Question

If \(x / y=199\), what percentage of \(x\) is \(x-y\) ? (A) 99 (B) 100 (C) 51 (D) 49 (E) Cannot be determined

Short answer

(A) 99

Step-by-step solution

- Express given equation

The problem states that \ \( \frac{x}{y} = 199 \). This can be rewritten to express \ \( x \) in terms of \ \( y \). Therefore, \ \( x = 199y \).

- Substitute the value of x

Substitute the value of \ \( x \) into the expression \ \( x - y \). So, \ \( x - y = 199y - y = 198y \).

- Find percentage

Now, find what percentage \ \( 198y \) is of \ \( 199y \). Using the formula for percentage: \ \( \text{Percentage} = \left( \frac{198y}{199y} \right) \times 100 \).

- Simplify

The \ \( y \) terms cancel out in the fraction, so we are left with: \ \( \left( \frac{198}{199} \right) \times 100 \approx 99.5\% \).

- Look at the given choices

Among the given options, the closest one to \ \( 99.5\% \) is \ \text{(A) 99.} \ So, the correct answer is \text{(A) 99.}

Key concepts

GMAT math strategies

When solving GMAT math problems, particularly those involving percentages, a systematic approach is essential. Start by understanding the problem statement. Break it down to identify key information and reframe the problem in simpler terms. This problem, for example, involves finding the percentage of one quantity with respect to another.
You can utilize GMAT-specific strategies such as:

• Rewriting equations to isolate variables
• Substitution to simplify expressions
• Elimination of variables when possible

Applying these strategies step by step can help arrive at the correct solution efficiently. In our problem, rewriting the original equation \(\frac{x}{y} = 199\) into \(x = 199y\) and then substituting this back into the expression makes it much easier to manage. Following this structured method ensures clarity and precision.

Percentage calculations

Percentages are a fundamental concept in GMAT math, requiring a good grasp of basic arithmetic. When given values like we see in the exercise, it's important to understand how to express one value as a percentage of another.
Here’s a simple formula to remember:
\(\text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100\).
In our specific problem, we need to find what percentage \(x - y \), which is 198y, is of x, which is 199y. By substituting these values into our percentage formula, it becomes \(\frac{198y}{199y} \times 100\). The y terms cancel out, simplifying our calculation to \(\frac{198}{199} \times 100\), which approximates to 99.5%.
This method works universally for many GMAT percentage problems, ensuring accuracy and simplifying even complex percentage calculations.

Test-taking techniques

Mastering test-taking techniques can significantly enhance your performance on the GMAT. Here are several techniques useful for math sections:

• Elimination: Quickly eliminate options that are clearly incorrect to narrow down your choices.
• Estimation: For problems involving complex calculations, approximate values to see which option is closest.
• Time Management: Allocate time wisely to ensure you complete all questions. Skip and return to complex problems if needed.

For the given problem, after calculating the value 99.5%, identify the answer choice that is nearest - Option (A) 99. Utilizing elimination and estimation, you can efficiently arrive at the correct choice. This way, even when exact calculations are challenging, you can confidently choose the closest approximation from the provided options.