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805+ (Hard)|   Tables|                  
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Official Explanation

For each of the following conclusions, select Supported if it is supported by the information in the table. Otherwise select Not supported.

Explanation

A majority of the respondents believe adding a website could benefit their businesses.

Adding the percentages in the "No benefit" and "Uncertain" rows for each group shows that the total percent of respondents who indicated that adding a website could not benefit their businesses or that they were uncertain whether adding a website would benefit their businesses was at most 37%—far less than 50%. This suggests that a majority of the respondents in each group, and thus a majority of all the respondents, believe that adding a website could benefit their businesses.

The correct answer is Supported.

Fewer than 25% of the respondents who believe a website could help expand their customer base also believe a website could help them maintain their current market share.

Each percentage in the "Preserve market share" row is less than one-fourth (25%) of the percentage in the same column in the "Expand customer base" row. Thus, the survey results suggest that the number of respondents who believe that adding a website could help them maintain their current market share is less than 25% of the number of respondents who believe that adding a website could help expand their customer base.

The correct answer is Supported.

Only a small proportion of the respondents are concerned that they are losing market share.

The "Preserve market share" row only lists the percentages of respondents who indicated that adding a website would help them preserve market share. Far more of the respondents may be concerned that they are losing market share, but nonetheless doubt that adding a website would help solve that problem.

The correct answer is Not Supported.
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­1. A majority of the respondents believe adding a website could benefit their businesses. => Supported

By a quick look, we can see that for each ethnic group, the total for [No Benefit] + [Uncertain] is less than 50%
=> That means [Benefit] > 50%


2. Fewer than 25% of the respondents who believe a website could help expand their customer base also believe a website could help them maintain their current market share. => Supported
 
For [Preserve market share] category, 4x of each ethnic group is
  • Latino: 24% < 26% in [Expand customer base]
  • African: 24% < 29%
  • Asian: 16% < 25%
  • Native: 24% < 25%
That means even all those in [Preserve market share] categor are also in [Expand customer base] category, that doesn't add up to 25% (or in other words, fewer than 25%)


3. Only a small proportion of the respondents are concerned that they are losing market share. => Not supported

Losing market share is not mentioned anywhere
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AditiDeokar
How does one calculate these percentages nad not exceed the 2.5 mins goal, suhc as 26% 459, etc, I could try approximations but how much can I approximate so that I don't get the wrong answer?

As shown HERE, you don't really need to calculate that at all.
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Question 3



“Losing market share” is not a category in the table at all. You cannot support this statement from the data





Please note the distinction between question 2 and 3

Fewer than 25% of the respondents who believe a website could help expand their customer base also believe a website could help them maintain their current market share.
Only a small proportion of the respondents are concerned that they are losing market share.


2 says maintain their current market share. - data of which is there in table

3 says losing market share, data of which is not there in table and hence not supported





@varunbharadwaj also gave a good explanation

The potential benefit listed is Preserve market share NOT Losing or Gaining market share.People gave opinion about only preserving market share not gaining or losing it.Information about losing market share is not available.

We only know that 94 % (100 - 6%) people think otherwise that Potential benefit is Gaining, Losing,Cant say etc .But we can find values of individuals.
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A company that designs websites primarily for minority-owned businesses conducted a survey of minority-owned businesses in the United States that do not currently have a website. The survey was designed to help determine what respondents see as the potential benefits of adding a website. The results of that survey are shown in the table.

Potential benefitLatino (459
respondents)
African American
(394 respondents)
Asian American
(438 respondents)
Native American
(279 respondents)
Expand customer base26%29%25%25%
Improve communication15%4%4%6%
Increase customer satisfaction5%17%28%6%
Increase ratio of profits to costs14%19%17%19%
Increase tax savings0%1%0%0%
Preserve market share6%6%4%6%
Save time4%3%13%2%
Other3%3%5%4%
No benefit27%17%22%21%
Uncertain10%11%13%10%

For each of the following conclusions, select Supported if it is supported by the information in the table. Otherwise select Not supported

ID: 100425
Stmt 1:
A majority of the respondents believe adding a website could benefit their businesses.
Supported
We see No benefit <50% each of categories of respondents.


Stmt 2:
Fewer than 25% of the respondents who believe a website could help expand their customer base also believe a website could help them maintain their current market share.
Supported



Potential benefitLatino (459
respondents)
African American
(394 respondents)
Asian American
(438 respondents)
Native American
(279 respondents)
Expand customer base26%29%25%25%
Improve communication15%4%4%6%
Increase customer satisfaction5%17%28%6%
Increase ratio of profits to costs14%19%17%19%
Increase tax savings0%1%0%0%
Preserve market share6%6%4%6%
Save time4%3%13%2%
Other3%3%5%4%
No benefit27%17%22%21%
Uncertain10%11%13%10%

Case 1:

Let's say there's no common respondent between "Expand customer base" and "Preserve market share"
In that case definitely we can say fewer than 25%...

