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The percentage of households with an annual income of more than $40,00

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Re: The percentage of households with an annual income of more than $40,00 [#permalink] New post  30 Jun 2019, 05:21
egmat wrote:
buymovieposters wrote:
I chose D. The OG says the answer is C and states that it can be inferred.

The reason I chose D was that the stem clearly states that the number of households with an annual income of more than $40k is higher in MC than in any other county.

D essentially restates the argument that MC has greatest number of households with with an annual income of more than $40k. I took this to mean that SC was considered to be "any of the other counties" and therefore could NOT have more people with an larger annual income above $40k.

Where did I go wrong???


Hi,

Coming straight to your question, you went wrong by confusing absolute numbers with percentages. The passage is talking about percentage of households while Option D is talking about actual number of households. These are nto the same things.

However, don't worry. This confuses so many of test takers. You are nor alone :)

To explain this, let's consider the following numbers:

Merton County

Population of MC: 100
Number of people with income above $40K: 60
Percentage of people with income above $40K: 60%

Number of people with income above $60K: 20
Percentage of people with income above $40K: 20%

Sommer County
Population of SC: 1000
Number of people with income above $40K: 400
Percentage of people with income above $40K: 40%

Number of people with income above $60K: 300
Percentage of people with income above $40K: 30%

Now, if you see all the statements in the passage holds; however, option D doesn't hold since MC has 60 people above 40K while SC has 400 people above 40K.

Hope this helps :)

Let me know if you have any further queries.

-Chiranjeev


Hi Payal,

In case choice D had % instead of absolute values, could this be the correct answer choice?

Then the choice D would read - "The percentage of households with an annual income of more than $40,000 is greater in Merton County than in Sommer County."

In that case, I think D should be the better answer choice than C. What you think?

Your response will be appreciated.

Jay
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Re: The percentage of households with an annual income of more than $40,00 [#permalink] New post  30 Jun 2019, 07:05
gmataquaguy wrote:
The percentage of households with an annual income of more than $40,000 is higher in Merton County than in any other county. However, the percentage of households with an annual income of $60,000 or more is higher in Sommer County.

I
(C) Some households in Merton County have an annual income between $40,000 and $60,000.

(D) The number of households with an annual income of more than $40,000 is greater in Merton County than in Sommer County.


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Only C & D are relevant and are close.
The reason why we can leave D out is as we are not sure whether D holds true or not . The figures for Merton county and Sommer county can be equal as well.
Hence only C.
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Re: The percentage of households with an annual income of more than $40,00 [#permalink] New post  17 Jul 2019, 17:59
We are told the percentage of income earners on >$40k is highest in Meriton (M)
We are told Sommer has highest % of households on >=$60k

Obviously there is a disparity between the numbers underlying those percentages.

A is incorrect because this cannot be inferred. For all we know the people in sommer in question could all be on $60k - thats it.
B is incorrect - this may or may not be true. Another county could have highest % of income earners on $50k
C is correct - We are told that M has highest % of income GREATER THAN $40k, so logically some income earners are on between $40 and $60k
D is incorrect and is a trap - we cannot infer anything on the number of households underlying these percentages
E is incorrect - we are only told about specific stratas within the population. Therefore we don't know the averages.
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Re: The percentage of households with an annual income of more than $40,00 [#permalink] New post  30 Aug 2019, 20:03
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I have 1 doubt here :

County M has highest 40k> percentage. So let say this percentage is 50% and in fact all are >60k
Now let say S has 40% between 40-60k.

Now S has highest % for >60k. Say 60% (remaining people ).

Now this situation is satisfying both the conditions. In this case we can have 0% for M between 40-60k. SO how is (c) right?
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Re: The percentage of households with an annual income of more than $40,00 [#permalink] New post  29 May 2020, 03:20
The percentage of households with an annual income of more than $40,000 is higher in Merton County than in any other county. However, the percentage of households with an annual income of $60,000 or more is higher in Sommer County.

The summary of the passage is as follows: There are so many people in Merton County who earn more than $40,000. We also have Sommer county, a county in which so many people earn more than $60,000.


If the statements above are true, which of the following must also be true?


