Statistics

[tallynik]

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.

My answer is 'b'.
Illustration

Population of Merton - 100
Salary Range 40-60K - 40%
Salary Range 60-79K - 10%
Salary 80K - 20%

Population of Sommer - 200
Salary Range 40-60K - 20 ie 10%
Salary Range 60-79K - 80 ie 40%
Salary 80K - 10 ie 5%

For Metron % above 40k = 70%, above 60 = 30%, @ 80 = 20%
For Sommer % above 60k = 45%, @ 80 = 5%

[raunekk]

imo:E

[tallynik]

E is the OA.
Can someone please explain further or point out flaws in my illustration.

[rohangupta83]

what if Sommer county has no household with income > $80,000 and Merton has 1% houses with income > 80,000

Nowhere in the passage is it mentioned that Sommer county does have households with more than $80,000 income. All its saying is that the percentage of households with an annual income of $60,000 or more is highest in Sommer county

I go for B

[logitech]

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?

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

Does this need to be true? Let's make it false: No household in Merton has an income between 40k and 60k, and see what happens:

If x% of households in Merton earn more than $40k, then x% would need to earn more than $60k - not a single Merton household earns between $40k and $60k. Now, suppose y% of Sommer county households make over $40k, and z% make over $60k. Clearly y >= z; fewer people earn over $60k than earn over $40k. But we know from the question that x > y (a higher percentage in Merton earn over $40k than in any other county). If x > y, and y >= z, then x > z, which contradicts information in the question (that Sommer has a higher percentage of $60k+ earners).

That is, if we assume B is false, we get a contradiction, so B must be true.

This is from :

https://www.beatthegmat.com/inference-qu ... 29-15.html

[vanessa.m]

I would go with option E as the correct option