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

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The percentage of households with an annual income of more than $40,00  [#permalink]

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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.


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Originally posted by gmataquaguy on 20 Aug 2004, 09:57.
Last edited by Bunuel on 08 Oct 2018, 08:45, edited 1 time in total.
Renamed the topic and edited the question.
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Re: QOTD: The percentage of households with an annual income of more  [#permalink]

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New post 08 Jan 2018, 07:10
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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]

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New post 20 Aug 2004, 10:08
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Answer is B.

Merlon has highest %>40

Summer has highest %> 60

If everyone in Merlon who made over 40,000 also made over 60,000, then Merlon would have the highest %> 60. Hence at least 1 person in Merlon must make between 40 and 60.
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Re: The percentage of households with an annual income of more than $40,00  [#permalink]

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New post 20 Aug 2004, 11:04
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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 highest in Sommer County.

If the statements above are true, which of the following can properly be concluded on the basis of them?

A) No household in Merton county has an annual income of $60,000 or more. - Household in Merton may have one or 2 or less people with 60K income. This is unknown. Hence - Out.

B) Some households in Merton county have an annual income between $40,000 and $60,000 - May be that some of the merton household have income more than 60K and none of them between 40k and 60K. This is not stated, and we cannot assume. - Hence OUT.

C) THe number of households with an annual income of more than $40,000 is greater in Merton than in Sommer County - This is clearly stated in the main statement. This is the correct one. Unless until stated or can be referred clearly, we cannot assume..

D) Average annual household income is higher in Sommer than in Merton County - We do not have numbers, hence we cannot know about the average. Hence OUT

E) The percentage of households with an annual income of $80,000 is higher in Sommer than in Merton County- Same case as D. Hence OUT.
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Re: The percentage of households with an annual income of more than $40,00  [#permalink]

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New post 20 Aug 2004, 12:35
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I am tempted to choose D. Let me explain.

Going by general fundamentals on avgs's we know that when it comes to weighted avg's the avg inclines itself towards that number whose weight is more. So the avg income in Somer county is more that in Merton county.

Let me elaborate with some numbers.

Merton county - majortiy if >40k income (Say 45k). Lets assume 100 people and 60 people with >40k income. The remaining would be less than 40k (say 35k).

Avg = (60*45 + 40*35)/100 = 41k (closer to 40k than 35k)

For Sommer country - going by the same logic and similar no.s, we have

Avg = (60*65 + 40*55)/100 = 61k (closer to 60k)

So D.
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Re: The percentage of households with an annual income of more than $40,00  [#permalink]

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New post 20 Aug 2004, 14:29
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Damn, i'm really trying to beat this one dead.

Lets think of it like this.

Lets assume for a second that M county has 40% population above 40,000 a year.

We know that S county has less than 40% population above 40,000 by the stimulus. We therefore also now that whatever percent of the population that makes greater than 60,000 is also less than 40% (since those who make greater than 60,000 are a subset of those who make greater than 40,000).

Now, if no one in M county made between 40000 and 60000, that would mean 40% of the population made more than 60000. (since 40% made more that 40000, and no one made between 40000 and 60000.

Since we know that that percent of people in S county who made more than 60000 is necessarily less than 40%, we arrive at the conclusion that
M is higher than S in terms of percentage making greater than 60000. This contradicts the second premise. Hence B must be true.

Some people must make between 40000 and 60000 in M, so that S (who lacks the biggest percentage in the 40000+ range, can gain the highest percentage in the 60000+ range.

Let me know if that makes sense!
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Re: The percentage of households with an annual income of more than $40,00  [#permalink]

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New post 10 Jan 2013, 12:54
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???
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Re: The percentage of households with an annual income of more than $40,00  [#permalink]

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New post 20 Jan 2013, 20:58
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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
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Re: The percentage of households with an annual income of more than $40,00  [#permalink]

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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 highest in Sommer county. If the statements above are true, which of the following can properly be concluded on the basis of them?

A. No household in Merton county has an annual income of $60,000 or more.
B. Some households in Merton county have an annual income between $40,000 and $60,000.
C. The number of households with an annual income of more than $40,000 is greater in Merton than in Sommer county.
D. Average annual household income is higher in Sommer than in Merton county.
E. The percentage of households with an annual income of $80,000 is higher in Sommer than in Merton county.

Hi, I added this as previous posts don't have OA.
Can anyone explain why A is wrong, please.
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Re: The percentage of households with an annual income of more than $40,00  [#permalink]

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New post 27 Mar 2014, 11:52
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goodyear2013 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 highest in Sommer county. If the statements above are true, which of the following can properly be concluded on the basis of them?

A. No household in Merton county has an annual income of $60,000 or more.
B. Some households in Merton county have an annual income between $40,000 and $60,000.
C. The number of households with an annual income of more than $40,000 is greater in Merton than in Sommer county.
D. Average annual household income is higher in Sommer than in Merton county.
E. The percentage of households with an annual income of $80,000 is higher in Sommer than in Merton county.

Hi, I added this as previous posts don't have OA.
Can anyone explain why A is wrong, please.

Dear goodyear2013,
I'm happy to help. :-)

Variants of this question are jumbled all over GC --- different orders and different combinations for the answer choices. FYI, in this configuration, (B) is the OA, not (C). Choice (C) makes the classic numbers/percentage confusion, a tried and true trap.