(A) The percentage of households with an annual income of $80,000 is higher in Sommer County than in Merton County. - According to the passage, the only thing that is common between the two counties is that both counties have many people who earn more than $40,000 annually. We do not have information with which we can reasonably conclude that the percentage of households with an annual income of $80,000 is higher in Sommer County than in Merton County. Hence, eliminate (A)

(B) Merton County has the second highest percentage of households with an annual income of $60,000 or more. -We cannot make this inference based on the information provided to us in the passage. It could very well be true that there's a third county with a greater percentage of households with an annual income of $60,000 or more. Hence, eliminate (B)

(C) Some households in Merton County have an annual income between $40,000 and $60,000. - We know for sure that there are many people in Merton County who earn more than $40,000 annually. Hence, we can certainly make (C) as an inference based on the information provided to us in the passage. Therefore, (C) is the right answer choice.

(D) The number of households with an annual income of more than $40,000 is greater in Merton County than in Sommer County. - We do not have exact numbers with which we can make such conclusions; the passage only deals in percentages. Therefore, eliminate (D)

(E) Average annual household income is higher in Sommer County than in Merton County. - Without knowing the actual population size of the two counties, we cannot make this inference. Hence, eliminate (E)
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Re: The percentage of households with an annual income of more than $40,00 [#permalink] New post  06 Jun 2020, 04:24
The percentage and absolute value is tricky in this question. We cannot convert percent into numbers without knowing population of countries in discussion

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Re: The percentage of households with an annual income of more than $40,00 [#permalink] New post  11 Jul 2020, 02:33
(A) The percentage of households with an annual income of $80,000 is higher in Sommer County than in Merton County.
We don't know ho many people in Merton county have an income of $80,000, so we cannot conclude

(B) Merton County has the second highest percentage of households with an annual income of $60,000 or more.
It might have these income, but we don't know for sure

(C) Some households in Merton County have an annual income between $40,000 and $60,000.
Yes, since the Sommer County has equal or more than $60,000, there are some households that have more than $40,000 and less than $60,000. CORRECT

(D) The number of households with an annual income of more than $40,000 is greater in Merton County than in Sommer County.
We cannot say that for sure, because in Sommer county there might be households with more than $ 40,000/60,000

(E) Average annual household income is higher in Sommer County than in Merton County.
we cannot calculate the Average annual income, so we cannot compare and conclude this
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Re: The percentage of households with an annual income of more than $40,00 [#permalink] New post  20 Jul 2020, 22:26
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I went by process of elimination

(A) The percentage of households with an annual income of $80,000 is higher in Sommer County than in Merton County.
> cannot be said, as both the county’s might not have any households with income more than 80K

(B) Merton County has the second highest percentage of households with an annual income of $60,000 or more.
>cannot be said, as we don’t have the data about rest all counties

(D) The number of households with an annual income of more than $40,000 is greater in Merton County than in Sommer County.
>We only know about proportions, not the actual numbers

(E) Average annual household income is higher in Sommer County than in Merton County.
>We only know about proportions, not the actual numbers

IMO its C
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Re: The percentage of households with an annual income of more than $40,00 [#permalink] New post  11 Oct 2020, 16:20
Hello GMATNinja

Passage says -The percentage of households with an annual income of $60,000 or more is HIGHER in SC. But as per your explanation, you are saying passage is saying- SC has HIGHEST Percentage of households with an annual income of $60,000 or more. Could you please explain. Is HIGHER mean HIGHEST in above passage.

GMATNinja wrote:
With questions like this, there isn't a whole lot of analysis to be done up front. As always, we have to make sure that we are paying attention to the details and that we understand the given facts. However, we don't have a conclusion or a line of reasoning that we can break down. So let's just make sure we are clear about the given information:

  • "The percentage of households with an annual income of more than $40,000 is higher in Merton County (MC) than in any other county." Note that we don't know about the NUMBER of households. Also notice that it says "more than $40,000", so this group does not contain households with an annual income equal to $40,000.
  • "The percentage of households with an annual income of $60,000 or more is higher in Sommer County (SC)." Again, we are dealing with percentages and not absolute numbers. However, in this case, the group includes the boundary figure ("$60,000 or more").

