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 benefit Latino (459 respondents) African American (394 respondents) Asian American (438 respondents) Native American (279 respondents) Expand customer base 26% 29% 25% 25% Improve communication 15% 4% 4% 6% Increase customer satisfaction 5% 17% 28% 6% Increase ratio of profits to costs 14% 19% 17% 19% Increase tax savings 0% 1% 0% 0% Preserve market share 6% 6% 4% 6% Save time 4% 3% 13% 2% Other 3% 3% 5% 4% No benefit 27% 17% 22% 21% Uncertain 10% 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 .

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 benefit Latino (459 respondents) African American (394 respondents) Asian American (438 respondents) Native American (279 respondents) Expand customer base 26% 29% 25% 25% Improve communication 15% 4% 4% 6% Increase customer satisfaction 5% 17% 28% 6% Increase ratio of profits to costs 14% 19% 17% 19% Increase tax savings 0% 1% 0% 0% Preserve market share 6% 6% 4% 6% Save time 4% 3% 13% 2% Other 3% 3% 5% 4% No benefit 27% 17% 22% 21% Uncertain 10% 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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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 JusTLucK04,

The percents in the table are specific enough to help you do a "comparison" instead of a calculation, but if you wanted to see the math, then here it is:

In the first column, we have 459 Latino respondents:

26% think that a website will help to expand the customer base:
26%(459) = about 119

6% think that a website will help maintain/preserve market share:
6%(459) = about 28

The second question in the set asks if the idea that the second number is LESS THAN 25% of the first number.

25%(119) = about 30. Since 28 < 30, this IS a reasonable/supported conclusion.

Now, performing these calculations is NOT really what this question is about (and it's not required either). The "shortcut" is to compare the percentages, since the percentages are both based on the SAME total number of respondents in the survey (and as such, THAT number doesn't really matter to this question).

In the Latino column...is 6% less than 1/4 of 25%.....YES
In the African American column...is 6% less than 1/4 of 29%....YES
In the Asian American column...is 4% less than 1/4 of 25%....YES
In the Native American column...is 6% less than 1/4 of 25%...YES

This is a constant, reasonable conclusion, so the answer to the second question is YES/SUPPORTED.

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Do we need to calculate in these types of questions because it has only asked whether it can be inferred from the data?

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Do we need to calculate in these types of questions because it has only asked whether it can be inferred from the data?

In integrated reasoning, for something to be "inferred," it must be true. For example, if you can find a true or false answer for a question, if the answer is false, it is not inferrable. IR inference and DS differ in this way.

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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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29 Mar 2024, 15:41

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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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26 Mar 2026, 23:55

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tushain

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 benefit	Latino (459 respondents)	African American (394 respondents)	Asian American (438 respondents)	Native American (279 respondents)
Expand customer base	26%	29%	25%	25%
Improve communication	15%	4%	4%	6%
Increase customer satisfaction	5%	17%	28%	6%
Increase ratio of profits to costs	14%	19%	17%	19%
Increase tax savings	0%	1%	0%	0%
Preserve market share	6%	6%	4%	6%
Save time	4%	3%	13%	2%
Other	3%	3%	5%	4%
No benefit	27%	17%	22%	21%
Uncertain	10%	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.

Show Spoiler

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 benefit	Latino (459 respondents)	African American (394 respondents)	Asian American (438 respondents)	Native American (279 respondents)
Expand customer base	26%	29%	25%	25%
Improve communication	15%	4%	4%	6%
Increase customer satisfaction	5%	17%	28%	6%
Increase ratio of profits to costs	14%	19%	17%	19%
Increase tax savings	0%	1%	0%	0%
Preserve market share	6%	6%	4%	6%
Save time	4%	3%	13%	2%
Other	3%	3%	5%	4%
No benefit	27%	17%	22%	21%
Uncertain	10%	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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Updated on: 20 Jul 2026, 01:17

Originally posted by GulfTube on 02 Jul 2026, 11:44.
Last edited by GulfTube on 20 Jul 2026, 01:17, edited 1 time in total.

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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 expand customer base, could be whole 6%, could be none, could be anywhere in between!

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03 Jul 2026, 02:14

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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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11 Jul 2026, 11:24

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Foe statement 2:

It is true that we don't know how much of the 6% overlaps with the 26%. However, the point is that if there is no overlap between the two, then the overlap is simply 0%, which is obviously less than 25%.

Now consider the other extreme case. Suppose there is complete overlap, meaning the entire 6% lies within the 26%. Even in that scenario, the overlap is only 6%, which is still less than 25% (6/26 which is 23%).

Since both extremes satisfy the condition, and every possible degree of overlap lies between these two cases, the overlap can never exceed 25%, and this will be true for all 4 sets of respondents - even in an extreme case if you assume complete overlap, it will be less than 25%. Therefore, the second statement is true.

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20 Jul 2026, 01:39

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This is what I have understood for second statement of this question:

Let total Latino respondents be x
Preserve market share: 0.06*x
Expand customer base: 0.26*x

of those who prefer expand customer base, how many also believe in preserving market share?
we know there could be complete overlap, some overlap or none at all.

