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

Question

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.

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 .

MartyMurray · Accepted Answer

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:   Can be determined, Can be determined, Cannot be determined

egmat · Answer

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.
 
 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.

https://www.youtube.com/watch?v=HpXywd6AcsQ

25kv175 · Answer

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

athena97 · Answer

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.

chetan2u · Answer

Deepa444 ,
Check the % for somewhat agree in reducing classes. It is 47%. If we are looking for most of 47% it would mean greater than 23.5%.
Now check the % for somewhat agree in adding music classes. It is just 22%, surely the  answer is No  even if all these 22% were also in the group of 47%.
Had the % been 27% or so, we would not have been able to determine as we do not know what role does this 27% play in 47%.

The solution for the entire question would be 
The question is more like a DS question, that is we have to find whether the question in the options can be answered from the information in the para.

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? 
Check the % for  somewhat agree  in reducing classes. It is 47%.
  If we are looking for most of 47% it would mean greater than 23.5%.

Now check the % for  somewhat agree  in adding music classes.
It is just 22%,  surely the answer is No even if all these 22% were also in the group of 47%.

Can be determined

2. What percentage of all respondents chose not to give an opinion about whether athletic facilities should be improved? 
 Adding the % in each row will give you the % of parents who responded.  In the row containing response to ímproving atheletic facilities', the % add up to 12+24+28+35 or 99% . So, 1% did not respond to the question. 
Can be determined

3. What percentage of all respondents indicated that they strongly disagreed with all four actions? 
We cannot find the distribution of parents within each % from the given information.
 It could be 2%, who strongly disagreed for reducing classes, as these 2% could be part of all the parents disagreeing strongly on all activities. But, it is equally possible that they answered differently for different activities. 
Cannot be determined

https://www.youtube.com/watch?v=qjqZ5kkvvT4

Gemmie · Answer

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.

chetan2u · Answer

The question is more like a DS question, that is we have to find whether the question in the options can be answered from the information in the para.

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? 
Check the % for  somewhat agree  in reducing classes. It is 47%.
  If we are looking for most of 47% it would mean greater than 23.5%.

Now check the % for  somewhat agree  in adding music classes.
It is just 22%,  surely the answer is No even if all these 22% were also in the group of 47%.

Can be determined

2. What percentage of all respondents chose not to give an opinion about whether athletic facilities should be improved? 
 Adding the % in each row will give you the % of parents who responded.  In the row containing response to ímproving atheletic facilities', the % add up to 12+24+28+35 or 99% . So, 1% did not respond to the question. 
Can be determined

3. What percentage of all respondents indicated that they strongly disagreed with all four actions? 
We cannot find the distribution of parents within each % from the given information.
 It could be 2%, who strongly disagreed for reducing classes, as these 2% could be part of all the parents disagreeing strongly on all activities. But, it is equally possible that they answered differently for different activities. 
Cannot be determined

KarishmaB · Answer

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

playthegame · Answer

Official Explanation from the Book

RO1: Evaluate 
From the last row of the table, 47 of the 100 parents surveyed somewhat agreed with reducing class size. For the majority of these 47 parents to somewhat agree with adding music classes, at least 24 parents would have to somewhat agree with adding music classes. But, only 22 parents somewhat agreed with adding music classes. Therefore, it can be determined from the given information that the answer to the question is No.

The correct answer is  Can be determined .

RO2: Evaluate 
The answer to this question is 100 − (12 + 24 + 28 + 35) = 100 − 99 = 1, which can be determined from the given information.

The correct answer is  Can be determined .

RO3: Evaluate 
The percentage of all respondents who indicated that they strongly disagreed with all four actions cannot be determined from the given information because the given information does not indicate, for example, whether the 17 parents who disagreed strongly with adding music classes were among the 20 parents who disagreed strongly with expanding library hours. The 17 parents who disagreed strongly with adding music classes, the 20 parents who disagreed strongly with expanding library hours, the 35 parents who disagreed strongly with improving athletic facilities, and the 2 parents who disagreed strongly with reducing class sizes could all be different individuals or there could be overlap between the groups.

The correct answer is  Cannot be determined .

HarishD · Answer

Explanation for 1st question:

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?

Adding music classes: 22%
Reducing class sizes: 47%

Case01: 22% is a part of 47% fully, in this case 22/47=0.468, So answer is a big NO, for "most respondents" is should be more than 0.5.

Case02: 22% is partially or not at all part of 47%, Again answer is NO.

For both the cases answer is NO. Hence, it can be determined.

