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805+ (Hard)|   Math Related|   Tables|            
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A school district surveyed 100 parents to gather their opinions on the 08 Jul 2025, 07:11
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For anyone having a hard time for the first question in this, as I also made the mistake. It means even if we assume that there is overlapp between the 2 groups only 22 people would somewhat agree regarding the music classes, and for majority we need 24. Hence, sufficient.

This is a really tricky one consider in 3rd part of this ques, you can't assume overlap as it is not given but in the first part you need to think on your toes that even if that was the case then also it won't be majority, hence data is sufficient. (Think of it like thinking of extreme case)

Whereas in 3rd part there could be multiple scenarios, 2%, 1% or even more so the way you read the question and understood it was right, it is just looking at the stem from a diff perspective.
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A school district surveyed 100 parents to gather their opinions on the 09 Nov 2025, 06:12
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KarishmaB

Thank you for this great answer! So, for the question, even if the number was 30% we still cannot determine the amount of people that somewhat agreed to both right (since we don't know who is voting what)? In that case, would we say Cannot be determined?
KarishmaB

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The table gives percentages but the number of participants were 100 hence it indicates the actual number of people.


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?

We know that we are only given the number of people who somewhat agreed to each activity, not who are the people who agreed to each. So it is possible that of the 47 people who "somewhat agreed" to reducing class size, none 'somewhat agreed' to adding music classes.
On the other extreme, it is possible that of the 47 people who "somewhat agreed" to reducing class size, 22 'somewhat agreed' to adding music classes too (because only 22 people 'somewhat agreed' to adding music classes).
This means that no matter what, of the 47, maximum 22 can "somewhat agree" with both.
For MOST of the 47 respondents to agree for music classes, at least 24 respondents must agree to music classes too. Hence, we can determine that most respondents who indicated they somewhat agreed that class sizes should be reduced did NOT indicate that they somewhat agreed that music classes should be added.

ANSWER: Can be determined

This is a trap question. You know that logic tells you that the people could be different. But ensure that you look at the actual given figures too. Perhaps most is just not possible.


What percentage of all respondents chose not to give an opinion about whether athletic facilities should be improved?

We know that 12 + 24 + 28 + 35 people gave their opinion on athletic facilities. Hence we can subtract this sum from 100 to get how many people did not give their opinions. We will not actually waste time finding it.

ANSWER: Can be determined.


What percentage of all respondents indicated that they strongly disagreed with all four actions?

We know that 2 people 'strongly disagreed' with reducing class size. Were they the same two people who strongly disagreed with all other activities too? We can't say. They may have agreed to other activities. So we cannot determine this.

ANSWER: Cannot be determined
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A school district surveyed 100 parents to gather their opinions on the 10 Nov 2025, 02:46
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Yes, if instead of 22, we had 30, then we cannot determine whether "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.


fujicosmic
KarishmaB

Thank you for this great answer! So, for the question, even if the number was 30% we still cannot determine the amount of people that somewhat agreed to both right (since we don't know who is voting what)? In that case, would we say Cannot be determined?

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A school district surveyed 100 parents to gather their opinions on the 18 Dec 2025, 19:48
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for Q1 Had it been 24% rather than 22%, we would not have been able to determine. Correct?

MartyMurray
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:
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Can be determined, Can be determined, Cannot be determined
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A school district surveyed 100 parents to gather their opinions on the 18 Dec 2025, 20:31
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vishwathols
for Q1 Had it been 24% rather than 22%, we would not have been able to determine. Correct?
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That's correct.
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A school district surveyed 100 parents to gather their opinions on the 10 Jan 2026, 08:18
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I have a doubt in question 1 - the solution stated says half of 47 is 23.5 and 22 is less so it can be determined.

While I get that it can be determined (after making a mistake)

But given that the question also states that - "Not every respondent gave an opinion for every activity"

We should check the total of the individual action and see how this "most" works out i.e.

50% of (98.2%) vs 50 % individual action ?
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A school district surveyed 100 parents to gather their opinions on the 10 Jan 2026, 08:59
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Rickooreoisb
I have a doubt in question 1 - the solution stated says half of 47 is 23.5 and 22 is less so it can be determined.

While I get that it can be determined (after making a mistake)

But given that the question also states that - "Not every respondent gave an opinion for every activity"

We should check the total of the individual action and see how this "most" works out i.e.

50% of (98.2%) vs 50 % individual action ?
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Did most respondents who indicated they somewhat agreed that class sizes should be reduced (47) also indicate that they somewhat agreed that music classes should be added?

