Question

Customers buy yellow, red and white cars in a ratio of \(1: 2: 3\). If, in total, 84 cars were sold, how many were red? A. 24 B. 25 C. 26 Answer D. 27 E. 28

Short answer

The number of red cars is 28.

Step-by-step solution

Determine the Total Parts

First, add the parts of the ratio together: 1 (yellow) + 2 (red) + 3 (white). The total parts = 1 + 2 + 3 = 6.

Calculate the Value of One Part

Divide the total number of cars sold by the total parts to find the value of one part. The value of one part = 84 / 6 = 14.

Find the Number of Red Cars

Multiply the value of one part by the number of parts for red cars. Number of red cars = 14 * 2 = 28.

Key concepts

Ratio Calculation

Ratios are a way to compare quantities of different items. They show the relative size of two or more values. In the given problem, customers buy yellow, red, and white cars in a ratio of 1:2:3 respectively. This means for every yellow car sold, two red cars, and three white cars are sold.

To solve problems involving ratios:

• Add up the parts of the ratio. For example, 1 (yellow) + 2 (red) + 3 (white) adds up to 6 parts.
• Divide the total number of items by the sum of the parts to find the value of one part. In this case, 84 cars divided by 6 parts equals 14.
• Multiply the value of one part by the applicable number of parts for the category you are interested in. Here, for red cars, it's 14 (value of one part) times 2 (red parts), which equals 28 red cars.

Following these steps ensures accurate ratio calculations in various problems.

Problem Solving in GMAT

The GMAT often includes problems that test your ability to understand and manipulate ratios. Knowing this strategy is crucial:

• Break down the problem into manageable steps.
• Translate the ratios into actual values using logical calculation methods.
• Double-check your calculations to avoid simple arithmetic errors.

For instance, the problem mentioned requires clear identification of the ratio parts and sequential steps:
We start by determining how many parts the ratio represents (1 yellow + 2 red + 3 white = 6 parts). Then, by dividing the total number of cars sold (84) by these parts, we find the value of one part (14). Finally, by multiplying the value of one part by the red parts (2), we discover that 28 red cars were sold. Practicing this approach can make GMAT ratio problems more manageable.

Mathematical Techniques

Understanding and applying the right mathematical techniques can simplify problem-solving. For ratio problems:

• Add the components of the ratios to find total parts.
• Use division to determine the value of one part.
• Multiplication helps identify the quantity corresponding to each part of the ratio.

Let's summarize:
Given the ratio, we added the parts (1 + 2 + 3 = 6). Then, we divided the total products sold by this sum to find what one part represents (84 / 6 = 14). Finally, we used multiplication to find how many red cars were there (14 * 2 = 28).

If these concepts are applied correctly, tackling ratio-based questions in exams can become a straightforward and logical process. Understanding the methodology behind each step reinforces your ability to solve similar problems effectively.