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A school district surveyed 100 parents to gather their opinions on the
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09 Oct 2023, 01:15
09 Oct 2023, 01:15
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Difficulty:
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Question Stats:
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72%
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A school district surveyed 100 parents to gather their opinions on the district's budgetary priorities. The table shows the percentages of all survey respondents who indicated that they strongly agreed, somewhat agreed, somewhat disagreed, or strongly disagreed that each of the four actions should occur. No other response options were available. No respondent could choose more than one response option for each action. Not every respondent gave an opinion for every activity.
(Sort ↕ the table by clicking on the headers)
For each of the following questions, select Can be determined if the answer to that question can be determined from the information given. Otherwise, select Cannot be determined.
| Actions | Strongly Agree | Somewhat Agree | Somewhat Disagree | Strongly Disagree |
|---|---|---|---|---|
| Adding music classes | 0.18 | 0.22 | 0.25 | 0.17 |
| Expanding library hours | 0.17 | 0.52 | 0.11 | 0.2 |
| Improving athletic facilities | 0.12 | 0.24 | 0.28 | 0.35 |
| Reducing class sizes | 0.4 | 0.47 | 0.11 | 0.02 |
For each of the following questions, select Can be determined if the answer to that question can be determined from the information given. Otherwise, select Cannot be determined.
| Can be determined | Cannot be determined | |
| Did most respondents who indicated they somewhat agreed that class sizes should be reduced also indicate that they somewhat agreed that music classes should be added? | ||
| What percentage of all respondents chose not to give an opinion about whether athletic facilities should be improved? | ||
| What percentage of all respondents indicated that they strongly disagreed with all four actions? |
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Official Answer
Did most respondents who indicated they somewhat agreed that class sizes should be reduced also indicate that they somewhat agreed that music classes should be added?: Can be determined
What percentage of all respondents chose not to give an opinion about whether athletic facilities should be improved?: Can be determined
What percentage of all respondents indicated that they strongly disagreed with all four actions?: Cannot be determined
Re: A school district surveyed 100 parents to gather their opinions on the
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22 Mar 2024, 04:24
22 Mar 2024, 04:24
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Expert Reply
This is such a beautiful question that is a time saver only if you do these two things – else it is a huge time hog.
So watch the solution to see how you can execute the above and how once you do the above, answering the 3 statements is a cakewalk.
As you watch the solution, I want you to focus on these points as well:
As I said – if you read the dataset with the mindset of ‘owning the dataset’, this question can be answered correctly in less time. But if you do not, then you will not only take longer to solve this question but also you will likely fall in the trap set in this question.
- Visualize the dataset to the degree that you understand the following:
- Sum of the numbers in the row will add up to less than or equal to 1.
- There is no information about overlap of the segments in a single column.
- Translate the statements by applying strategic pausing technique so that you can effectively use your understanding of the dataset above to answer the question.
So watch the solution to see how you can execute the above and how once you do the above, answering the 3 statements is a cakewalk.
As you watch the solution, I want you to focus on these points as well:
- Observe how both statements 1 and 3 are focused on point 1b above. Statement 1 can be determined BUT statement 3 cannot be determined. You will have extracted everything from the solution if you can reason out why this is the case.
- Observe how statement 2 is a direct application of 1a.
As I said – if you read the dataset with the mindset of ‘owning the dataset’, this question can be answered correctly in less time. But if you do not, then you will not only take longer to solve this question but also you will likely fall in the trap set in this question.
Tutor
Joined: 11 Aug 2023
Posts: 965
Given Kudos: 87
GMAT 1: 800 Q51 V51
Re: A school district surveyed 100 parents to gather their opinions on the
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09 Oct 2023, 11:52
09 Oct 2023, 11:52
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Expert Reply
Question 1
Did most respondents who indicated they somewhat agreed that class sizes should be reduced also indicate that they somewhat agreed that music classes should be added?
This question is tricky to find the answer to since we have only aggregate percentage information on how people responded and don't know how each survey responded responded. So, we may get the impression that there's no way to answer this question.
However, if we notice the following, we can see that we can determine the answer to this question.
47% of the respondents somewhat agreed that class sizes should be reduced.
22% of the respondents somewhat agreed that music classes should be added.
