Question

What is the value of \(x y ?\) (1) \(1 / x=12\) (2) \(2 / y=10\) 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

Short answer

C. 1 and 2 together (need both).

Step-by-step solution

Understand the given information

The exercise gives two pieces of information: (1) \( \frac{1}{x} = 12\) (2) \( \frac{2}{y} = 10\)

Solve for x using (1)

To find \(x\) from the first statement, we start with: \[ \frac{1}{x} = 12 \]Taking the reciprocal of both sides, we get: \[ x = \frac{1}{12} \]

Solve for y using (2)

To find \(y\) from the second statement, we start with: \[ \frac{2}{y} = 10 \]Solving for \(y\), we get: \[ y = \frac{2}{10} = \frac{1}{5} \]

Calculate xy

Multiply the values of \(x\) and \(y\) together to find \(xy\): \[ xy = \left(\frac{1}{12}\right) \times \left(\frac{1}{5}\right) = \frac{1}{60} \]

Determine the sufficiency

Since both pieces of information together allow for the calculation of \(xy\), the answer is: C. 1 and 2 together (need both).

Key concepts

Quantitative Reasoning

Quantitative reasoning is a critical component of the GMAT exam. This skill encompasses the ability to handle numbers, interpret graphs, and solve mathematical problems effectively. In this exercise, we're asked to determine the value of the product of two variables, x and y. Understanding how to manipulate algebraic expressions and equations is essential. Here, we start with two given equations and must derive meaningful conclusions from them. Mastering quantitative reasoning involves recognizing the relationships between numbers and applying logical steps to solve problems methodically.

Data Sufficiency Problem

Data Sufficiency problems are unique to the GMAT exam. They are designed to test not just your ability to solve problems, but also your ability to judge which information is necessary to obtain a solution. This type of question generally provides two statements and asks you to determine whether they are sufficient to answer the question. In our exercise, we have two statements with equations related to x and y. The key is to analyze each statement independently and then together. By doing so, you can determine if the information given is enough to solve for the product xy. This type of problem tests both your mathematical skills and your logical reasoning abilities.

Problem Solving Techniques

Effective problem solving on the GMAT involves breaking down the problem into manageable steps and applying relevant techniques. Here are some techniques used in this exercise:

• Isolate Variables: First, isolate the variables x and y in their respective equations to get explicit values.
• Reciprocal Calculation: When given a reciprocal expression such as 1/x=12, take the reciprocal of both sides to solve for x.
• Equation Manipulation: For the equation 2/y=10, solve for y by re-arranging and simplifying the equation.
• Multiplication: Finally, multiply the isolated values of x and y to find the product xy.

Using these techniques ensures a structured approach and minimizes errors, which is vital for success in the GMAT math section.

GMAT Math Section

The GMAT math section is designed to assess your mathematical reasoning skills and ability to solve quantitative problems. It includes two types of questions: Problem Solving and Data Sufficiency. In this section of the GMAT, you need to be comfortable with basic algebra, geometry, arithmetic, and word problems. Familiarity with mathematical concepts and formulas is crucial.

• Problem Solving: These questions test your ability to use mathematical concepts to solve specific problems. You need to understand the problem, plan a solution, carry out your plan, and then check your work.
• Data Sufficiency: These questions assess your ability to analyze data and decide if there's enough information to solve a problem. They require a level of critical thinking beyond simple calculations.

By practicing these types of questions, you can enhance your skills and become adept at tackling the math section of the GMAT effectively.