“Not every respondent gave an opinion for every activity” only means some people skipped some actions, so a row may add to less than 1. It does not change what “most of the 47” means, because the 47 already counts only the respondents who did answer “somewhat agree” for reducing class sizes.

“Most of the 47” means more than half of 47, so at least 24 people. That threshold does not change.
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A school district surveyed 100 parents to gather their opinions on the 11 May 2026, 09:13
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Hello KarishmaB, am I correct in my understanding of first question that we can be certain in stating the extreme that "it is possible that of the 47 people who "somewhat agreed" to reducing class size, none 'somewhat agreed' to adding music classes" because 47+22 is 69 which is less than a 100, meaning out of the 47 saying somewhat agreed" to reducing class size, it is possible to assign 22 people to some other response for adding music classes without any overlap.

Whereas, had it been a number which exceeds 100, there would definitely have been an overlap in the respondents who said "somewhat agreed" to reducing class size and also 'somewhat agreed' to adding music classes". But since the overlap would not enable us to determine if it is less or more than 24 respondents (MOST of the 47 respondents), the answer then would be cannot determine because of that insufficiency.
KarishmaB

­
The table gives percentages but the number of participants were 100 hence it indicates the actual number of people.


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?

We know that we are only given the number of people who somewhat agreed to each activity, not who are the people who agreed to each. So it is possible that of the 47 people who "somewhat agreed" to reducing class size, none 'somewhat agreed' to adding music classes.
On the other extreme, it is possible that of the 47 people who "somewhat agreed" to reducing class size, 22 'somewhat agreed' to adding music classes too (because only 22 people 'somewhat agreed' to adding music classes).
This means that no matter what, of the 47, maximum 22 can "somewhat agree" with both.
For MOST of the 47 respondents to agree for music classes, at least 24 respondents must agree to music classes too. Hence, we can determine that most respondents who indicated they somewhat agreed that class sizes should be reduced did NOT indicate that they somewhat agreed that music classes should be added.

ANSWER: Can be determined

This is a trap question. You know that logic tells you that the people could be different. But ensure that you look at the actual given figures too. Perhaps most is just not possible.


What percentage of all respondents chose not to give an opinion about whether athletic facilities should be improved?

We know that 12 + 24 + 28 + 35 people gave their opinion on athletic facilities. Hence we can subtract this sum from 100 to get how many people did not give their opinions. We will not actually waste time finding it.

ANSWER: Can be determined.


What percentage of all respondents indicated that they strongly disagreed with all four actions?

We know that 2 people 'strongly disagreed' with reducing class size. Were they the same two people who strongly disagreed with all other activities too? We can't say. They may have agreed to other activities. So we cannot determine this.

ANSWER: Cannot be determined
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A school district surveyed 100 parents to gather their opinions on the 11 May 2026, 21:01
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Hello KarishmaB, am I correct in my understanding of first question that we can be certain in stating the extreme that "it is possible that of the 47 people who "somewhat agreed" to reducing class size, none 'somewhat agreed' to adding music classes" because 47+22 is 69 which is less than a 100, meaning out of the 47 saying somewhat agreed" to reducing class size, it is possible to assign 22 people to some other response for adding music classes without any overlap.

Whereas, had it been a number which exceeds 100, there would definitely have been an overlap in the respondents who said "somewhat agreed" to reducing class size and also 'somewhat agreed' to adding music classes". But since the overlap would not enable us to determine if it is less or more than 24 respondents (MOST of the 47 respondents), the answer then would be cannot determine because of that insufficiency.

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Take a simpler case.

Say in a group of 100 people, 10 people said "reduce class size".
Say in the same group of 100, 3 people said "Add music classes".
Now maximum how many people could have said both the things? Only 3. After all, only 3 people said "Add music classes." So at most only 30% of those who said "reduce class size" could have also said "Add music class" (3 of the 10).
It is possible that no one said both the things and these 10 and the 3 are different people but if I want to find the MAXIMUM possible number who could have said both, it would be 3.

This is what question 1 is all about.
Of 100, 47 somewhat agreed to reducing class size.
Of 100, 22 somewhat agreed to adding music classes.

So at most 22 could have said both. Now "MOST" respondents who somewhat agreed to reducing class size would be 24 (more than 50% of 47). Is it possible that 24 somewhat agreed to adding music classes? NO. After all, only 22 people somewhat agreed to adding music classes.
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