Question

According to the table shown, the estimated number of home-schooled students in State A is approximately what percent greater than the number in State D ?
\begin{tabular}{|l|l|} \hline State & Number (in thousand)
\hline A & 181
\hline B & 125
\hline C & 103
\hline D & 79
\hline E & 72
\hline \end{tabular}

• A. 25%
• B. 55%
• C. 100%
• D. 125%
• E. 155%

Hint:

For "percent greater than X" problems, always remember that the value of X is the denominator of the fraction. A common error is to divide by the wrong number. Approximating the denominator to a round number (like 79 to 80) is a great strategy for quickly estimating the answer in multiple-choice questions.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This problem requires calculating the percentage increase from one value to another using data from a table. The formula for "percent greater than" or "percent increase" is crucial.
Step 2: Key Formula or Approach:
Percent Greater = \(\frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100%\)
In this context, the number of students in State A is the "New Value," and the number in State D is the "Original Value" because we are asking how much greater A is *than D*.
Step 3: Detailed Explanation:
From the table:
- Number of students in State A = 181 thousand.
- Number of students in State D = 79 thousand.
1. Find the difference (the amount of increase).
\[ \text{Increase} = 181 - 79 = 102 \text{ thousand} \] 2. Divide the increase by the original value (State D's number).
\[ \frac{102}{79} \] 3. Approximate the result and convert to a percentage.
To make the division easier, we can approximate 79 as 80.
\[ \frac{102}{79} \approx \frac{102}{80} = \frac{10.2}{8} = 1.275 \] Converting this decimal to a percentage:
\[ 1.275 \times 100% = 127.5% \] This value is very close to 125%.
Step 4: Final Answer:
The number of students in State A is approximately 125% greater than the number in State D. This corresponds to option (D).