If the statements above are true, which of the following must also be true?

Quote:
(A) The percentage of households with an annual income of $80,000 is higher in Sommer County than in Merton County.

MC might have, for example, 2% earning $80k+ while SC only has 1% (or less!) earning $80k+. As long as SC has a higher percentage with an annual income between $60k and $80k, SC could still have a higher percentage earning $60k+. Choice (A) does not have to be true, so eliminate this one.

Quote:
(B) Merton County has the second highest percentage of households with an annual income of $60,000 or more.

There could be a third county that has a higher percentage earning $60k than MC. As we'll see in the explanation for choice (C), this would not necessarily mean that the third county has a higher percentage earning above $40k than MC. Choice (B) might be true, but it does not have to be true. Eliminate (B).

Quote:
(C) Some households in Merton County have an annual income between $40,000 and $60,000.

Let's think about this logically. MC has the highest percentage above $40k. SC has the highest percentage of $60k or more. So how could that be true? Let's start by ignoring the group earning between $40-60k. We know that the percentage earning $60k or more in MC is lower than the percentage earning $60k or more in SC. So if we omit the group earning between $40-60k, it would look like SC has a greater percentage earning above $40k. But we know that the opposite is true: the percentage earning above $40k is higher in MC than in SC.

So how can we make the $40k+ percentage higher in MC without changing the fact that the $60k+ percentage is higher in SC? The only option is to make the $40-60k percentage higher in MC. In other words, if the $40k percentage is higher in MC even though the $60k percentage is LOWER in MC, then the percentage BETWEEN $40k and $60k must be higher in MC. In that case, the statement in choice (C) would have to be true, so hang on to this one.

Quote:
(D) The number of households with an annual income of more than $40,000 is greater in Merton County than in Sommer County.

The given facts pertain to percentages, not absolute numbers. SC might have a much greater population than MC, in which case choice (D) might not be true. Eliminate (D).

Quote:
(E) Average annual household income is higher in Sommer County than in Merton County.

This might be true, but it depends on information that we are not given. SC might have a small percentage earning above $60k while MC has NO households earning above $60k. But MC might have a much larger percentage earning $40-60k. Furthermore, SC could have a much larger percentage earning less than, say, $20k, and that would drag down the overall average. We do not have enough information to determine whether (E) is true, so eliminate this one.

(C) is the best answer.
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Re: The percentage of households with an annual income of more than $40,00 [#permalink] New post  18 Oct 2020, 20:26
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AliciaSierra
Let me answer that on GMATNinja's behalf.
You have eagle's eye as i didn't notice that in his solution 'highest' is mentioned.

Either we can say 'MC has HIGHER percentage ... more than $40,000 than any other county' or 'MC has HIGHEST percentage of households with an annual income of more than $40,000'. The key here is the word 'any' which includes every county other than MC.
Similarly, we can say 'SC has HIGHER percentage of households with an annual income of $60,000 or more than MC'. We can also say that 'SC has HIGHEST percentage of households with an annual income of $60,000 or more' as it is a possibility. However, we can't be sure that SC has HIGHEST as there can be XC, with smaller number of total households, which has HIGHER percentage than SC has, though this is irrelevant as none of the choices suggest that SC has HIGHEST households with an annual income of $60,000 or more.

'SC has HIGHEST percentage of households with an annual income of $60,000 or more' is a possibility - may or may not be true. And that's why B is also a possibility.

gmataquaguy wrote:
The percentage of households with an annual income of more than $40,000 is higher in Merton County than in any other county. However, the percentage of households with an annual income of $60,000 or more is higher in Sommer County.

If the statements above are true, which of the following must also be true?

(A) The percentage of households with an annual income of $80,000 is higher in Sommer County than in Merton County.
(B) Merton County has the second highest percentage of households with an annual income of $60,000 or more.
(C) Some households in Merton County have an annual income between $40,000 and $60,000.
(D) The number of households with an annual income of more than $40,000 is greater in Merton County than in Sommer County.
(E) Average annual household income is higher in Sommer County than in Merton County.


