What is the value of \(x y\) ? (1) \(x=3 y\) (2) \(y^2=6\) 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

The Graduate Management Admission Test, or GMAT, is a standardized test primarily used for admission to graduate business programs globally. It assesses various skills such as analytical writing, quantitative reasoning, and verbal reasoning.

The GMAT is well-regarded for its data sufficiency questions. These unique questions require critical thinking and problem-solving skills, often involving algebra and other mathematical concepts. By understanding these questions, you can effectively prepare for the GMAT and enhance your chances of admission to prestigious business schools.

In the context of the given exercise, the test evaluates your ability to deduce the value of a variable using given conditions.
This involves breaking down and correlating the information provided in the problem to find a comprehensive answer.

Data sufficiency questions are a vital part of the GMAT. These questions don't require you to solve the problem completely but to assess if the information given is enough to reach a conclusion.

Let's break down data sufficiency with the given exercise. The problem is asking for the value of the product of two variables, which are x and y. We are given two statements:

• Statement 1: \( x = 3y \)
• Statement 2: \( y^2 = 6 \)

To solve data sufficiency questions:

• Analyze each statement independently first and determine if it can provide a sufficient answer.
• Then, consider the two statements together and see if they provide enough data when combined.

In this case, neither statement 1 nor statement 2 alone can determine the value of \( xy \). Therefore, we combine both: From statement 2, we know \( y \) can be \( \sqrt{6} \) or \( -\sqrt{6} \). Using this value in statement 1, we can find \( x \), and hence calculate \( xy \).

It’s essential to confirm that the combined information gives a unique value—in this problem, results in \( xy = 18 \).

Algebra plays a significant role in solving GMAT data sufficiency problems. It's about forming equations and solving for unknown values using given data.

For instance, in the provided exercise, we use algebra to manipulate and solve equations:

• Statement 1 offers the equation \( x = 3y \). This is a relationship between the variables x and y.


• Statement 2 provides \( y^2 = 6 \). Solving for y, we get \( y = \sqrt{6} \) or \( y = -\sqrt{6} \).

By combining these, we substitute \( y \)'s values from Statement 2 into the equation from Statement 1 to find \( x \):

When \( y = \sqrt{6} \): \( x = 3\sqrt{6} \)
When \( y = -\sqrt{6} \): \( x = -3\sqrt{6} \)

Consequently, \( xy \) is:

• For \( y = \sqrt{6} \) and \( x = 3\sqrt{6} \): \( xy = 3\sqrt{6} \cdot \sqrt{6} = 3\cdot 6 = 18 \).
• For \( y = -\sqrt{6} \) and \( x = -3\sqrt{6} \): \( xy = -3\sqrt{6} \cdot -\sqrt{6} = -3\cdot -6 = 18 \).

Thus, combining algebraic methods with critical reasoning provides us with the final solution: \( xy = 18 \).
Grasping these fundamentals ensures you can tackle similar problems efficiently.