Why is (A) wrong? The short answer is: it's too extreme. When you are drawing a conclusion or inference on the GMAT CR, any choice with "always", "never", "no", "none", "every", etc. are usually not going to work. Any answer making any kind of absolute statement typically does not work.

Think about it. The prompt says: "the percentage of households with an annual income of $60,000 or more is highest in Sommer county." What could this mean? Well, it could mean:
Sommer county: 10% of households have income > $60K
Merton county: 5% of households have income > $60K
This would be 100% consistent with the information in the prompt. If 5% of the households in Merton county have incomes over $60,000, then that's obvious more than zero. Choice (A) makes the fallacy that if P > Q, then it must be true that Q is zero. That's far too much of a leap, given only that P > Q.

Does this make sense?
Mike :-)
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Re: The percentage of households with an annual income of more than $40,00  [#permalink]

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New post 06 May 2014, 01:24
B is the correct answer! I met it in the OG 13th and Im sure that the correct one is B, NOT C
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Re: The percentage of households with an annual income of more than $40,00  [#permalink]

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New post 06 May 2014, 06:26
nhanqtvn wrote:
B is the correct answer! I met it in the OG 13th and Im sure that the correct one is B, NOT C

everyone is saying the answer is B but when i marked B as my answer the system gave C as the right one.
Can anyone check on this
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Re: The percentage of households with an annual income of more than $40,00  [#permalink]

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New post 06 May 2014, 13:57
tyagigar wrote:
nhanqtvn wrote:
B is the correct answer! I met it in the OG 13th and Im sure that the correct one is B, NOT C

everyone is saying the answer is B but when i marked B as my answer the system gave C as the right one.
Can anyone check on this

Dear tyagigar,
I just changed the OA in the top entry to (B). I had said that in my post, the second on the page, but this brings everything on the page into consistency.

My friend, don't naively assume that questions on all GMAT Club are entered flawlessly with no absolutely errors. Anyone, ANYONE, can submit a question here. "Anyone" is an awfully big category --- someone who barely knows English, someone who has been awake for 30 hours, someone who is drunk, etc. Many people are quite careful, but some people entering questions make all kinds of mistakes --- spelling mistakes, missing sentences, missing diagrams, and yes, entering the wrong letter as the OA. Don't naively assume that the way it was entered by the first person is perfect. If everyone on the page, including experts, agrees that the answer is something else, that's a very good sign that the system, based on how the first person entered it, is not to be trusted.

Does all this make sense?
Mike :-)
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Re: QOTD: The percentage of households with an annual income of more  [#permalink]

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New post 15 Apr 2017, 07:30
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Economist 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.


Source : OG2017, Diagnostic Test, V72, P35

Merton County
 
Step 1: Identify the Question

The question asks which of the answers must also be true, so this is an Inference question.

Step 2: Deconstruct the Argument

>40K: M highest %
>60K: S % > M %

Step 3: Pause and State the Goal

On Inference questions, the answer is something that must be true based on the information in the argument. If any part of an answer is not supported by the given information, then that answer is not correct.

Step 4: Work from Wrong to Right

(A) The argument confirms that the percentage of households in Sommer County with incomes above $60,000 is higher than the percentage in Merton County, but no information is provided about incomes over $80,000. This answer might not be true if many households in Sommer County have incomes between $60,000 and $80,000.
(B) No other counties are mentioned in the argument. Merton County could be the county with the second highest percentage of incomes over $60,000 (after Sommer County), but there could be other counties above Merton.
(C) CORRECT. For Merton County to have the highest percentage of households with income over $40,000 but not the highest percentage with income over $60,000, some households must be in the first group (over $40,000) but not the second group (over $60,000). These households are those with income between $40,000 and $60,000.
(D) The argument provides information only about percentages of households in each county with certain income levels. The number of households with these income levels depends on the size of the county. If Merton County has many fewer households than Sommer County, this answer might not be true.
(E) The argument provides information only about the percentage of households exceeding particular income thresholds; this information is not sufficient to calculate averages. Consider what might happen to average income if one household with an annual income of $10B moved from one county to the other.
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Re: QOTD: The percentage of households with an annual income of more  [#permalink]

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New post 08 Jan 2018, 08:42
souvik101990 wrote:

Verbal Question of The Day: Day 195: Critical Reasoning


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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.


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(A) The percentage of households with an annual income of $80,000 is higher in Sommer County than in Merton County. - We can't be sure about it. Maybe, Merton County has more people with annual income greater than $80,000, considering that >$40000 includes all such incomes.
(B) Merton County has the second highest percentage of households with an annual income of $60,000 or more. - We don't have enough information to conclude that. What about the data of other counties?
(C) Some households in Merton County have an annual income between $40,000 and $60,000. - This could be true. Maybe, Merton County has many individuals with annual incomes between $40000 and $60000 and therefore, it cannot exceed the annual income of Sommer County.
(D) The number of households with an annual income of more than $40,000 is greater in Merton County than in Sommer County. - From the evidence cited above, this could not be concluded with surety. Maybe, greater percentage of households in Sommer County have annual income less than $40,000
(E) Average annual household income is higher in Sommer County than in Merton County. - We can't conclude this. If 70% households in Merton County have incomes greater than $40,000, while only 15% households have income greater than $60,000, we could have an exception. Additionally, we don't have any info on sample size of both counties. Thus, inconclusive.

Thus, C is the answer.
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