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This might have come many times. The percentage of

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This might have come many times. The percentage of [#permalink]

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New post 11 Aug 2009, 05:33
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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: This might have come many times. The percentage of [#permalink]

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New post 11 Aug 2009, 06:05
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Economist wrote:
This might have come many times.

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

Can anyone give an example on why D is wrong ? If the percent of households within each county is considered then always average annual household income will be greater in Sommer.
Eg. 50% of all households in Sommer have 60,000 and 49% of all households in Merton have 59,000 income. As per my understanding Sommer's average will always be greater than Merton if we consider "percentage of households separately within each group". Where is the flaw?


Lets say I add the premises - The percentage of households with an annual income below $10,000 is also highest in Sommer.
I hope you are getting, what I am setting. :)

You are neglecting the remaining households. In this kind of scenarios, information is incomplete to make such strong inferences as in D.
Also in case of averages, remember that just having the highest values does not suggest the average value will be high.

e.g.
Set 1 (Merton, M)- 41,41,41,41
Set 2 (Sommer, S) - 61,5,5,5

Lets check if satisying the premises of the question
M has >40 (100%), S has 25%
S has >60 (25%). S has 0%
==> average Annual income of M is higher


Set 1 (Merton, M)- 41,41,41,41
Set 2 (Sommer, S) - 500,5,5,5
==> Average annual income of S is higher

Also, in your example, I do not understand your sample figures. Can you explain why you pick that figures 49% and 50%?
M can have x% 40000+ as it has highest % over 40,000
S can have y% 60000+ as it has highest % over 60,000
But, y < x
as 60000+ is a subset of 40000+

if y > x the first premise will be broken.
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Re: This might have come many times. The percentage of [#permalink]

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New post 11 Aug 2009, 06:26
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B. very clear....since Morten has highest percentage of 40,000++s, and Sommer has higher percentage of 60,000, thus not all Morten's 40,000s can be 60,000+ households, therefore some must fall between 40,000 and 60,000

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Re: This might have come many times. The percentage of [#permalink]

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New post 11 Aug 2009, 06:27
agree with sudeep's explanation on why D is wrong btw.

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Re: This might have come many times. The percentage of [#permalink]

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New post 11 Aug 2009, 06:39
Clearly B

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Re: This might have come many times. The percentage of [#permalink]

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New post 11 Aug 2009, 10:50
sudeep wrote:
Economist wrote:
This might have come many times.

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

Can anyone give an example on why D is wrong ? If the percent of households within each county is considered then always average annual household income will be greater in Sommer.
Eg. 50% of all households in Sommer have 60,000 and 49% of all households in Merton have 59,000 income. As per my understanding Sommer's average will always be greater than Merton if we consider "percentage of households separately within each group". Where is the flaw?


Lets say I add the premises - The percentage of households with an annual income below $10,000 is also highest in Sommer.
I hope you are getting, what I am setting. :)

You are neglecting the remaining households. In this kind of scenarios, information is incomplete to make such strong inferences as in D.
Also in case of averages, remember that just having the highest values does not suggest the average value will be high.

e.g.
Set 1 (Merton, M)- 41,41,41,41
Set 2 (Sommer, S) - 61,5,5,5

Lets check if satisying the premises of the question
M has >40 (100%), S has 25%
S has >60 (25%). S has 0%
==> average Annual income of M is higher


Set 1 (Merton, M)- 41,41,41,41
Set 2 (Sommer, S) - 500,5,5,5
==> Average annual income of S is higher

Also, in your example, I do not understand your sample figures. Can you explain why you pick that figures 49% and 50%?
M can have x% 40000+ as it has highest % over 40,000
S can have y% 60000+ as it has highest % over 60,000
But, y < x
as 60000+ is a subset of 40000+

if y > x the first premise will be broken.

