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Chapter 5: Problem 17

If \(x / y=-10\), what percentage of \(x\) is \(x-10 y\) ? A. \(10 \%\) B. \(200 \%\) C. \(50 \%\) D. \(100 \%\) E. Cannot be determined

Short Answer

Expert verified
The percentage of \( x \) that \( x - 10y \) is 200%.

Step by step solution

01

Understand the given equation

The given equation is \( \frac{x}{y} = -10 \). This means that x is -10 times y, or mathematically, \( x = -10y \).
02

Substitute the value of x

Substitute \( x = -10y \) into the expression \( x - 10y \). Thus, the expression becomes: \[ x - 10y = -10y - 10y = -20y \].
03

Calculate the percentage

Now, find what percentage \( -20y \) is of \( x \). Using the value of \( x = -10y \), calculate the percentage: \[ \frac{-20y}{x} \times 100 \% = \frac{-20y}{-10y} \times 100 \% = 2 \times 100 \% = 200 \% \], so the answer is 200%.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

percentage calculation
Percentage calculation is about expressing one number as a fraction of another number and then multiplying by 100 to get a percentage. In our problem, to find what percentage \(-20y\) is of \(x\), we use the formula for percentage:
  • First, replace \(x\) with its equivalent value from the given equation, which is \(-10y\).
  • Next, rewrite the expression using this substitution: \[-20y / -10y = 2\].
  • Finally, multiply the result by 100 to get the percentage: \[2 \times 100\% = 200\%\].
So, \(-20y\) is 200\% of \(x\). Breaking this into steps helps in understanding the method.
algebraic substitution
Algebraic substitution involves replacing a variable with a given value or another expression to simplify and solve equations. In this problem, the goal is to substitute and simplify the expression to find the percentage.
  • You start with \( x / y = -10 \) and reformulate it as \( x = -10y \).
  • This tells us that every time we see \(x\), we can replace it with \(-10y\).
  • Then, substitute \(x\) in the expression \( x - 10y \) with \(-10y\).
  • The expression becomes: \( -10y - 10y = -20y \).
This substitution step is crucial in breaking down the problem and making the calculation easier.
graduate level test preparation
GMAT math problems often require a firm understanding of algebra and percentage calculations. Preparing for them involves practicing various types of problems, like this one. Here are a few tips:
  • Understand the problem: Carefully read the problem statement. Identify what is given and what needs to be found.
  • Break it down: Simplify the problem by breaking it into smaller, manageable steps.
  • Practice regular substitution: Be comfortable with making algebraic substitutions as this technique frequently appears in GMAT problems.
  • Review fundamental math concepts: Focus especially on algebra, percentages, and arithmetic to strengthen your calculation skills.
  • Practice with timed exercises: Test yourself under timed conditions to improve speed and accuracy.
Developing these skills through consistent practice will enhance your ability to solve GMAT math problems like a pro.

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