Question

In \(2010,\) a basketball team won 30 percent of its 20 basketball games. In 2011 , the team won 28 percent of its 25 basketball games. What was the percent increase from 2010 to 2011 in the number of basketball games the team won? $$\begin{array}{l} 5 \% \\ 14 \frac{2}{7} \% \\ 16 \frac{2}{3} \% \\ 23 \frac{1}{3} \% \\ 60 \% \end{array}$$

Short answer

The percent increase in the number of basketball games the team won is 16 2/3%.

Step-by-step solution

Determine number of games won in 2010

Calculate the number of games won in 2010: The team won 30% of its 20 games. To find this, use the formula: \( \text{Number of games won in 2010} = \frac{30}{100} \times 20 = 0.30 \times 20 = 6 \ \text{So, the team won 6 games in 2010.}\)

Determine number of games won in 2011

Calculate the number of games won in 2011: The team won 28% of its 25 games. To find this, use the formula: \( \text{Number of games won in 2011} = \frac{28}{100} \times 25 = 0.28 \times 25 = 7 \ \text{So, the team won 7 games in 2011.}\)

Calculate the increase in the number of games won

Find the increase in the number of games won from 2010 to 2011: \( \text{Increase in number of games won} = \text{Number of games won in 2011} - \text{Number of games won in 2010} \ = 7 - 6 = 1 \ \text{So, the increase is 1 game.}\)

Calculate the percent increase

Calculate the percent increase from 2010 to 2011 using the formula: \( \text{Percent Increase} = \frac{\text{Increase in number of games won}}{\text{Number of games won in 2010}} \times 100 \ = \frac{1}{6} \times 100 \ = 16 \frac{2}{3} \ \text{Therefore, the percent increase is } 16 \frac{2}{3} \text{ percent.}\)

Key concepts

Mathematics Problem Solving

Mathematics problem solving involves breaking down a complex problem into simpler steps. In this exercise, we calculated the percent increase in the number of games won by a basketball team from 2010 to 2011.

We started by determining the number of games won each year. Breaking the problem into smaller parts helps you see the overall path to the solution more clearly.

Remember to carefully read the problem and understand what is being asked. This ensures you use the correct method and focus on the right parts of the problem.

Percentage Calculation

Percentage calculation is a fundamental skill in math, essential for various real-life applications. In this problem, we calculated the team’s winning percentages for two consecutive years.

To find the percentage of games won, we used the formula: \( \text{Number of games won} = \frac{\text{percentage}}{100} \times \text{total games} \). For 2010: \( \frac{30}{100} \times 20 = 6 \). For 2011: \( \frac{28}{100} \times 25 = 7 \).

Understanding how to apply these basic calculations is crucial for interpreting data and making informed decisions based on percentages.

GMAT Preparation

For those preparing for the GMAT, mastering problems like this is key. The GMAT often includes percentage problems that involve multiple steps and comparisons.

Our problem required not just finding individual percentages, but also calculating the percent increase. This multi-step approach is typical of quantitative questions on the GMAT.

Practice problems like these to enhance your quantitative reasoning skills, and remember to always check your work for accuracy. This habit of thorough verification ensures reliable answers under exam pressure.

Data Analysis

Data analysis requires interpreting numerical information and drawing meaningful conclusions. In this example, we analyzed the basketball team's performance data over two years.

By calculating the percent increase, we quantified the team's improvement. The formula used was: \( \text{Percent Increase} = \frac{\text{Increase}}{\text{Original Amount}} \times 100 \). Here, the increase was 1 game, and the original number was 6, leading to \( \frac{1}{6} \times 100 = 16 \frac{2}{3} \text{ percent} \).

Such analysis is crucial in various fields, from sports to business performance metrics, allowing stakeholders to make data-driven decisions.

Quantitative Reasoning

Quantitative reasoning involves using mathematical concepts to interpret and solve problems. It’s more than just calculation - it’s about understanding relationships and making logical decisions.

In our exercise, we not only calculated how many games were won but also interpreted the significance of the changes over the years. The ability to articulate why and how changes occur, and quantify them accurately, is a core aspect of quantitative reasoning.

Building these skills enables you to tackle more complex problems, whether in standardized tests, academic settings, or real-world situations requiring analytical thinking.