AliciaSierra wrote:
Hello GMATNinja

Passage says -The percentage of households with an annual income of $60,000 or more is HIGHER in SC. But as per your explanation, you are saying passage is saying- SC has HIGHEST Percentage of households with an annual income of $60,000 or more. Could you please explain. Is HIGHER mean HIGHEST in above passage.

GMATNinja wrote:
With questions like this, there isn't a whole lot of analysis to be done up front. As always, we have to make sure that we are paying attention to the details and that we understand the given facts. However, we don't have a conclusion or a line of reasoning that we can break down. So let's just make sure we are clear about the given information:

  • "The percentage of households with an annual income of more than $40,000 is higher in Merton County (MC) than in any other county." Note that we don't know about the NUMBER of households. Also notice that it says "more than $40,000", so this group does not contain households with an annual income equal to $40,000.
  • "The percentage of households with an annual income of $60,000 or more is higher in Sommer County (SC)." Again, we are dealing with percentages and not absolute numbers. However, in this case, the group includes the boundary figure ("$60,000 or more").

If the statements above are true, which of the following must also be true?

Quote:
(A) The percentage of households with an annual income of $80,000 is higher in Sommer County than in Merton County.

MC might have, for example, 2% earning $80k+ while SC only has 1% (or less!) earning $80k+. As long as SC has a higher percentage with an annual income between $60k and $80k, SC could still have a higher percentage earning $60k+. Choice (A) does not have to be true, so eliminate this one.

Quote:
(B) Merton County has the second highest percentage of households with an annual income of $60,000 or more.

There could be a third county that has a higher percentage earning $60k than MC. As we'll see in the explanation for choice (C), this would not necessarily mean that the third county has a higher percentage earning above $40k than MC. Choice (B) might be true, but it does not have to be true. Eliminate (B).

Quote:
(C) Some households in Merton County have an annual income between $40,000 and $60,000.

Let's think about this logically. MC has the highest percentage above $40k. SC has the highest percentage of $60k or more. So how could that be true? Let's start by ignoring the group earning between $40-60k. We know that the percentage earning $60k or more in MC is lower than the percentage earning $60k or more in SC. So if we omit the group earning between $40-60k, it would look like SC has a greater percentage earning above $40k. But we know that the opposite is true: the percentage earning above $40k is higher in MC than in SC.

So how can we make the $40k+ percentage higher in MC without changing the fact that the $60k+ percentage is higher in SC? The only option is to make the $40-60k percentage higher in MC. In other words, if the $40k percentage is higher in MC even though the $60k percentage is LOWER in MC, then the percentage BETWEEN $40k and $60k must be higher in MC. In that case, the statement in choice (C) would have to be true, so hang on to this one.

Quote:
(D) The number of households with an annual income of more than $40,000 is greater in Merton County than in Sommer County.

The given facts pertain to percentages, not absolute numbers. SC might have a much greater population than MC, in which case choice (D) might not be true. Eliminate (D).

Quote:
(E) Average annual household income is higher in Sommer County than in Merton County.

This might be true, but it depends on information that we are not given. SC might have a small percentage earning above $60k while MC has NO households earning above $60k. But MC might have a much larger percentage earning $40-60k. Furthermore, SC could have a much larger percentage earning less than, say, $20k, and that would drag down the overall average. We do not have enough information to determine whether (E) is true, so eliminate this one.

(C) is the best answer.

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Re: The percentage of households with an annual income of more than $40,00 [#permalink] New post  06 Nov 2020, 15:58
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AliciaSierra wrote:
Hello GMATNinja

Passage says -The percentage of households with an annual income of $60,000 or more is HIGHER in SC. But as per your explanation, you are saying passage is saying- SC has HIGHEST Percentage of households with an annual income of $60,000 or more. Could you please explain. Is HIGHER mean HIGHEST in above passage.

GMATNinja wrote:
With questions like this, there isn't a whole lot of analysis to be done up front. As always, we have to make sure that we are paying attention to the details and that we understand the given facts. However, we don't have a conclusion or a line of reasoning that we can break down. So let's just make sure we are clear about the given information:

  • "The percentage of households with an annual income of more than $40,000 is higher in Merton County (MC) than in any other county." Note that we don't know about the NUMBER of households. Also notice that it says "more than $40,000", so this group does not contain households with an annual income equal to $40,000.
  • "The percentage of households with an annual income of $60,000 or more is higher in Sommer County (SC)." Again, we are dealing with percentages and not absolute numbers. However, in this case, the group includes the boundary figure ("$60,000 or more").

