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The percentage of households with an annual income of more

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Director
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The percentage of households with an annual income of more [#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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Re: The percentage of households with an annual income of more [#permalink]

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27 Mar 2014, 10:52
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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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Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

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The percentage of households with an annual income of more [#permalink]

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27 Mar 2014, 08:57
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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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20 Aug 2004, 09:08
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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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20 Aug 2004, 10:04
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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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Director
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20 Aug 2004, 11:35
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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 [#permalink]

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20 Jan 2013, 19:58
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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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20 Aug 2004, 10:51
Carsen: The Stimilus says that the percentage of household is higher in Merton county but it says nothing about the "the number".....We just know about the percentages but nothing about absolute numbers.

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20 Aug 2004, 11:01
carsen wrote:
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.

I disagree. We know that the percentage in Merlon of >40K is greater than the percentage in Sommer of 40K.

HENCE, if no one made between 40K and 60K in Merlon, the greatest percentage of >60K would be MERLON and not summer, therefore, it is necessary that atleast 1 person make between 40K and 60K in Merlon.

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20 Aug 2004, 11:11
I agree with SigEpUCI.....I also chose "B" as my Final Answer.

After a while i will post the official answer (the reason i posted this question is coz i was shocked when i saw the OA). I dont understand how it could be the Official Answer.

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CR - Annual Income [#permalink]

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20 Aug 2004, 11:46
D?

more people * 40000 = average salary high

more people * 60000 = average salary becomes less

consider a pyramid structure

top = more salary ,less people
mid= more people than top less salary that top
low= most people, less salary
Hence avg comes down

Initially I chose C , but this might be true?

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CR- Annual income [#permalink]

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20 Aug 2004, 11:56
A) No household in Merton county has an annual income of \$60,000 or more.

< Cannot be inferred from passage >

B) Some households in Merton county have an annual income between \$40,000 and \$60,000

< Cannot be inferred from passage >

C) THe number of households with an annual income of more than \$40,000 is greater in Merton than in Sommer County

<high percentage might not reflect high numbers ,since 90% of 100 < 10% of 500000)

D) Average annual household income is higher in Sommer than in Merton County

<option that might be true>

E) The percentage of households with an annual income of \$80,000 is higher in Sommer than in Merton County.
< Cannot be inferred from passage >

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20 Aug 2004, 11:57
How about this as a rebuttal to D.

Summer county, 1 person > 60000, 100 people at 1000 yearly income.
Merlot, 0 person > 60000, 100 peaple at 40000.

summer average = 1100
merlot average = 40000

Clearly D is not correct.

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20 Aug 2004, 12:20
SigEUCI,

The stimulus reads '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'

The above info is given already. Why do we need to presume the numbers you have outlined..
Summer county, 1 person > 60000, 100 people at 1000 yearly income.
1 person is wrong, it should be atleast 51%. Others can be 1000 perfect.

Merlot, 0 person > 60000, 100 peaple at 40000. Again 51% should be astleast 41k 9or any number just above 40k)

[summer average = 1100
merlot average = 40000] ..this will change.
[/i]

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20 Aug 2004, 12:26
venksune wrote:
SigEUCI,

The stimulus reads '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'

The above info is given already. Why do we need to presume the numbers you have outlined..
Summer county, 1 person > 60000, 100 people at 1000 yearly income.
1 person is wrong, it should be atleast 51%. Others can be 1000 perfect.

Merlot, 0 person > 60000, 100 peaple at 40000. Again 51% should be astleast 41k 9or any number just above 40k)

[summer average = 1100
merlot average = 40000] ..this will change.
[/i]

In order to disapprove a conclusion of "True for all X", one just needs to show a single case when the conclusion is not False. I assigned arbitrary numbers to show that answer D does not hold true for every case.

where did greater than 51% come from?

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20 Aug 2004, 12:30
From the stimulus..

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

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20 Aug 2004, 12:34
Let me shoot down 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..]

This is definately not the case.

Houses in Merlot = 10, all of them make >40000 and all < 60000= hence 100%

House in Summer = 100, 20 > 40000 and all make > 60000 = hence 20% > 40000, BUT more numbers.

So C (just like D) can not be concluded. To be a valid answer, it must hold true for every possible assignment that obeys the rules in the premise.

Proof by contradiction for B. (HERE IT IS)

Assume B is not true.

We know that the %>40 in Merlot is greater than the %>40 in Sumner.

if B is not true, than everyone in Merlot makes >60. in that case, the first premise that Merlot has the highest proportion over 40 really means, Merlot has the highest proportion over 60. This directly contradicts the second premise. Hence B can not be false, and must be true.

If someone would like to assign numbers to the problem in an attempt to prove B wrong, I would love to see it.

If the OA is not B, then the OA is wrong. Whats the source of this question?

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20 Aug 2004, 12:36
venksune wrote:
From the stimulus..

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

The percentages are relative to one another.

If the percent of people >40 in Merton is 2%, and in every other county (including Sommer) is 1%, the premises are still valid.

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20 Aug 2004, 12:48
This is getting even better. SigEpUCI, dont mistake me, I am stretching this argument so as to get it right - not in the sense of an argument. Ok, here is my defense,

1. B is a right assumption - need not be a conclusion.
2. Going by your argument, if people in Merton county can have a 60K earning - then people in Sommer country can be assumed to have a number like 100K.
3. I just read the 2%, 1% stuff you had replied on - I think the stimulus perhaps have been wrongly read. My understanding is that the stimulus says that majority of people in Merton county has incomes >than 40k and that the majority of people in Sommer county has incomes >than 60k.

The more this stimulus is creating discussion - the ambiguity of the stimulus is only getting stronger. So, if not anything, I agree that the question is not the GMAT quality.

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20 Aug 2004, 13:21
venksune wrote:
This is getting even better. SigEpUCI, dont mistake me, I am stretching this argument so as to get it right - not in the sense of an argument. Ok, here is my defense,

1. B is a right assumption - need not be a conclusion.
2. Going by your argument, if people in Merton county can have a 60K earning - then people in Sommer country can be assumed to have a number like 100K.
3. I just read the 2%, 1% stuff you had replied on - I think the stimulus perhaps have been wrongly read. My understanding is that the stimulus says that majority of people in Merton county has incomes >than 40k and that the majority of people in Sommer county has incomes >than 60k.

The more this stimulus is creating discussion - the ambiguity of the stimulus is only getting stronger. So, if not anything, I agree that the question is not the GMAT quality.

Yeah, agree with that. I'm not trying to get into an arugment here, only a friendly debate. However, I don't agree that B is an assumption, i think B can absoluty be concluded from the premises. If you could provide a situation where the premises are both true, and B is not true, i would be very impressed!

I'm curious to see what the OA is, lets have it!

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