Case 2:
Let's say maximum common respondents

Expand customer base, 25% of each category: 26/4 = 6.5, 29/4 = 7.25, 25/4 = 6.25, 25/4 = 6.25
Preserve market share 6, 6, 4, 6

Clearly
Fewer than 25% of the respondents who believe a website could help expand their customer base also believe a website could help them maintain their current market share.

Stmt 3:
Only a small proportion of the respondents are concerned that they are losing market share.
Not Supported
What is small proportion, also preserving doesn't mean concern for loosing
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But we cannot figure out that what percentage of 6% latino who said preserve market share overlap with expand customer base. similarly, for other minorities.

question asks about the percentage who chose expand customer base also chose preserve market share, and whether it can be determined that this percentage is less than 25%
since we do not know about the overlap, how can we comment that YES it is less than 25% and hence 'supported'? we do not that out of the 6% latino who choose preserve market share, what percentage also chose preserve market share, could be whole 6%, could be none, could be anywhere in between!
EMPOWERgmatRichC
Hi mimishyu,

Since this discussion is spread over several posts in this thread, I'm going to consolidate all of the relevant information here:

Based on the table (and the description above it), we can deduce that some people in this survey responded to MORE than one category. Here's why:

1) If you add up all of the percentages in the first column, you end up with a total of 110%. That would not happen if each person chose just one reason. Thus, some of those people chose 2 (or more) reasons.
2) The text above the survey states that the survey "...was designed to help determine what respondents see as the potential BENEFITS of adding a website". The word "benefits" is plural; if each person chose just ONE option, then the wording would have stated "...was designed to help determine what respondents see as the potential BENEFIT (singular) of adding a website".

Thus, while we don't know which people chose more than one option from the list, we do know that some of them did.

Question 2 from the set of 3 focuses on a COMPARISON: is one number (PMS) less than 25% of another number (ECB). Your calculations here are correct; we have....

Preserve Market Share(PMS) : 28 Respondents
Expand Customer Base (ECB): 30 Respondents

In simple terms, is 28 less than 30? YES - it clearly is. This does not change regardless of the number of people who are in "both" groups because the overall totals (28 and 30) will still be the same. You are given EXACT data/numbers to work with here, and no 'hypothetical' situation changes those numbers.

Even if you did not do that math though, you can still determine that Question 2 can be inferred based on the percents in each column of the table:
-In the Latino column...what is 25% of 26%? It's 6.5%...Is PMS less than ECB?... is 6% less than 6.5%?.....YES
-In the African American column...what is 25% of 29%? It's 7.25%...Is PMS less than ECB?.....is 6% less than 7.25%....YES
-In the Asian American column...what is 25% of 25%? It's 6.25%....Is PMS less than ECB?.....is 4% less than 6.25%....YES
-In the Native American column...what is 25% of 25%? It's 6.25%....Is PMS less than ECB?....is 6% less than 6.25%....YES

Since each individual column gives us a 'YES' result, summing up all of those numbers would also give us a "YES" result (we'd just be dealing with one big calculation instead of four smaller ones.

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Hi GulfTube,

You've actually spotted the exact fact that makes this statement hold; you just need to push it one step further.

You're right that we don't know the true overlap - it could be the whole preserve-market-share group, none of them, or anywhere in between. Here's the key idea the earlier posts were circling: the people who chose BOTH benefits can never outnumber the smaller of the two groups. Since "preserve market share" is the smaller group in every column, the overlap can't be bigger than that entire "preserve market share" count.

So the worst case - the biggest the overlap could possibly be - is that 100% of the preserve-market-share people also chose expand-customer-base. If even that worst case stays under 25%, then every other case does too.

Testing it column by column

This directly settles your "other minorities" worry - check each group:

- Latino: preserve 6% vs. 25% of expand = 25% x 26% = 6.5% - 6% < 6.5%
- African American:6% vs. 25% x 29% = 7.25% - ✓
- Asian American:4% vs. 25% x 25% = 6.25% - ✓
- Native American:6% vs. 25% x 25% = 6.25% - ✓

In every column, even if all preserve-market-share respondents also chose expand-customer-base, they still form fewer than 25% of the expand group. Holds for every column - holds for all respondents combined. That's why it's Supported.

A quick rehearsal to lock it in

Suppose 40 people chose A and 8 chose B. How many could have chosen both? At most 8 - the overlap can never exceed the smaller group. So "both" is at most 8/40 = 20% of the A group, no matter how the overlap actually falls. Same move here: cap the overlap at the smaller "preserve" figure, then compare.

Answer: Supported

GulfTube
But we cannot figure out that what percentage of 6% latino who said preserve market share overlap with expand customer base. similarly, for other minorities.

question asks about the percentage who chose expand customer base also chose preserve market share, and whether it can be determined that this percentage is less than 25%
since we do not know about the overlap, how can we comment that YES it is less than 25% and hence 'supported'? we do not that out of the 6% latino who choose preserve market share, what percentage also chose preserve market share, could be whole 6%, could be none, could be anywhere in between!

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