If the statements above are true, which of the following must also be true?

Quote:
(A) The percentage of households with an annual income of $80,000 is higher in Sommer County than in Merton County.

MC might have, for example, 2% earning $80k+ while SC only has 1% (or less!) earning $80k+. As long as SC has a higher percentage with an annual income between $60k and $80k, SC could still have a higher percentage earning $60k+. Choice (A) does not have to be true, so eliminate this one.

Quote:
(B) Merton County has the second highest percentage of households with an annual income of $60,000 or more.

There could be a third county that has a higher percentage earning $60k than MC. As we'll see in the explanation for choice (C), this would not necessarily mean that the third county has a higher percentage earning above $40k than MC. Choice (B) might be true, but it does not have to be true. Eliminate (B).

Quote:
(C) Some households in Merton County have an annual income between $40,000 and $60,000.

Let's think about this logically. MC has the highest percentage above $40k. SC has the highest percentage of $60k or more. So how could that be true? Let's start by ignoring the group earning between $40-60k. We know that the percentage earning $60k or more in MC is lower than the percentage earning $60k or more in SC. So if we omit the group earning between $40-60k, it would look like SC has a greater percentage earning above $40k. But we know that the opposite is true: the percentage earning above $40k is higher in MC than in SC.

So how can we make the $40k+ percentage higher in MC without changing the fact that the $60k+ percentage is higher in SC? The only option is to make the $40-60k percentage higher in MC. In other words, if the $40k percentage is higher in MC even though the $60k percentage is LOWER in MC, then the percentage BETWEEN $40k and $60k must be higher in MC. In that case, the statement in choice (C) would have to be true, so hang on to this one.

Quote:
(D) The number of households with an annual income of more than $40,000 is greater in Merton County than in Sommer County.

The given facts pertain to percentages, not absolute numbers. SC might have a much greater population than MC, in which case choice (D) might not be true. Eliminate (D).

Quote:
(E) Average annual household income is higher in Sommer County than in Merton County.

This might be true, but it depends on information that we are not given. SC might have a small percentage earning above $60k while MC has NO households earning above $60k. But MC might have a much larger percentage earning $40-60k. Furthermore, SC could have a much larger percentage earning less than, say, $20k, and that would drag down the overall average. We do not have enough information to determine whether (E) is true, so eliminate this one.

(C) is the best answer.

You’re right to note that Sommer County (SC) does not necessarily have the highest percentage of households with an annual income of $60,000 or more, when compared to that of all other counties. However, SC does have the higher percentage of households at that income level, when compared to that of Merton County (MC). So, the distinction between higher and highest depends on what exactly is being compared. Sorry, I should have made that clearer in the original explanation.

In any case, the point still stands that because SC has a higher percentage of households earning $60k or more than MC has, some households in MC must have an annual income between $40,000 and $60,000. For that reason, (C) is correct.

I hope that helps!
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Re: The percentage of households with an annual income of more than $40,00 [#permalink] New post  22 Dec 2020, 09:03
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gmataquaguy wrote:
The percentage of households with an annual income of more than $40,000 is higher in Merton County than in any other county. However, the percentage of households with an annual income of $60,000 or more is higher in Sommer County.

If the statements above are true, which of the following must also be true?


(A) The percentage of households with an annual income of $80,000 is higher in Sommer County than in Merton County.

(B) Merton County has the second highest percentage of households with an annual income of $60,000 or more.

(C) Some households in Merton County have an annual income between $40,000 and $60,000.

(D) The number of households with an annual income of more than $40,000 is greater in Merton County than in Sommer County.

(E) Average annual household income is higher in Sommer County than in Merton County.



(A) We are said about 60,000 income of Sommer's not about The percentage of households with an annual income of $80,000 is higher in Sommer County than in Merton County.

(B) Maybe or may not be. Not certain. OUT.

