In a recent poll, residents of a certain community were asked to

Question

In a recent poll, residents of a certain community were asked to indicate a preference from among 5 options (Options A-E) for a community development project. Each respondent indicated a unique preferred option and each was asked to indicate whether an option other than his or her preferred option would be acceptable, and if so, which one he or she most preferred. Each respondent who indicated an acceptable option other than his or her preferred option indicated a unique second preference.

The table shows the distribution of the second preferences, grouped by the respondents' first preferences. For example, among respondents for whom Option D was the first preference, 15.0% indicated that Option E was acceptable and was most preferred when compared to Options A, B, and C.

--------------------------Second preference

First preference	A	B	C	D	E
A	—	5%	4%	2%	4%
B	30%	—	5%%	4%	1%
C	15%	4%	—	2%	13%
D	10%	3%	1%	—	15%
E	1%	2%	2%	5%	—

For each of the following options, select Yes if, among the respondents who selected that option as their first preference, the majority indicated that at least one of the other options was acceptable. Otherwise, select No.

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KarishmaB · Accepted Answer

We need to be very careful with the wording of the question.

Each respondent indicated a unique preferred option and each was asked to indicate whether an option other than his or her preferred option would be acceptable, and if so, which one he or she most preferred. Each respondent who indicated an acceptable option other than his or her
preferred option indicated a unique second preference.

What does each row give us?

B 30% — 5% 4% 1%
This says that of all the people who chose B as their first preference - say there were 100 such people, 30 chose A as second preference, 5 chose C as second preference, 4 chose D as second preference and 1 chose E as second preference. So 30 + 5 + 4 + 1 = 40 people chose a second preference. What about the other 60 who chose B as first preference? They did not select a second preference.

For each of the following options, select Yes if, among the respondents who selected that option as their first preference, the majority indicated that at least one of the other options was acceptable. Otherwise, select No.

We select "Yes" only if majority of the people (more than 50 out of 100) indicated that at least one of the other options was acceptable i.e. if more than 50 gave a second preference.

A - Only 15% gave a second preference. So majority did not give a second preference.
B - Only 40% gave a second preference. So majority did not give a second preference.
C - Only 34% gave a second preference. So majority did not give a second preference.

Select  No, No, No

rn1112 · Answer

For each of the following options, select Yes if, among the respondents who selected that option as their first preference, the majority indicated that at least one of the other options was acceptable. Otherwise, select No.

For a 'majority' to indicate that atleast one of the other options was acceptable, the total of precentages in a particular row (for First Preference) needs to be > 50 %

Option A : 5 + 4 + 3 + 4 = 15 % < 50 %; hence, NO
Option B : 30 + 5 + 4 + 1 = 40 % < 50 % ; hence, NO
Option C : 15 + 4 + 2 + 13 = 34 % < 50 %; hence, NO

NO, NO , NO is the corrrect answer

andrewjohn8 · Answer

Bunuel , would you be willing to format the table in there for us? Thank you!

Bunuel · Answer

_________________
Done. Thank you!

aakarsh1001 · Answer

andrewjohn8   Bunuel , I think there's a typo in the questions
"For example, among respondents for whom Option D was the first preference, 15.0% indicated that Option E was acceptable and was most preferred when compared to Options A, B, and C.", shouldn't it be 14% instead of 15%
?

Bunuel · Answer

There was a typo. Edited. Check the screenshot:

https://gmatclub.com/forum/download/file.php?id=77653

AditiDeokar · Answer

Do we have to check if there is a majority >50% who voted for a second preference or just check if the second prefernce options surpass 50%?

Bunuel · Answer

You just add the second preference percentages in that row and see whether the total is greater than 50%.

Because each respondent can name at most one acceptable alternative, the row total equals the percent who found at least one other option acceptable. If that total is over 50%, then a majority did. If it is 50% or less, then a majority did not.

liberoasperiores · Answer

Each respondent who indicated an acceptable option other than his or her preferred option indicated a unique second preference. 
Is it because of this info that overlap =0?

Bunuel · Answer

No.

That sentence does not mean “no overlap across the whole poll.”

It only means this: for any given first preference group, each respondent can name at most one second preference, so a respondent cannot be counted in two second preference columns.

So overlap across columns (within the same row) is 0 automatically, but you still have overlap across rows because different first preference groups can choose the same second preference (for example, both B first and C first can pick A second).

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First preference	A	B	C	D	E
A	—	5%	4%	2%	4%
B	30%	—	5%%	4%	1%
C	15%	4%	—	2%	13%
D	10%	3%	1%	—	15%
E	1%	2%	2%	5%	—

First preference	A	B	C	D	E
A	—	5%	4%	2%	4%
B	30%	—	5%%	4%	1%
C	15%	4%	—	2%	13%
D	10%	3%	1%	—	14%
E	1%	2%	2%	5%	—

First preference	A	B	C	D	E
A	—	5%	4%	2%	4%
B	30%	—	5%%	4%	1%
C	15%	4%	—	2%	13%
D	10%	3%	1%	—	15%
E	1%	2%	2%	5%	—

First preference	A	B	C	D	E
A	—	5%	4%	2%	4%
B	30%	—	5%%	4%	1%
C	15%	4%	—	2%	13%
D	10%	3%	1%	—	15%
E	1%	2%	2%	5%	—

First preference	A	B	C	D	E
A	—	5%	4%	2%	4%
B	30%	—	5%%	4%	1%
C	15%	4%	—	2%	13%
D	10%	3%	1%	—	14%
E	1%	2%	2%	5%	—

First preference	A	B	C	D	E
A	—	5%	4%	2%	4%
B	30%	—	5%%	4%	1%
C	15%	4%	—	2%	13%
D	10%	3%	1%	—	15%
E	1%	2%	2%	5%	—

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In a recent poll, residents of a certain community were asked to

First preference	A	B	C	D	E
A	—	5%	4%	2%	4%
B	30%	—	5%%	4%	1%
C	15%	4%	—	2%	13%
D	10%	3%	1%	—	15%
E	1%	2%	2%	5%	—

First preference	A	B	C	D	E
A	—	5%	4%	2%	4%
B	30%	—	5%%	4%	1%
C	15%	4%	—	2%	13%
D	10%	3%	1%	—	14%
E	1%	2%	2%	5%	—

First preference	A	B	C	D	E
A	—	5%	4%	2%	4%
B	30%	—	5%%	4%	1%
C	15%	4%	—	2%	13%
D	10%	3%	1%	—	15%
E	1%	2%	2%	5%	—