Question

According to the table above, 100 -Watt bulbs made up what fraction of the working lightbulbs? A) $\frac{1,230}{3,614}$ B) $\frac{2,384}{3,614}$ C) $\frac{271}{398}$ D) $\frac{2,384}{2,655}$

Short answer

Based on the given data, the correct fraction representing the fraction of 100-Watt working lightbulbs among the total working lightbulbs is $\frac{1,230}{3,614}$. Therefore, the answer is A) $\frac{1,230}{3,614}$.

Step-by-step solution

Identify the relevant information from the table

From the table provided in the problem, we can find the number of 100-Watt bulbs and the total number of working lightbulbs.

Write down the total number of 100-Watt working lightbulbs and total working lightbulbs

Let's assume the total number of 100-Watt working lightbulbs is represented as A and the total number of working lightbulbs is represented as B.

Determine the correct fraction from the given options

Now, we have to find the correct fraction from the given options A, B, C, and D, which represents the fraction of 100-Watt working lightbulbs among total working lightbulbs, i.e., $\frac{A}{B}$. Option A: $\frac{1,230}{3,614}$ Option B: $\frac{2,384}{3,614}$ Option C: $\frac{271}{398}$ Option D: $\frac{2,384}{2,655}$

Compare each option to the relevant information from the table

Based on the table provided in the exercise, identify the correct option by comparing each of the options with the numbers in the table.

Choose the correct option

After comparing the options with the given data, choose the option that correctly represents the fraction of 100-Watt working lightbulbs among the total working lightbulbs.

Key concepts

Fraction Comparison

Understanding how to compare fractions is critical when dealing with proportion-related problems, like the one students often encounter on the SAT. When comparing fractions, we aim to determine which fraction is greater or whether they are equivalent.

There are several strategies to compare fractions. One method is to find a common denominator, which allows direct comparison of the numerators – the larger the numerator, the larger the fraction. However, when the denominators are different, this process can be time-consuming. A quicker strategy, especially useful for multiple-choice questions, is to cross-multiply. If we have two fractions, $\frac{a}{b}$ and $\frac{c}{d}$, we multiply 'a' by 'd' and 'b' by 'c'. Then we compare those products to decide which fraction is larger.

In SAT math problems, efficiency is key: identifying the correct fraction from multiple choices can save time. With practice, you can develop intuition for these comparisons without calculating each time, but to begin with, it's recommended to work through the steps methodically to ensure accuracy.

Interpreting Data Tables

Data tables are commonly used to present information in a structured and easy-to-interpret way. Being able to read and interpret data tables is essential, not just for the SAT, but in many areas of academic and professional life. The crucial first step is identifying what each column and row represents. After that, it's a matter of extracting the correct data points relevant to the question at hand.

For a problem from an SAT perspective, this often means locating specific values and understanding what they imply in the context of the question. Recognizing trends, comparing quantities, and drawing the right conclusions is part of the skill set assessed. As with all SAT test preparation, practice with a range of tables – some straightforward and others more complex – will help build confidence and accuracy under test conditions.

When presented with a table, take a moment to note what the headings indicate about the data. Check whether the information is provided in totals, percentages, or another form. Also, pay attention to any footnotes that might offer valuable context or clarification. Practice with different types of data presentations will sharpen your ability to glean the necessary information quickly and accurately.

SAT Test Preparation

When prepping for the SAT, especially the math section, a strategic approach to studying is instrumental. It's essential to not only understand the mathematical concepts but to practice applying these concepts to the types of problems you'll encounter on the test.

Start with a thorough review of fundamental math concepts, from arithmetic to algebra to geometry. Then, gradually focus on more complex problems. Using timed practice tests can help you build speed and accuracy, while also familiarizing yourself with the test format and question styles.

Remember to review your mistakes closely – this is where your most valuable learning happens. Identify patterns in the errors you make, and then address those areas with focused study. The key is to practice consistently and analyze your performance effectively to make the best use of your study time.

Tips for Effective SAT Math Preparation

• Understand the underlying concepts thoroughly.
• Develop a study plan that includes consistent and varied practice.
• Use official practice materials to get a sense of the real test format.
• Work on pacing to ensure you can complete all sections in the allotted time.
• Review wrong answers carefully to learn from your mistakes.

By incorporating these strategies into your SAT test preparation routine, you'll be better equipped to handle whatever questions the test may throw at you.