate through operations is key to solving problems.
For instance, if we know that **xy > 0**, it means the product of **x** and **y** is positive. This information helps us deduce the possible values of **x** and **y**. They must either be both positive or both negative. Sorting out these kinds of variable interactions is what makes algebra both challenging and rewarding.

Inequalities show the relationship between two expressions that may not be equal. For example, **xy > 0** means that the product of **x** and **y** is greater than zero.
These inequalities can tell us crucial information about the variables involved.
Looking at **y < 0** specifically, it informs us that **y** is a negative number. This piece of information restricts the possible values for **y**.
When working with inequalities, always pay attention to the sign ('greater than' or 'less than'). It informs the direction of the relationship between the variables. Combining multiple inequalities often helps determine specific values or ranges for variables.

Logic and reasoning are fundamental in solving GMAT problems. They involve making connections and deductions based on given statements.
Let’s break down the logical steps for this problem. First, Statement (1) says **xy > 0**. This means **x** and **y** have the same sign, either both positive or both negative.
Next, using Statement (2) that **y < 0**, we learn that **y** is negative.
Combining these statements logically, if **y** is negative and the product **xy** is positive, **x** must also be negative. This follows because a negative multiplied by a negative results in a positive.
Understanding how to connect these statements is crucial in drawing the right conclusion.

Data sufficiency is a unique type of question on the GMAT. It tests whether the given information is enough to solve a problem.
For this problem, we have two statements.

• Statement (1): **xy > 0**
• Statement (2): **y < 0**

First, we examine each statement individually. From Statement (1), we only know **x** and **y** share the same sign.
From Statement (2), we know **y** is negative but nothing about **x** directly.
However, combining both statements gives us enough info: **y** is negative. For **xy > 0**, **x** must also be negative. Therefore, to determine whether **x** is positive or negative, both statements are required.
Thus, the correct answer is C: we need both statements to determine the sign of **x**.