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# This might have come many times. The percentage of

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Director
Joined: 01 Apr 2008
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Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
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This might have come many times. The percentage of [#permalink]

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11 Aug 2009, 04:33
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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. [Reveal] Spoiler: OA If you have any questions you can ask an expert New! Director Joined: 05 Jun 2009 Posts: 849 WE 1: 7years (Financial Services - Consultant, BA) Followers: 11 Kudos [?]: 306 [2] , given: 106 Re: This might have come many times. The percentage of [#permalink] ### Show Tags 11 Aug 2009, 05:05 2 This post received KUDOS 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. _________________ Consider kudos for the good post ... My debrief : http://gmatclub.com/forum/journey-670-to-720-q50-v36-long-85083.html Senior Manager Joined: 17 Jul 2009 Posts: 299 Concentration: Nonprofit, Strategy GPA: 3.42 WE: Engineering (Computer Hardware) Followers: 1 Kudos [?]: 41 [1] , given: 9 Re: This might have come many times. The percentage of [#permalink] ### Show Tags 11 Aug 2009, 05:26 1 This post received KUDOS 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 Senior Manager Joined: 17 Jul 2009 Posts: 299 Concentration: Nonprofit, Strategy GPA: 3.42 WE: Engineering (Computer Hardware) Followers: 1 Kudos [?]: 41 [0], given: 9 Re: This might have come many times. The percentage of [#permalink] ### Show Tags 11 Aug 2009, 05:27 agree with sudeep's explanation on why D is wrong btw. Intern Joined: 29 Jun 2009 Posts: 15 Location: Dallas TX Followers: 0 Kudos [?]: 3 [0], given: 0 Re: This might have come many times. The percentage of [#permalink] ### Show Tags 11 Aug 2009, 05:39 Clearly B Director Joined: 01 Apr 2008 Posts: 897 Name: Ronak Amin Schools: IIM Lucknow (IPMX) - Class of 2014 Followers: 28 Kudos [?]: 626 [0], given: 18 Re: This might have come many times. The percentage of [#permalink] ### Show Tags 11 Aug 2009, 09:50 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 Manager Joined: 21 Jun 2009 Posts: 156 Followers: 4 Kudos [?]: 9 [0], given: 1 Re: This might have come many times. The percentage of [#permalink] ### Show Tags 11 Aug 2009, 14:25 B Dont look too hard on CRs, they will backfire. Director Joined: 25 Oct 2008 Posts: 608 Location: Kolkata,India Followers: 12 Kudos [?]: 766 [0], given: 100 Re: This might have come many times. The percentage of [#permalink] ### Show Tags 11 Aug 2009, 20:00 yup..familiar problem..B it is! _________________ http://gmatclub.com/forum/countdown-beginshas-ended-85483-40.html#p649902 Senior Manager Joined: 21 Dec 2009 Posts: 268 Location: India Followers: 10 Kudos [?]: 225 [0], given: 25 Re: This might have come many times. The percentage of [#permalink] ### Show Tags 03 Sep 2010, 14:42 B is the answer _________________ Cheers, SD Director Joined: 21 Dec 2010 Posts: 649 Followers: 17 Kudos [?]: 212 [0], given: 51 Re: This might have come many times. The percentage of [#permalink] ### Show Tags 28 Apr 2011, 10:31 i did not plug any numbers to make the conclusion , intuitively B _________________ What is of supreme importance in war is to attack the enemy's strategy. GMAT Club Legend Joined: 01 Oct 2013 Posts: 10444 Followers: 887 Kudos [?]: 192 [0], given: 0 Re: This might have come many times. The percentage of [#permalink] ### Show Tags 04 Jun 2014, 07:28 Hello from the GMAT Club VerbalBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. Intern Joined: 27 Oct 2015 Posts: 18 Followers: 2 Kudos [?]: 4 [0], given: 175 Re: This might have come many times. The percentage of [#permalink] ### Show Tags 12 Nov 2015, 08:17 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.

Thank you!
Peace!
Manager
Joined: 12 Sep 2015
Posts: 112
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Kudos [?]: 7 [0], given: 24

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

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14 Nov 2015, 02:30
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.
This might have come many times. The percentage of   [#permalink] 14 Nov 2015, 02:30
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