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

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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.

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

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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. _________________

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

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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

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

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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.

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

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04 Jun 2014, 08:28

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

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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.

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

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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.

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