Critical Reasoning

greenwich 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.

For conclusion/inference questions, we're looking for a statement that MUST BE TRUE. If there are circumstances where the statement is not necessarily true, we can eliminate that statement.

A. No household in Merton county has an annual income of $60,000 or more.
Seems pretty extreme.
Given the information in the passage, the following scenario is possible:
Merton county has 3 households and their incomes are $41K, $41K, $61K
Sommer county has 4 households and their incomes are $1, $61K, $61K, $61K
This demonstrates that answer choice A NEED NOT BE TRUE.
Eliminate A

B. Some households in Merton county have an annual income between $40,000 and $60,000.
I like the word "some" here. It's not an extreme word. In fact, it means "at least one"
I'll spend a bit of time trying to think of a counter-example that will allow me to eliminate B.
I can't think of such a counter-example, so I'll keep B for now and move on to ...

C. The number of households with an annual income of more than $40,000 is greater in Merton than in Sommer county.
Hmmm. The passage tells us about PERCENTAGES of households, but this answer choice is about NUMBERS of households. This is a common trap on the GMAT, so I'm already somewhat leery.
Given the information in the passage, the following scenario is possible:
Merton county has 2 households and their incomes are $41K, $41K
Sommer county has 4 households and their incomes are $1, $41K, $41K, $61K
Here, the NUMBER of Sommer county households making more that $40K is greater than the NUMBER in Merton county.
This demonstrates that answer choice C NEED NOT BE TRUE.
Eliminate C

D. Average annual household income is higher in Sommer than in Merton county.
Given the information in the passage, the following scenario is possible:
Merton county has 3 households and their incomes are $41K, $41K, $500K
Sommer county has 4 households and their incomes are $1, $61K, $61K, $61K
Notice that the AVERAGE household income is higher in Merton than in Sommer
This demonstrates that answer choice D NEED NOT BE TRUE.
Eliminate D

E. The percentage of households with an annual income of $80,000 is higher in Sommer than in Merton county.
Hmmm, there has been no mention of the $80K+ income range, so I already have a good feeling that this statement need not be true.
In fact, if I check my scenario for statement D (above) we see that this demonstrates that answer choice E NEED NOT BE TRUE.
Eliminate E

By the process of elimination, the correct answer must be B

Cheers,
Brent