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Numbers based CR

by sukhman » Wed Feb 24, 2016 8:30 am
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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by shona04 » Thu Feb 25, 2016 3:09 am
IMO C

OA pls
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by MartyMurray » Thu Feb 25, 2016 5:13 am
Getting this one right takes not making unwarranted assumptions and not getting sucked in by trap answers.

(A) The percentage of households with an annual income of $80,000 is higher in Sommer County than in Merton County.

That the percentage of households with an annual income above $60,000 is higher in Sommer County does not mean that necessarily the percentage with an annual income of $80,000 is higher. In fact $80,000 is so specific that it's conceivable that no households have that income.

(B) Merton County has the second highest percentage of households with an annual income of $60,000 or more.

Nice trap answer. Other than that Sommer County has the most families with incomes over $60,000, we really don't know anything about counties and incomes of $60,000.

(C) Some households in Merton County have an annual income between $40,000 and $60,000.

We know that some households in Merton county have incomes over $40,000. We also know that in Sommer County the percentage of households with incomes over $40,000 is lower than the percentage of households with incomes over $40,000 in Merton county. So if all of the households in Merton County that have incomes over $40,000 actually were to have incomes over $60,000, then Merton County rather than Sommer County would be the county with the greatest percentage of households having incomes over $60,000. So some of the households that have incomes over $40,000 in Merton County must have incomes that are not greater than $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.

The prompt does not provide information that can be used to determine this, because the prompt discusses percentages rather than absolute differences.

(E) Average annual household income is higher in Sommer County than in Merton County.

This is another potential trap answer. That a greater percentage of households have incomes over $60,000 does not mean that overall the average income in Sommer county is higher. Conceivably there could be in Sommer County just one household with an income over $60,000 and the rest could have incomes below $10,000.

The correct answer is C.
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