(C) Yes, the passage confirms that. Correct.

(D) The passage gave percentage not number. The number maybe greater or lower with regard to the total population of each county. OUT.

(E) We are given information only about a certain level of income. Some other people may have very lower level income or nearest to the have Average annual household income is higher in Sommer County than in Merton County. For the variations, the average will vary.

The answer is C
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Re: The percentage of households with an annual income of more than $40,00 [#permalink] New post  03 Feb 2021, 15:07
The percentage of households with an annual income of more than $40,000 is higher in Merton County than in any other county. However, the percentage of households with an annual income of $60,000 or more is higher in Sommer County.

If the statements above are true, which of the following must also be true?


(A) The percentage of households with an annual income of $80,000 is higher in Sommer County than in Merton County. X
Annual Income Sommer % Merton %
40K-60K 30 40
60K-80K 40 30
80K+ 30 30

i.e. it does not HAVE TO BE TRUE that the % of households with income of 80 grand is higher in Sommer County…

(B) Merton County has the second highest percentage of households with an annual income of $60,000 or more.
We have no way of knowing this from the passage.

(C) Some households in Merton County have an annual income between $40,000 and $60,000.
Correct. The passage states that the % of households with income of MORE than 40K is higher in Merton…so even if nobody makes more than 40,002, we know that at least one household makes 40,001.

(D) The number of households with an annual income of more than $40,000 is greater in Merton County than in Sommer County.
Incorrect. Do not conflate “number” with percentages…in fact, there may be more households in Sommer County with income of 40K + relative to Merton….but because of population distributions the percentage is lower

(E) Average annual household income is higher in Sommer County than in Merton County. X
Percentage is not the same as average
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Re: The percentage of households with an annual income of more than $40,00 [#permalink] New post  23 May 2022, 07:53
AndrewN

Please share your evaluation for my reasoning below:-

PA:-%age of households with annual income more than $40K is higher in Merton County than in any other county. %age of households with annual income of equal to or more than $60K is higher in Somer County than in any other county.

Option A:- This is the incorrect answer choice because households with income equal to or more than $60K are higher in SC. But we don't know the upper limit of this income. The upper limit could be till $70K or $80K. We don't know. Hence, this is incorrect.

Option B:- This is the incorrect answer choice because from the passage above we know that the %age of households with income =>$60K is highest in MC, but we don't know the second highest. It could be SC or any other county. Hence, this is the incorrect answer choice.

Option C:- This is the correct answer choice because the %age of households with income >$40K is highest in SC and the %age of households with income >=$60K is highest in MC. So in between 40K and 60K, there would be some households. Hence, this is the correct answer choice.

Option D:- The passage above talks about percentage. This answer choice is talking about number of households. Hence, we cannot conclude this statement with surety.

Option E:- No mention of per-month income in SC or MC. Average annual household income could be higher in SC or MC. Hence, not necessarily a must be true answer.

Thanks
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Re: The percentage of households with an annual income of more than $40,00 [#permalink] New post  23 May 2022, 08:14
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krndatta wrote:
AndrewN

Please share your evaluation for my reasoning below:-

PA:-%age of households with annual income more than $40K is higher in Merton County than in any other county. %age of households with annual income of equal to or more than $60K is higher in Somer County than in any other county.

Option A:- This is the incorrect answer choice because households with income equal to or more than $60K are higher in SC. But we don't know the upper limit of this income. The upper limit could be till $70K or $80K. We don't know. Hence, this is incorrect.

Option B:- This is the incorrect answer choice because from the passage above we know that the %age of households with income =>$60K is highest in MC, but we don't know the second highest. It could be SC or any other county. Hence, this is the incorrect answer choice.

Option C:- This is the correct answer choice because the %age of households with income >$40K is highest in SC and the %age of households with income >=$60K is highest in MC. So in between 40K and 60K, there would be some households. Hence, this is the correct answer choice.

Option D:- The passage above talks about percentage. This answer choice is talking about number of households. Hence, we cannot conclude this statement with surety.

Option E:- No mention of per-month income in SC or MC. Average annual household income could be higher in SC or MC. Hence, not necessarily a must be true answer.

