Question

There are 200 students in one year, divided into 10 groups. Is it possible to know the average score for all the year? (1) The average score is known for groups 1, 2, 3, 4 and 5 (2) The average score is known for groups \(5,6,7,8,9\) and 10 A. 1 alone, not 2 alone B. 2 alone, not 1 alone C. 1 and 2 together (need both) D. 1 alone or 2 alone E. 1 and 2 together are not sufficient

Short answer

C: 1 and 2 together (need both)

Step-by-step solution

Understand the information given

There are 200 students in total, divided into 10 groups. We need to find if it is possible to know the average score for all students in the year based on the known average scores for different groups.

Analyze Statement (1)

Statement (1) provides the average scores for groups 1, 2, 3, 4, and 5. From this information alone, we don't know anything about the scores of groups 6, 7, 8, 9, and 10. Therefore, we cannot calculate the average score for all 200 students.

Analyze Statement (2)

Statement (2) provides the average scores for groups 5, 6, 7, 8, 9, and 10. From this information alone, we don't know anything about the scores of groups 1, 2, 3, and 4. Hence, similar to statement (1), this alone is not sufficient to find the average score for all the students.

Combine Statements (1) and (2)

If we combine the information from statements (1) and (2), we have the average scores for all the groups: 1, 2, 3, 4, 5 from statement (1) and 5, 6, 7, 8, 9, 10 from statement (2). Notice that group 5 is repeated in both statements. By having the averages for all 10 groups, we can combine these to find the overall average score for all 200 students.

Conclusion

Since both sets of information together (statements (1) and (2)) provide the necessary data to find the average score for the entire year, but neither alone is sufficient, we conclude that both statements together are needed.

Key concepts

average score calculation

To understand how to calculate an average score, let's look at what an average represents: the sum of all values divided by the total number of values. For example, if you want to calculate the average score of a class of students, you would add up all the individual scores and then divide by the number of students.

Mathematically, if you have scores of different groups, you need to know the individual scores for each group to find the overall average. If you only have the average scores for each group, you must also know the number of students in each group.

To break it down for our problem: if the average scores for groups 1 to 5 are known but not for 6 to 10, we can't calculate the overall average without those additional groups. The same applies if only groups 6 to 10 are known without groups 1 to 5. Thus, knowing the averages for all individual groups is essential for calculating the total average score for the 200 students.

data sufficiency

Data sufficiency questions are a critical part of the GMAT exam. They test your ability to determine whether the information given is enough to solve a problem, rather than actually solving it.

For data sufficiency questions, you often need to analyze each statement alone before combining them. Here's a step-by-step guide for such problems:

• First, understand the question and determine what specific information is required to answer it.
• Second, analyze each statement independently. Ask yourself, 'Is this statement alone enough to provide the required information?'
• Third, combine the statements to see if together they provide sufficient information to answer the question.

In our example, neither Statement (1) nor (2) alone provides enough information to calculate the overall average score. However, when combined, they give the average scores for all 10 groups, making it possible to find the overall average score for all students.

GMAT test preparation

Preparing for the GMAT involves understanding different types of questions, including problem-solving and data sufficiency. Successful test preparation requires strong mathematical, analytical, and critical thinking skills.

Here are essential tips for GMAT preparation:

• Focus on understanding fundamental mathematical concepts, including arithmetic, algebra, and geometry.
• Practice data sufficiency questions regularly to get familiar with the format and develop a strategy for quick analysis.
• Develop a study schedule to cover all sections of the GMAT, including quantitative, verbal, and integrated reasoning.
• Take timed practice tests to improve time management and reduce exam-day anxiety.
• Review your answers, especially the incorrect ones, to understand where you went wrong and how you can improve.

By breaking down the study plan into manageable sections and practicing consistently, you can enhance your skills and increase your confidence for the exam day.