Question

Is \(2 x / 5-3 y / 4>0\) ? (1) \(x>2 y\) (2) \(x>1^7 / 8 y\) 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

The required inequality isn’t formed based on assumptions separately.

Step-by-step solution

Rewrite the initial inequality

Start by rewriting the initial inequality in a more manageable form. The inequality given is: \[\frac{2x}{5} - \frac{3y}{4} > 0\] Multiply both sides by 20 to clear the fractions:\[20 \left(\frac{2x}{5} - \frac{3y}{4}\right) > 20 \times 0 \longrightarrow 8x - 15y > 0\]}, {

Analyze Statement 1

Statement (1) says \( x > 2y \). Multiply both sides by 8 to see how it relates to our inequality: \[8x > 16y\]. This is different from \( 8x - 15y > 0 \) and does not directly help us conclude anything.

Analyze Statement 2

Statement (2) says \( x > \frac{7}{8} y \). Multiply both sides by 8 to check again:\[8x > 7y \Rightarrow 8x - 15y > 0\] is not soluble as we don’t have such relationship within the math

Combine both statements

Now combine them both and analyze one more time if both assumptions(1) & (2) were resulting correctly. \[ x - 2 y & x > \frac{7}{8} y \] These values proves almost within the range.So, Unsufficient Statements since alone.

Key concepts

GMAT Quantitative Reasoning

GMAT quantitative reasoning tests your ability to interpret, analyze, and solve quantitative problems. It covers topics such as arithmetic, algebra, geometry, and data analysis. The problems typically involve numerical data and require careful reading and interpretation. To excel, practice breaking down complex problems into manageable steps.

For instance, in the given problem, the inequality involving fractions \( \frac{2x}{5} - \frac{3y}{4} > 0 \) needs simplification before we can analyze the statements. Rewriting the inequality by multiplying both sides by 20 gives us \[ 8x - 15y > 0 \]. This step simplifies the problem significantly and is an essential approach in GMAT quantitative reasoning.
Focus on the logical sequence of operations, clear the fractions, and align inequality expressions to compare terms directly.

Inequality Analysis

Analyzing inequalities requires understanding how to manipulate and compare expressions systematically. In the provided exercise, we simplified \( \frac{2x}{5} - \frac{3y}{4} > 0 \) to \[ 8x - 15y > 0 \].
To evaluate whether statements (1) and (2) help solve this inequality, we need to transform them similarly and check if they align.

For Statement (1) \( x > 2y \), multiplying both sides by 8 results in \[ 8x > 16y \], which is different from \[ 8x - 15y > 0 \]. Statement (1), therefore, does not directly help.
For Statement (2) \( x > \frac{7}{8} y \), multiplying both sides by 8 results in \[ 8x > 7y \], which does not directly match \[ 8x - 15y > 0 \] either.
Combining both statements still does not provide the needed relation to solve the inequality definitively. Remember, when analyzing inequalities, ensure all terms are comparable and transformations are equivalent.

Data Sufficiency

Data sufficiency problems on the GMAT require you to decide whether the provided statements give enough information to answer the question. It’s not about solving the problem completely but determining if you have sufficient data to solve it.

Consider our problem: Are the statements (1) \( x > 2y \) and (2) \( x > \frac{7}{8} y \) sufficient to establish \[ 8x - 15y > 0 \]?
From our analysis:

• Statement (1) alone gives \[ 8x > 16y \], which doesn't help with \[ 8x - 15y > 0 \]
• Statement (2) alone gives \[ 8x > 7y \], which also doesn't align with \[ 8x - 15y > 0 \]
• Combining both still doesn't give a conclusive answer, proving insufficiency

Thus, statements together are not sufficient.
Always verify if combining statements derives a direct and conclusive result. This is a crucial skill in tackling GMAT data sufficiency questions effectively.