Should the choices made by 100 participants in a survey about Product

Question

Should the choices made by 100 participants in a survey about Product X be said to proportionately represent the preferences of the entire population?

(1) ﻿﻿﻿In the survey of 100 participants, 70% said they preferred Product X.

﻿﻿﻿﻿(2) While the survey provided valuable insights into Product X, the small sample may not be representative of the entire population's preferences.

Source: Official Guide 2024-25 (DI Review)
ID: 700337

MartyMurray · Accepted Answer

Should the choices made by 100 participants in a survey about Product X be said to proportionately represent the preferences of the entire population?

This question is pretty tricky. It's easy to get the impression that the question is asking whether the participants in the survey are representative of the population as a whole.

That's not the question asked though. The question is more mathematical; it's whether the responses "proportionately represent the preferences of the entire population."

And here's the thing, the survey responses could proportionately represent the preferences of the entire population even if the sample made up of the survey participants is not representative of the entire population and even if the  sample is small.

(1) ﻿﻿﻿In the survey of 100 participants, 70% said they preferred Product X.

This statement is clearly insufficient because it doesn't provide information on the preferences of the entire population. So, it doesn't indicate whether 70 percent preferring Product X proportionally represents the preferences of the entire population. In the entire population, 70 percent or some other percentage could prefer Product X.

Insufficient.

﻿﻿﻿﻿(2) While the survey provided valuable insights into Product X, the small sample may not be representative of the entire population's preferences.

This statement is tricky. It indicates that the sample is so small that it may not be representative of the entire population. So, we could get the impression that this statement is sufficient because it indicates that the sample is too small to reliably represent the entire population.

However, the question is not whether the sample reliably represents the entire population. It's whether the responses proportionately represent the preferences of the entire population.

Regardless of how small the sample is, the responses could proportionally represent the preferences of the entire population. For instance, a tiny sample of ten people could proportionally represent the preferences of the entire population if 7 out of 10 prefer Product X and 70 percent of the members of the population do as well.

So, this choice doesn't indicate whether the responses proportionately represent the preferences of the entire population since they could even though the sample or partcipants may be  too small to reliably represent the entire population.

Insufficient.

(1) and (2) combined

With the statements combined, we still don't know whether 70% of participants preferring Product X matches the percentage of the entire population preferring Product X.

Insufficient.

Correct answer:  E

KarishmaB · Answer

Question: Should we say that the survey results of 100 people represent the preferences of the entire population?

We need data to answer this question. It is possible that survey results do represent the preferences of the entire population and it is possible that they do not. A sample may or may not represent the preferences of the entire population (depending on whether it has biases or not etc.)

(1) ﻿﻿﻿In the survey of 100 participants, 70% said they preferred Product X.

The actual result of the survey is irrelevant. Our question is whether the result represents the preferences of the entire population.
Irrelevant data.

﻿﻿﻿﻿(2) While the survey provided valuable insights into Product X, the small sample may not be representative of the entire population's preferences.

This option tells us nothing about whether the results are representative of the entire population's preferences.
The small sample may not be representative of the entire population's preferences, but that also means that it may be. We are not given that "this small sample is not representative of the entire population's preferences". All we are given is that it may not be. But we already know that. It may or may not be.

Hence insufficient alone.

Combining data from both statements won't help because statement 1 gives irrelevant data and statement 2 gives something we already know. 
 Answer (E)

GMATinsight · Answer

OFFICIAL EXPLANATION:

Inference (1) Whatever specific percentage of the survey participants said they preferred Product X, the percentage of individuals with that preference in a much larger population might be exactly the same or much different. Thus, whether the survey participants’ choices should be said to proportionately represent the entire population’s preferences cannot be determined from (1) alone; NOT sufficient.

(2) The statement that a small sample may not be representative of a population’s preferences suggests that the sample also may be representative of that population’s preferences. Thus, whether the survey participants’ choices should be said to proportionately represent the entire population’s preferences cannot be determined from (2) alone; NOT sufficient.

If (1) and (2) are both true, it is possible that 70% of the broader population prefers Product X, just as 70% of the survey respondents claimed to prefer it, but it’s also possible that some much different percentage of the broader population prefers Product X. Thus, whether the survey participants’ choices should be said to proportionately represent the entire population’s preferences cannot be determined even from both statements together.

The correct answer is E; both statements together are still not sufficient.

PReciSioN · Answer

MartyMurray  , but statement 2 says " may not be representative of the entire population's  preferences."    Not   "may not be representative of the entire population" 
Isn't not being representative of a groups preferences essentially mean that you don't proportionately represent their preference. 
I believe that E should be the answer since may not be is, logically speaking, equivalent to may be and doesn't tell us much.

sayan640 · Answer

MartyMurray  , I also think the way   PReciSioN  thought.  
Would you  like to check your explanation again , in the light of our arguments ( highlighted part )  KarishmaB

SundayRoast · Answer

Thank you for the detailed response as for the DS its so hard to tell if they are dealing with absolute yes/no answers, partially yes or no, in general etc. Any tips? Thank you!

cledgard · Answer

I disagree with the answer: If the question had been "do the choices made by 100 participants in a survey about Product X proportionately represent the preferences of the entire population? " I would have answered E because I cannot know the answer.
However, the question is stated differently: Should the choices made by 100 participants in a survey about Product X  be said to  proportionately represent the preferences of the entire population? Stated that way, looking at statement (2) I can infer that it cannot be said to proportionally represent. Whether the survey may be representative or not, compels me to answer that the choices should not be said to represent the population, for the simple reason that I do not know whether they do.
The problem is in the question itself: "should be said". None of the explanations address this problem. It is not the same to ask "whether they represent" as to ask "whether they can be said to represent". In the former I would say I do not know E; in the latter I woud answer NO, 2 is sufficient. This answer does not mean that the choices are not representative; it means that the choices cannot be said to be representative.
This small change in semantics is important. In OG 2025, in 2- part analysis and in data sufficiency, I have found several exercises in which the answers focus on so small differences in semantics.
I really would like some expert opinion on this subject.  KarishmaB

KarishmaB · Answer

Hi Clipper,

Thank you for the shoutout. 
I get where you are coming from and a phrasing as you described would make the question clearer, I agree, but the way I interpret the current phrasing is this:

Should A be said to proportionately represent B?

Well, if I find that the population's (say 10k people) preferences are 7k in favor and 3k against and the survey's 100 people's preferences are 70 in favor and 30 against, then A should be said to  proportionately represent B.

If I find that the population's (say 10k people) preferences are 5k in favor and 5k against and the survey's 100 people's preferences are 70 in favor and 30 against, then A should be said to not proportionately represent B.

Whether something should be said to proportionately represent something else depends on what I find from the data. The way I see it, without the data, I cannot make a call. After all, statement 2's only concern is that the sample is small and may not represent the population. But I am not given anything about what exactly the data says. For sufficiency, I must answer with a definite Yes or a No.

Am I sure that the answer to the below question is NO?
"Should A be said to proportionately represent B?"

I am not sure. Hence (E) seems to make sense to me.

BinodBhai · Answer

(1) Doesn't even address the question. So insufficient. Out.

(2) 'may' means ambiguity. So it can be Yes or No. So Insufficient. Out

1+2 - again doesn't ans.  E

vallequalle · Answer

I dont think the 'may' is the word to focus on here even though it might be tempting.

Should the choices made by 100 participants in a survey about Product

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