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A school district surveyed 100 parents to gather their opinions on the

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Sajjad1994
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A school district surveyed 100 parents to gather their opinions on the [#permalink] New post   09 Oct 2023, 01:15
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95% (hard)

Question Stats:

28% (03:05) correct 72% (03:05) wrong based on 531 sessions
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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.
ActionsStrongly
Agree		Somewhat
Agree		Somewhat
Disagree		Strongly
Disagree
Adding music classes0.180.220.250.17
Expanding library hours0.170.520.110.2
Improving athletic facilities0.120.240.280.35
Reducing class sizes0.40.470.110.02
(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.­
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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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
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Re: A school district surveyed 100 parents to gather their opinions on the [#permalink] New post   22 Mar 2024, 04:24
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­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.
  1. 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.
  2. 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:
  1. 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.
  2. 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.


­
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Re: A school district surveyed 100 parents to gather their opinions on the [#permalink] New post   09 Oct 2023, 11:52
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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:
Show Spoiler
Can be determined, Can be determined, Cannot be determined
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Re: A school district surveyed 100 parents to gather their opinions on the [#permalink] New post   09 Oct 2023, 09:20
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NO
YES
NO
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Re: A school district surveyed 100 parents to gather their opinions on the [#permalink] New post   09 Oct 2023, 11:15
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Answer should be:

YES - Because, if we take an example that all 22% are from that 47%, which still means that its not the majority. Therefore, it can be determined.

YES

NO
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Re: A school district surveyed 100 parents to gather their opinions on the [#permalink] New post   12 Oct 2023, 08:24
My logic for solving these questions:

1) Reducing class sizes ->47%
Adding music classes ->22%
The question asks if we can find if most (ie at least 50%) agreed on both. 50% of 47 is 23.5. 22 is less than half of 47. So it can be determined that no, most of them did not agree on both.
So answer for 1) ->Can be determined.

2) Adding all the response percentages for athletic facilities gives 99%. This means that 1% of the respondents did not give an opinion on athletic facilities.
So answer for 2) ->Can be determined.

3) The question clearly says "Not every respondent gave an opinion for every activity." Also there is no way to determine if there is an overlap of the respondents. The number of respondents who disagreed on all the four actions may well be 0,1 or any number.
So answer for 3) ->Cannot be determined.
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JoeAa
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Re: A school district surveyed 100 parents to gather their opinions on the [#permalink] New post   29 Dec 2023, 05:20
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MartyMurray wrote:
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:
Show Spoiler
Can be determined, Can be determined, Cannot be determined



for Q1 how do you know that 47% of ppl is the exact 22% ppl?
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Re: A school district surveyed 100 parents to gather their opinions on the [#permalink] New post   12 Mar 2024, 00:24
In question one - how do we know we are evaluating or comparing the same people?
In a previous question I did a calculation based on it and it came out wrong because - we cannot overlap percentages as there could be different people and now this question and confused me a bit honestly!

GMATCoachBen karishma Can you help?
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Re: A school district surveyed 100 parents to gather their opinions on the [#permalink] New post   12 Mar 2024, 08:16
1.Missed the word 'most' in the question statement and thus marked incorrectly as 'cannot be determined'

2. All of them had to give a opinion on a topic, but if we add up percenatages , it adds upto 99%. Regardless, chose 'can be determined for this

3. Cannot be determined, because we can predict the percentage of overlap
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Re: A school district surveyed 100 parents to gather their opinions on the [#permalink] New post   29 Mar 2024, 15:30
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? => Can be determined

47% Somewhat Agree with Class size actions
=> Most of them means more than 23.5%
 
So even all respondents Somewhat Agree with Music class action also Somewhat Agree with Class size actions
==> That's only 22%, yet reaching 23.5% requirement
==> So the answer for the Question is No and that means the answer can be determined

2. What percentage of all respondents chose not to give an opinion about whether athletic facilities should be improved? => Can be determined

There is one 1 hidden column (title No opinion), of which figures could be calculated by 100% subtracting the total of the 4 columns

3. What percentage of all respondents indicated that they strongly disagreed with all four actions? => Cannot be determined

One Strongly Disagree with one action may have a different opinion to another action.
There are too many possibilities form the provided table.
 
 
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Re: A school district surveyed 100 parents to gather their opinions on the [#permalink]
29 Mar 2024, 15:30
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