Chapter 3: Problem 43
Is \(x / 8>y / 12 ?\)
(1) \(3 x>2 y\)
(2) \(x
Short Answer
Expert verified
A. 1 alone, not 2 alone
Step by step solution
01
Understand the Inequality
We need to determine if the inequality \(\frac{x}{8} > \frac{y}{12}\) is true.
02
Simplify the Inequality
Multiply both sides by 96 to eliminate the denominators: \(96 \times \frac{x}{8} > 96 \times \frac{y}{12} \) simplifies to \(12x > 8y \).
03
Simplify Further
Divide both sides of the inequality by 4 to obtain: \(3x > 2y\).
04
Analyze Statement (1)
Statement (1) says \(3x > 2y\). This matches the simplified inequality \(3x > 2y\), so statement (1) alone is sufficient.
05
Analyze Statement (2)
Statement (2) says \(x < y\). This does not provide information regarding the inequality \(3x > 2y\), so statement (2) alone is not sufficient.
06
Combine Statements
Since statement (1) alone is sufficient to answer the question, and statement (2) alone is not, there is no need to combine them.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
GMAT problem-solving
The GMAT tests your problem-solving skills through various types of questions, one of which includes inequalities. It's important to approach these questions with a clear strategy in mind.
Start by carefully reading the problem to understand what is being asked. In this case, we need to determine if \(\frac{x}{8} > \frac{y}{12}\) is true.
After understanding the problem, simplify the given inequality to make it easier to work with. Multiplied by 96, the inequality simplifies to \(12x > 8y\). By dividing both sides by 4, we get \(3x > 2y\).
Next, evaluate any given statements systematically and see if they help prove or disprove the inequality. Always revisit the problem to ensure you're solving the right question.
Finally, use logical reasoning to determine which statements are necessary to reach a conclusion. This avoids unnecessary calculations and helps efficiently solve the problem.
Start by carefully reading the problem to understand what is being asked. In this case, we need to determine if \(\frac{x}{8} > \frac{y}{12}\) is true.
After understanding the problem, simplify the given inequality to make it easier to work with. Multiplied by 96, the inequality simplifies to \(12x > 8y\). By dividing both sides by 4, we get \(3x > 2y\).
Next, evaluate any given statements systematically and see if they help prove or disprove the inequality. Always revisit the problem to ensure you're solving the right question.
Finally, use logical reasoning to determine which statements are necessary to reach a conclusion. This avoids unnecessary calculations and helps efficiently solve the problem.
inequalities in algebra
Understanding inequalities in algebra is crucial for solving GMAT problems involving comparisons between variables. An inequality indicates that one side is either greater than or less than the other.
In our example, the inequality \(3x > 2y\) tells us that for any value of x and y that makes this true, \( \frac{x}{8} > \frac{y}{12}\) will also be true. The steps for solving the inequality involve:
It is also crucial to interpret the inequality correctly: \( x < y\) doesn't necessarily mean \( 3x > 2y \) is true. Properly simplifying and solving inequalities in algebra requires practice but is highly beneficial for GMAT preparation.
In our example, the inequality \(3x > 2y\) tells us that for any value of x and y that makes this true, \( \frac{x}{8} > \frac{y}{12}\) will also be true. The steps for solving the inequality involve:
- Identifying the inequality and related expressions
- Simplifying the inequality to a more manageable form
- Assessing given conditions to see if they support the simplified inequality
It is also crucial to interpret the inequality correctly: \( x < y\) doesn't necessarily mean \( 3x > 2y \) is true. Properly simplifying and solving inequalities in algebra requires practice but is highly beneficial for GMAT preparation.
GMAT preparation
Proper GMAT preparation involves familiarizing yourself with the types of questions you'll encounter, like inequality problems. Focus on developing clear methods for solving problems step-by-step.
Start by practicing problems that require you to simplify inequalities. Develop a habit of breaking down complex expressions into simpler ones. This example demonstrated simplifying \( \frac{x}{8} > \frac{y}{12} \) to \( 3x > 2y \).
Learn to identify which statements provide necessary information to solve the problem. In this instance, statement (1) was sufficient by itself, while statement (2) was not.
Staying organized, practicing regularly, and understanding the underlying concepts will make you well-prepared for these types of problems on the GMAT.
Start by practicing problems that require you to simplify inequalities. Develop a habit of breaking down complex expressions into simpler ones. This example demonstrated simplifying \( \frac{x}{8} > \frac{y}{12} \) to \( 3x > 2y \).
Learn to identify which statements provide necessary information to solve the problem. In this instance, statement (1) was sufficient by itself, while statement (2) was not.
- Regular practice can help you recognize these patterns and become more efficient in solving them.
- Understand the logic behind combining statements verses using them separately.
Staying organized, practicing regularly, and understanding the underlying concepts will make you well-prepared for these types of problems on the GMAT.