Lets start with complete overlap: all those who said PMS also said ECB. then 0.06x/0.26x = 23% since this is fewer than 25%, any fewer overlap will certainly be less than 25% b/c as overlap of PMS with ECB decreases the numerator of above fraction will decrease while denominator remains same. Thereby we can confidently say that for any overlap, the percentage is less than 25%. which is why this statement is supported.

Let's also check for other minorities:
African American: 0.06/0.29 = 20.7% (you could bypass this calculation by observing that the numerator is same as Latino but denominator has increased, thereby the fraction will be lesser than that of Latino anyway)
Asian American: 0.04/0.25 = 16% (complete overlap is less than 25% hence any fewer overlap will be surely less than 25%)
Native American: 0.06/0.25 = 24% (less than 25%)

this confirms that for all minorities, complete overlap of PMS & ECB is less than 25% thereby any lesser overlap will surely be less than 25%. statement is supported.

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21 Jul 2026, 09:26

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For anyone echoing the same sentiment in 2026:

If I say doing XYZ will preserve my market share does not necessarily mean that I am concerned about my market share. In fact the survey does not give us any data about any concerns the respondents may have. It just explores "benefit - if so of what variety - or no benefit". Marking "preserve market share" on a survey simply means those people think that the market share will be maintained but the survey data by itself does not for sure tell us whether these people are worried about their current market share. Maybe they are happy with whatever the market share is currently but think maintaining the same would be a benefit.

Similarly, if I mark "increase customer base" on a survey that does not necessarily mean that I am worried about my current customer base - it simply means that whatever is the current base can be increased further.

Important to not make assumptions that are not necessarily supported by the passage/data here. Again - CR proficiency would typically help you avoid such traps.

keats

If you can shed light on C part of the question. How is it not supported ?

The people who say 'Preserve Market Share' probably will be the ones who dread that they will lose market share. So, why can't I infer the same ?

Please if you can take me in the right direction ?

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22 Jul 2026, 07:48

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Statement 1,
Answer: Supported
Explanation: To determine if more than 50% believe a website could benefit them, we can look at the respondents who explicitly stated there is "No benefit" or were "Uncertain." If we add the percentages of these two groups together for each demographic:

Latino: 27% (No benefit) + 10% (Uncertain) = 37%
African American: 17% (No benefit) + 11% (Uncertain) = 28%
Asian American: 22% (No benefit) + 13% (Uncertain) = 35%
Native American: 21% (No benefit) + 10% (Uncertain) = 31%

Statement 2,
Answer: Supported
Explanation: This conclusion asks us to look at the overlap between two groups: those who chose Expand customer base and those who chose Preserve market share.
Even without knowing exactly how many people chose both, we can find the maximum possible overlap. The maximum number of people who could have chosen both is limited by the total number of people in the smaller group ("Preserve market share"). Let's calculate the ratio of the smaller group to the larger group for each column:

Latino: 6% (Preserve) / 26% (Expand) = 23.1%
African American: 6% (Preserve) / 29% (Expand) = 20.7%
Asian American: 4% (Preserve) / 25% (Expand) = 16.0%
Native American: 6% (Preserve) / 25% (Expand) = 24.0%

Statement 3,
Answer: Not supported
Explanation: This statement requires an assumption that the data does not provide. The survey measures what respondents view as the potential benefits of adding a website.
While it is true that a small proportion of respondents (4% to 6%) believe a website will help them preserve their market share, we cannot logically conclude that the rest are not concerned about losing market share. It is entirely possible that many respondents are highly concerned about losing market share, but they simply do not believe a website is the correct tool to solve that specific problem. Because the survey does not measure general business anxieties, this conclusion is not supported by the table.

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16 Aug 2026, 04:48

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Statement 1
"A majority of the respondents believe adding a website could benefit their businesses."
Total Respondents: 459 + 394 + 438 + 279 = 1,570 total respondents.
Respondents who DO NOT see a potential benefit:
"No benefit":
Latino: 27% x 459 = approx 124
African American: 17% x 394 = approx 67
Asian American: 22% x 438 = approx 96
Native American: 21% x 279 = approx 59
"Uncertain":
Latino: 10% x 459 = approx 46
African American: 11% x 394 = approx 43
Asian American: 13% x 438 = approx 57
Native American: 10% x 279 = approx 28
Total non-benefiting / uncertain respondents = 124 + 67 + 96 + 59 + 46 + 43 + 57 + 28 = 520.
Respondents who DO see a benefit: 1,570 - 520 = 1,050.
Percentage who see a benefit: 1,050/1,570 approx 66.9%, which is greater than 50% (a majority).

This can obviously be inferred without calculation

Verdict: Supported

Statement 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."
The survey allows respondents to select potential benefits, but the table only lists the overall percentage for each benefit independently.
It provides no data on overlap (i.e., how many individual people selected both "Expand customer base" and "Preserve market share").
Verdict: Not supported

Statement 3
"Only a small proportion of the respondents are concerned that they are losing market share."
The survey asks respondents what they see as potential benefits of adding a website (e.g., "Preserve market share").
It does not survey respondents about their concerns, fears, or whether they are currently losing market share. Inferring voter motivation or concern from a list of potential benefits is an unstated assumption.
Verdict: Not supported

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