Thanks

Hello, krndatta. You seem to have a handle on this must be true question. When you have to deal in absolutes, sometimes the task can seem simpler. I agree with your analysis of each option. In fact, you may want to check out this sister question that I dug up from the vault last month and scroll down for my own analysis to compare to yours. There is only one answer choice that is different in that question, even if the order of the other answer choices has been shuffled around.

Thank you for thinking to ask. Keep up the fine work.

- Andrew
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Re: The percentage of households with an annual income of more than $40,00 [#permalink] New post  31 Oct 2022, 14:49
GMATNinja wrote:
With questions like this, there isn't a whole lot of analysis to be done up front. As always, we have to make sure that we are paying attention to the details and that we understand the given facts. However, we don't have a conclusion or a line of reasoning that we can break down. So let's just make sure we are clear about the given information:

  • "The percentage of households with an annual income of more than $40,000 is higher in Merton County (MC) than in any other county." Note that we don't know about the NUMBER of households. Also notice that it says "more than $40,000", so this group does not contain households with an annual income equal to $40,000.
  • "The percentage of households with an annual income of $60,000 or more is higher in Sommer County (SC)." Again, we are dealing with percentages and not absolute numbers. However, in this case, the group includes the boundary figure ("$60,000 or more").

If the statements above are true, which of the following must also be true?

Quote:
(A) The percentage of households with an annual income of $80,000 is higher in Sommer County than in Merton County.

MC might have, for example, 2% earning $80k+ while SC only has 1% (or less!) earning $80k+. As long as SC has a higher percentage with an annual income between $60k and $80k, SC could still have a higher percentage earning $60k+. Choice (A) does not have to be true, so eliminate this one.

Quote:
(B) Merton County has the second highest percentage of households with an annual income of $60,000 or more.

There could be a third county that has a higher percentage earning $60k than MC. As we'll see in the explanation for choice (C), this would not necessarily mean that the third county has a higher percentage earning above $40k than MC. Choice (B) might be true, but it does not have to be true. Eliminate (B).

Quote:
(C) Some households in Merton County have an annual income between $40,000 and $60,000.

Let's think about this logically. MC has the highest percentage above $40k. SC has the highest percentage of $60k or more. So how could that be true? Let's start by ignoring the group earning between $40-60k. We know that the percentage earning $60k or more in MC is lower than the percentage earning $60k or more in SC. So if we omit the group earning between $40-60k, it would look like SC has a greater percentage earning above $40k. But we know that the opposite is true: the percentage earning above $40k is higher in MC than in SC.

So how can we make the $40k+ percentage higher in MC without changing the fact that the $60k+ percentage is higher in SC? The only option is to make the $40-60k percentage higher in MC. In other words, if the $40k percentage is higher in MC even though the $60k percentage is LOWER in MC, then the percentage BETWEEN $40k and $60k must be higher in MC. In that case, the statement in choice (C) would have to be true, so hang on to this one.

Quote:
(D) The number of households with an annual income of more than $40,000 is greater in Merton County than in Sommer County.

The given facts pertain to percentages, not absolute numbers. SC might have a much greater population than MC, in which case choice (D) might not be true. Eliminate (D).

Quote:
(E) Average annual household income is higher in Sommer County than in Merton County.

This might be true, but it depends on information that we are not given. SC might have a small percentage earning above $60k while MC has NO households earning above $60k. But MC might have a much larger percentage earning $40-60k. Furthermore, SC could have a much larger percentage earning less than, say, $20k, and that would drag down the overall average. We do not have enough information to determine whether (E) is true, so eliminate this one.

(C) is the best answer.


Ok Gentlemen, here we go again ... I have some issue with this question ... it says - which of the following MUST BE TRUE?

My logic with (C) was -

If MC has the highest percent of > $40k annual income resident it could also meant that all of them are in two sets: Under $40k (30%), Above $60k (70%), so none b/w 40-60 is possible. Whereas SC could have 90% > $60k and 10% below $60k. This will still keep the above statement true but there will not be any MC resident with income between 40k and 60k, what am I missing? I picked (C) twice by POE but I cannot justify my answer 100% of the time .... yes there's possibility that some of MC resident will make between 40-60k but it's not bullet proof, can you please help GMATNinja or AndrewN?
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The percentage of households with an annual income of more than $40,00 [#permalink] New post  24 Nov 2022, 23:43
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IN2MBB2PE wrote:

Ok Gentlemen, here we go again ... I have some issue with this question ... it says - which of the following MUST BE TRUE?