Since 22% is less than half of 47%, we know for sure that it is NOT the case that most respondents who indicated they somewhat agreed that class sizes should be reduced also indicate that they somewhat agreed that music classes should be added. After all, "most" of 47% is more than half of 47% or at least 24% of the respondents., which is greater than 22%.
So, even without knowing how individual respondents responded, we can answer this question.
Mark "Can be determined."
Question 2
What percentage of all respondents chose not to give an opinion about whether athletic facilities should be improved?
Since the text information says, "No respondent could choose more than one response option for each action," we know that the percentages in the four columns for "Improving athletic facilities" add up to the total percentage of respondents who chose to give an opinion about whether athletic facilities should be improved."
So, we can calculate the percentage who chose not to give an opinion about whether athletic facilities should be improved by totaling the four percentages in the four columns and subtracting from 100.
Knowing that we can calculate the percentage this question asks about, we can answer this question, "Can be determined," without doing the math.
If you want to see how the math works, it's 1.00 - (0.12 + 0.24 + 0.28 + 0.35) = 1.0 - 0.99 = 0.01 or 1%.
Mark "Can be determined."
Question 3
What percentage of all respondents indicated that they strongly disagreed with all four actions?
This question is tricky since we might get the impression we can simply take the smallest of the four percentages in the Strongly Disagree column, 0.02, as the percentage of all respondents who indicated that they strongly disagreed with all four actions.
However, we have to keep in mind that respondents who strongly disagreed with one action may not have strongly disagreed with another. So, the respondents who strongly disagreed with one action may or may not be the same as those who strongly disagreed with one or more of the other actions.
Thus, it could be that 2% of the respondents strongly disagreed with all four actions, 0% of the respondents strongly disagreed with all four actions, or a percentage between 2% and 0% strongly disagreed with all four actions.
So, the information provided does not allow us to answer this question.
Mark "Cannot be determined."
Correct Answer:
Did most respondents who indicated they somewhat agreed that class sizes should be reduced also indicate that they somewhat agreed that music classes should be added?
This question is tricky to find the answer to since we have only aggregate percentage information on how people responded and don't know how each survey responded responded. So, we may get the impression that there's no way to answer this question.
However, if we notice the following, we can see that we can determine the answer to this question.
47% of the respondents somewhat agreed that class sizes should be reduced.
22% of the respondents somewhat agreed that music classes should be added.
Since 22% is less than half of 47%, we know for sure that it is NOT the case that most respondents who indicated they somewhat agreed that class sizes should be reduced also indicate that they somewhat agreed that music classes should be added. After all, "most" of 47% is more than half of 47% or at least 24% of the respondents., which is greater than 22%.
So, even without knowing how individual respondents responded, we can answer this question.
Mark "Can be determined."
Question 2
What percentage of all respondents chose not to give an opinion about whether athletic facilities should be improved?
Since the text information says, "No respondent could choose more than one response option for each action," we know that the percentages in the four columns for "Improving athletic facilities" add up to the total percentage of respondents who chose to give an opinion about whether athletic facilities should be improved."
So, we can calculate the percentage who chose not to give an opinion about whether athletic facilities should be improved by totaling the four percentages in the four columns and subtracting from 100.
Knowing that we can calculate the percentage this question asks about, we can answer this question, "Can be determined," without doing the math.
If you want to see how the math works, it's 1.00 - (0.12 + 0.24 + 0.28 + 0.35) = 1.0 - 0.99 = 0.01 or 1%.
Mark "Can be determined."
Question 3
What percentage of all respondents indicated that they strongly disagreed with all four actions?
This question is tricky since we might get the impression we can simply take the smallest of the four percentages in the Strongly Disagree column, 0.02, as the percentage of all respondents who indicated that they strongly disagreed with all four actions.
However, we have to keep in mind that respondents who strongly disagreed with one action may not have strongly disagreed with another. So, the respondents who strongly disagreed with one action may or may not be the same as those who strongly disagreed with one or more of the other actions.
Thus, it could be that 2% of the respondents strongly disagreed with all four actions, 0% of the respondents strongly disagreed with all four actions, or a percentage between 2% and 0% strongly disagreed with all four actions.
So, the information provided does not allow us to answer this question.
Mark "Cannot be determined."
Correct Answer:
Can be determined, Can be determined, Cannot be determined