Thanks sudeep for taking out time to explain so much ! :) +1 Kudo to you.
That is where I goofed up the entire question. Guess I am frustrated now..
I was trying to compare percentages of 60+ and 40+ in each set with a blank mindset of M only having values between 40-60 and nothing else. So I had only two sets in mind: M (40-60) and S(60+). Also when the question says percentage of households, I interpreted as "% of households within M" ...so M has more % of 40-60 values within M, and S has more % ( greater than % value of M ) of 60+ within S.

COMPLETE goof up :(
Anyways I need a break now :)

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Re: This might have come many times. The percentage of [#permalink]

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New post 11 Aug 2009, 15:25
B
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Re: This might have come many times. The percentage of [#permalink]

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New post 11 Aug 2009, 21:00
yup..familiar problem..B it is!
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Re: This might have come many times. The percentage of [#permalink]

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New post 03 Sep 2010, 15:42
B is the answer
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Re: This might have come many times. The percentage of [#permalink]

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New post 28 Apr 2011, 11:31
i did not plug any numbers to make the conclusion , intuitively B
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Re: This might have come many times. The percentage of [#permalink]

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Re: This might have come many times. The percentage of [#permalink]

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New post 12 Nov 2015, 09:17
Hi everyone,

Could anyone explain me why Merton County households' income must be between 40,000 and 60,000?

Well, as it is stated in question the income is higher than 40,000$, I am not denying it, BUT why I have to admit that 60,000 is the maximum possible income for Merton County, as for me I haven't see any logical point for such reasoning. The explanation in Official Guide is not strong enough for me, therefore I am asking you to help me. :roll:

Thank you!
Peace!

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Re: This might have come many times. The percentage of [#permalink]

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New post 14 Nov 2015, 03:30
Did somebody switch answer choices? You all are saying B is correct, yet C is the official answer. The arguments for B are based on the facts from answer choice C.

Though my predecessor made a very good point. If I understand you correctly, studentsensual, what you are saying is that perhaps some households have income of more than 60k and no household has income between 40k and 60k. This could well be, indeed. If so, the argument for C/B would be broken.

Any comment?

edit: I read the statement again. As it turns out, if this was the case, then Merton would actually have higher percentage of those household with income of more than 60k. Which cannot be true as it has already been proven otherwise by the argument itself.

For example,
Merton:
n=100
<40k - 60%
>40k - 40%

and

Country B:
n=100
<40k - 70%
>40 - 30%

Let say that all those household from country B that have more than 40k (30%) have also more than 60k. This makes country B country with the highest percentage of those with households' income of more than 60k. Now, if Merton has no household with income between 40k and 60k, that would mean that the household with more than 40k income actually have income of more than 60k. Which cannot be true, because this would make Merton the country with the highest percentage of households with income of more than 60k.

studentsensual, hope this helps.

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Re: This might have come many times. The percentage of [#permalink]

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New post 15 Apr 2017, 07:30
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: This might have come many times. The percentage of [#permalink]

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New post 01 May 2017, 02:46
well

if the % of households with an annual income of MORE than 40,000 is higher in Merton Country than ....

then we can conclude that there are some households in Merton Country which have an annual income between 40,000 and 60,000 (i.e. MORE than 40,000)


But nonetheless poorly phrased :evil: :evil: :evil:
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Re: This might have come many times. The percentage of [#permalink]

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New post 01 May 2017, 02:48
studentsensual wrote:
Hi everyone,

Could anyone explain me why Merton County households' income must be between 40,000 and 60,000?

Well, as it is stated in question the income is higher than 40,000$, I am not denying it, BUT why I have to admit that 60,000 is the maximum possible income for Merton County, as for me I haven't see any logical point for such reasoning. The explanation in Official Guide is not strong enough for me, therefore I am asking you to help me. :roll:

Thank you!
Peace!


well

if the % of households with an annual income of MORE than 40,000 is higher in Merton Country than ....

then we can conclude that there are some households in Merton Country which have an annual income between 40,000 and 60,000 (i.e. MORE than 40,000)


But nonetheless poorly phrased :evil: :evil: :evil:
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Re: This might have come many times. The percentage of   [#permalink] 01 May 2017, 02:48
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