My logic with (C) was -

If MC has the highest percent of > $40k annual income resident it could also meant that all of them are in two sets: Under $40k (30%), Above $60k (70%), so none b/w 40-60 is possible. Whereas SC could have 90% > $60k and 10% below $60k. This will still keep the above statement true but there will not be any MC resident with income between 40k and 60k, what am I missing? I picked (C) twice by POE but I cannot justify my answer 100% of the time .... yes there's possibility that some of MC resident will make between 40-60k but it's not bullet proof, can you please help


Hey IN2MBB2PE,

I can help with this query 😊.

    1. I looked at the example numbers you have provided. Here is what you are missing!

    2. I can see that you are not 100% sure that option C is Must-Be-True. This video will provide you with clarity about why this choice works beautifully.


There is an important learning here. For me, this question demonstrates the importance of visualizing the given data carefully, keeping every single piece of information in mind. Once small slip can prove disastrous.


Hope this helps!
Harsha
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Re: The percentage of households with an annual income of more than $40,00 [#permalink] New post  30 Nov 2022, 19:39
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IN2MBB2PE wrote:
Ok Gentlemen, here we go again ... I have some issue with this question ... it says - which of the following MUST BE TRUE?

My logic with (C) was -

If MC has the highest percent of > $40k annual income resident it could also meant that all of them are in two sets: Under $40k (30%), Above $60k (70%), so none b/w 40-60 is possible. Whereas SC could have 90% > $60k and 10% below $60k. This will still keep the above statement true but there will not be any MC resident with income between 40k and 60k, what am I missing? I picked (C) twice by POE but I cannot justify my answer 100% of the time .... yes there's possibility that some of MC resident will make between 40-60k but it's not bullet proof, can you please help GMATNinja or AndrewN?

The passage gives us two conditions:

    1) The percentage of households with an annual income of more than $40,000 is higher in Merton County than in any other county.
    2) The percentage of households with an annual income of $60,000 or more is higher in Sommer County.

Your analysis violates the first condition -- 70% of Merton County's population makes over $40,000, while 90% of Sommer County's population makes over $40,000 (because someone who makes over 60k definitely makes over 40k). That's not possible given the info in the passage.

If Merton County has a greater percentage over $40,000, but Sommer has a greater percentage over $60,000, then the ONLY place where Merton can be "winning" against Sommer is in the $40-60k bracket. That's why (C) is the correct answer.

I hope that helps!
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Re: The percentage of households with an annual income of more than $40,00 [#permalink] New post  11 Dec 2022, 04:57
egmat wrote:
IN2MBB2PE wrote:

Ok Gentlemen, here we go again ... I have some issue with this question ... it says - which of the following MUST BE TRUE?

My logic with (C) was -

If MC has the highest percent of > $40k annual income resident it could also meant that all of them are in two sets: Under $40k (30%), Above $60k (70%), so none b/w 40-60 is possible. Whereas SC could have 90% > $60k and 10% below $60k. This will still keep the above statement true but there will not be any MC resident with income between 40k and 60k, what am I missing? I picked (C) twice by POE but I cannot justify my answer 100% of the time .... yes there's possibility that some of MC resident will make between 40-60k but it's not bullet proof, can you please help


Hey IN2MBB2PE,

I can help with this query 😊.

    1. I looked at the example numbers you have provided. Here is what you are missing!

    2. I can see that you are not 100% sure that option C is Must-Be-True. This video will provide you with clarity about why this choice works beautifully.


There is an important learning here. For me, this question demonstrates the importance of visualizing the given data carefully, keeping every single piece of information in mind. Once small slip can prove disastrous.


Hope this helps!
Harsha



Thanks Harsha and GMATNinja for the responses, now I understand what I was missing, much appreciated!
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Re: The percentage of households with an annual income of more than $40,00 [#permalink]
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