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My feeling is that if the answer key says anything but B, the key is wrong. The answer can only be B.
I have written the problem out again. I will try to accept each answer as true, and see where we get. Let us say, for the first few answer choices, that the number of people in Merton is 1000, and the number of people in Sommer is 10.
Given:
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.
Let's say that Merton has 30% (300 people) earning higher than 40K, with one person (0.1%) earning 62K. To justify the original premise, 10% (1 person) of Sommer has incomes over 60K. So A is out.
B) Some households in Merton county have an annual income between $40,000 and $60,000.
There is no way around this. Even if some people have more than $60,000, it cannot be that no one has between 40-60K.
C) The number of households with an annual income of more than $40,000 is greater in Merton than in Sommer County
In the above case, this is true. Let's see if we can find numbers that defeat this premise:
Let's take: 100 in Summer, 30% over 60K (30 people); 10 in Merton, 40% over 40K (4 people).
D) Average annual household income is higher in Sommer than in Merton County
Take the new numbers from C) above.
It's possible to say that all the rest have 0 income (70x0 + 30X60)/100 = 18K; Merton take 6 people with 35K and the 4 above at 45K. No computing, Merton is higher.
E) The percentage of households with an annual income of $80,000 is higher in Sommer than in Merton County.
No information.
Leanna

Aha!!! This question is a classic GMAT Trap. I still fell for the wrong choice - C, before, I checked the argument once again. The answer is "VERY CLEARLY B".

A note of caution - Always think twice when you see a question with percentages and numbers.

First let us weed out the irrelevant and wrong choices. A, D and E are out, as we cannot conclude any of those statements.

Now consider the following example

Lets assume that Merton county has 5000 residents, of which 2500 earn more than $40,000, and 5 residents earn more than $60,000. Therefore 50% of the residents earn more than $40,000 a year

Lets assume that Sommer county has 20,000 residents, of which 5000 earn more than $40,000 and 100 residents earn more than $60,000. Therefore 20% of the residents earn more than $40,000 a year, BUT, Sommer county has 2,500 residents more than Merton county who earn more than $40,000

From the above example. C cannot be inferred. But, B is 100% true.

It is definately not (C)
Suppose:
Population of M county is 10 people
Population of S county is 100 people
In county M there are 9 people who earn more than 40K - 90%
In county S there are 80 people who earn more than 40K - 80% of which 40 people earn more than 60K - 40%.
80>8. I hope, that would help.

the answer is (B)
This is rather good question, but the answer is too simple and promitive.

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

- Definitely true although it is stating something that is too obviously true.

C. The number of households with an annual income of more than $40,000 is greater in Merton than in Sommer county.

- A higher percentage in A than B does not necessarily gurantee a higher NUMBER of occurances in A than B. For example, 5 out of 10 in A represents 50 % while 10 out of 40 in B represents only 25%, but the number of occurances (in terms of events) is higher in B.

E. The percentage of households with an annual income of $80,000 is higher in Sommer than in Merton county.

- This is another close one, but this is tough to prove. If the majority of the household incomes are in the range between $60,000-$80,000 in Sommer, and only very few earn more than $80,000, this may not be the case.

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.

We can assume here that in most people in Merton county can have more than 60K annual income.

Only B can give a proper conclusion that some household can have income b/w 40k and 60k

A â€“ extreme wording
B â€“ yes, can be concluded.
C â€“ absolute numbers are not discussed, just the percentages.
D â€“ cannot be concluded from the info given.
E â€“ Out of scope.

A. No household in Merton county has an annual income of $60,000 or more. can't say. B. Some households in Merton county have an annual income between $40,000 and $60,000. has to be else, Merton would have the highest percentage in place of Sommer C. The number of households with an annual income of more than $40,000 is greater in Merton than in Sommer county. Can't say D. Average annual household income is higher in Sommer than in Merton county. Can't say E. The percentage of households with an annual income of $80,000 is higher in Sommer than in Merton county.

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 on $60,000 or more.

This is a sweeping generalization. There can be 10 households in Merton and 5 households can be getting 40K per annum while 3 can get 200 grand per household and remaining 2 getting 100K

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

True. Since the % of households having 40k or more is highest here there MUST be a few households falling in this bracket

C. The number of households with an annual income of more than $40,000 is greater in Merton than in Sommer county.

The premise talks about % tages so confirming the conclusion based on %tages is risky

Eg: Merton has 10 families in its county and Sommer has 50 families.

The statistical sampling is not uniform so ruled out

D. Average annual household income is higher in Sommer that in Merton county.

We cannot say that again. Suppose there are 4 families in Sommet which has 60K and 1 family with 5 K

Annual average is 13K

Whre as if Merton has 5 families with 40k each then Merton's average is greater than sommet though Sommet has greater % of 60K

E. The percentage of households with an annual income of $80,000 is higher in Sommer than in Merton county.

Again this leads to nothing. If 1 family in Sommet has 80k and Morten non then that doesnt lead to anything

Re: CR : Statistics lovers will love this one [#permalink]

Show Tags

26 Nov 2006, 20:38

My logic:
>60,000 :Sommer
>40,000:Merton

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 on $60,000 or more.
>>>Merton has income >40 K. Income of 60K is therefore possible.Therefore Incorrect

B. Some households in Merton county have an annual income between $40,000 and $60,000.
>>>Possible.

C. The number of households with an annual income of more than $40,000 is greater in Merton than in Sommer county.
>>>Nos of people with an annual income of more than $40,000 in Merton and Sommer counties is unkown.So cannot draw this conclusion

D. Average annual household income is higher in Sommer that in Merton county.
>>>Nos of people in Sommer and Merton counties is not given.So cannot draw this conclusion

E. The percentage of households with an annual income of $80,000 is higher in Sommer than in Merton county.
>>>Nos of people in Sommer and Merton counties is not given.So cannot draw this conclusion
_________________

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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.

The only information we are provided has to do with percentages (not actual #'s). This is an important point to keep in mind. A - We cannot conclude this. We are only told Sommer county has a higher percentage with a $60k+ annual income B- Must be true C - Number? We can't conclude anything about actual numbers when we are only provided with a percent D - Average? Same as C E - $80,000? We are not given any info about an $80,000 figure

M county's Ci - 40K+ > all county's Sommer's 60k+ >all county's

letz take only M and S as available counties. Assume M has 100 ppl and S has 100 ppl all ppl in M has income of 41k and 1 ppl in S has 61k and rest all has 1k. Now i can prove D as wrong.

A - beware of extreme words. - it is stictly saying NO which is not possible. B - should be possible.Because if all ppl. more than 40k+ is also more than 60+ then it will contradict Stmt 2. So hold it. C - repeating the premise. D - as i stated above. E - it may or may not be.

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