KarishmaB · Answer

Video solution to this question: https://youtu.be/UtEAoNLP4dw The question is looking for Data Sufficiency. Remember that we don't always need to calculate the answer to say that the data is sufficient but we must consider the given data carefully. 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? respondents who indicated they somewhat agreed that class sizes should be reduced - 47 respondents who somewhat agreed that music classes should be added - 22 Did most of the 47 respondents (means 24 or more) somewhat agreed that music classes should be added? Well, since only 22 respondents somewhat agreed that music classes should be added, certainly it is not possible that most of the 47 respondents fall in this set. Hence we know that the answer is certainly NO and hence the data is sufficient to give us an answer. ANSWER: Can be determined nikitathegreat Freddy12 Had it been 25 instead of 47, the answer would have been "Cannot be determined". It is possible that these 25 are the same people who lie in the 47 group. It is possible that they do not. Hence, our answer is MAY or MAY NOT BE.

KarishmaB · Answer

Video Solution to this question: https://youtu.be/UtEAoNLP4dw What percentage of all respondents chose not to give an opinion about whether athletic facilities should be improved? We know what percentage of all respondents chose to give an opinion (we just have to add all 4 figures for 'athletic facilities should be improved') So if we subtract that sum from 1, we will get the answer. But we will not perform this calculation. We know that we have the data for it. ANSWER: Can be determined What percentage of all respondents indicated that they strongly disagreed with all four actions? We know that we do not have a value for the overlap of 'strongly disagreed' for all 4 actions so we should not be able to find this percentage. But one trap that I can foresee here is that for one or more of the actions, no respondents 'strongly disagreed' then we will know that 0% respondents indicated that they strongly disagreed with all four actions. But looking at the data I can see that some people 'strongly disagreed' for each action. So there may be an overlap of all 4 or there may not be. We have no way of calculating. ANSWER: Cannot be determined

zoezhuyan · Answer

hi  MartyMurray , I am struggling with Q1,
because I cannot figure out it refers to the percentage or the those people who somewhat agreed that class sizes should be reduced also those who somewhat agreed that music classes should be added.

would you please clarify further ?

thanks in advance.

bb · Answer

There is 100 respondents so I think it does not matter really if it is people or percentages. You can use percentages without complicating things.

MartyMurray · Answer

All the percentages in the table are of "all survey respondents."

So, the percentages in different cells of the table are all percentages of the same group of people. What that means is that the numbers in the different cells can be compared with each other.

Thus, for example, 0.12 in one cell represents a number of people that is half the number of people represented by 0.24 in another cell. Similarly, 0.12 represents a number of people that's about a quarter of the people represented by the number 0.47 in another cell.

So, 0.22 in the Somewhat Agree cell in the Adding music classes row represents both less than half the percentage and less than half the number of people represented by 0.47 in the Somewhat Agree cell in the Reducing class sizes row.

PeachSnapple1 · Answer

Fairly easy question, took me sub 1 minute.

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?  
So we have 22% somewhat agree with adding music classes, and 47% somewhat agree reduce class sizes. Even if those 22% completely overlaps with the 47%, 22/47 < 50% -->  we can determine the answer to this question , which is NO.

2. What percentage of all respondents chose not to give an opinion about whether athletic facilities should be improved? 
100 - (12+24+28+35) will give me an answer -->  we can determine the answer.

What percentage of all respondents indicated that they strongly disagreed with all four actions? 
We don't know about the overlapping among those four actions -->  cannot determine

PeachSnapple1 · Answer

There are some possible traps in this kind of question, I will note here for my own sake.

For question 1, if instead of having 22% and 47%, I have 30% and 47%. If that was the case, I cannot determine the answer, because if those 30% completely overlaps with 47%, then the answer would be YES. However, if there are 0% overlap, then the answer would be NO. 
Just note the relation between two numbers. If A/B < 1/2, then even if A is completely overlapped with B, we would still determine the answer.

eshika23 · Answer

For statement 1, what if all 22(who selected music class) were part of other category and none of them choose somewhat agree for expanding classes. Since somewhat agree was 47 and 53 respondents choose other category so it is easily possible all 22 responses belong to other and not to somewhat agree for expanding.

can you please help me where i might be wrong here

can you please help me where i might be wrong here

Bunuel · Answer

Statement 1 asks: "Did most respondents who somewhat agreed with reducing class sizes also somewhat agree with adding music classes?" We know: 47 people somewhat agreed with reducing class sizes. Only 22 people somewhat agreed with adding music classes. Even if all 22 were among the 47 , that’s still less than half (47/2 = 23.5). So not most . That means the answer can be determined, and it’s No . GMAT-Club-Forum-rv1url3p.png

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

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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

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?

GMAT Graphs and Tables (G&T) Questions

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

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615 to 715 in 15 Days (Ria's Strategies)

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745 with Only Self-Prep and GMAT Club

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