Question

What percentage of people watch all the three movies? (a) \(40 \%\) (b) \(6 \%\) (c) \(9 \%\) (d) \(12 \%\)

Short answer

Answer: The exercise appears to be incomplete or missing some data that would help us make a better decision. However, options (b) 6%, (c) 9%, and (d) 12% seem more reasonable than option (a) 40%. Without additional information, an educated guess would need to be made among options (b), (c), and (d).

Step-by-step solution

Identifying the information given:

In this problem, we are given four options of percentages of people who watch all three movies. Our task is to find the correct one.

Understanding percentages:

To find the percentage of people who watch all three movies, we will need to understand how percentages work. A percentage is a portion of 100. For example, if 40% of people watch all three movies, that means 40 people out of 100 watch all three movies.

Analyzing the given options:

We will now analyze each option and choose the correct one.

Option (a): 40%

If we choose option (a) as the correct answer, this means that 40 out of every 100 people watch all three movies. However, this seems like quite a high percentage, so let's check the other options.

Option (b): 6%

If we choose option (b) as the correct answer, this means that 6 out of every 100 people watch all three movies. This percentage seems more reasonable. Let's still compare with the other options.

Option (c): 9%

If we choose option (c) as the correct answer, this means that 9 out of every 100 people watch all three movies. This percentage seems reasonable too. Let's continue to the last option.

Option (d): 12%

If we choose option (d) as the correct answer, this means that 12 out of every 100 people watch all three movies. This percentage also seems reasonable.

Conclusion:

Since it is clear that option (a) is too high, we can eliminate it. From the remaining options, there is no definitive way to determine which percentage is correct without additional information. The exercise seems to be incomplete or missing some data that would help us make a better decision. However, if this were a multiple-choice exam question, the student could make an educated guess among options (b), (c), and (d).

Key concepts

Percentage Calculation

Understanding percentage calculation is essential for solving a wide range of problems, whether in the classroom or real-world scenarios. A percentage represents a part per hundred, and it can be visualized as a fraction of 100. To calculate the percentage of a particular value, you can use the formula: \( \text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100 \)

Applying this formula involves identifying the 'part' (the quantity we're focusing on) and the 'whole' (the total quantity or 100%), then multiplying the resulting fraction by 100 to convert it into a percentage. It's a fundamental concept in arithmetic and is often used to compare quantities, understand proportions, and interpret statistical data. In the example below, understanding percentage calculation would allow one to infer what portion of the population watches all three movies when given a specific number or total viewers.

Quantitative Aptitude

Quantitative aptitude refers to one's ability to handle numerical and mathematical reasoning. It's imperative in various standardized tests and is also a vital skill in academic and professional settings. Problems requiring quantitative aptitude often test your understanding of basic concepts of arithmetic, algebra, geometry, and data interpretation.

When answering a quantitative aptitude question, reading and analyzing the problem carefully is critical. First, decipher what is being asked, and then recall the mathematical concepts needed to solve the problem. In most cases, you would apply formulas, identify patterns, or break down the problem into smaller, more manageable steps. For example, in the problem about the percentage of people watching movies, an understanding of percentages, ratio, and probability might be required to provide a full solution. Enhancing your quantitative aptitude can be achieved through practice, familiarizing oneself with various types of mathematical problems, and sharpening problem-solving techniques.

Multiple-choice Exam Strategy

Multiple-choice exams can be challenging, but with the right strategies, you can increase your chances of selecting the correct answer, even when unsure of the solution. One effective strategy is the process of elimination, as seen in the provided example. In this strategy, you discard the most obviously incorrect answers to narrow down the choices.

Another key tactic is to look for patterns in the questions and answers. Sometimes, the phrasing of the question or the nature of the options can provide clues about the correct answer. Additionally, students should be wary of answers that are 'extremes' or seem out of place compared to the other options. Carefully managing time is also crucial; if you're stuck on a question, it's often better to move on and return to it later. Lastly, educated guessing is an important part of multiple-choice strategy. If you've eliminated one or more options, an educated guess between the remaining choices is better than leaving the question blank.