Question Pack 1 Hard CR The percentage of households with an

[richachampion]

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. The percentage of households with an annual income between $40,000 and $60,000 is higher in Merton County than in Sommer County.
D. The total 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.

[richachampion]

there are various versions to this question, but this is the one with exactly the same option choice as asked in the question pack 1.

OA : C

[DavidG@VeritasPrep]

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. The percentage of households with an annual income between $40,000 and $60,000 is higher in Merton County than in Sommer County.
D. The total 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.

Boiled way down, we have two facts

Merton County: highest percentage of households earning 40,000+
Sommer County: highest percentage of households earning 60,000+

A) No way to know. It's possible that a large percentage of Sommer County households earning 60,000+ are just beyond the threshold, and thus make less than 80,000. A is out.

B) No way to know. It's possible that a large percentage of Merton County households earning 40,000+ are below 60,000. B is out

C) Looks good. Consider what would happen if this weren't the case. If Sommer County had a higher percentage of households earning between 40,000 and 60,000, and we already know that they have the highest percentage of households earning 60,000, then they'd have to have the highest percentage of households earning 40,000+. (In other words, if you're ahead in the 40-60 range and you're ahead in the 60+ range, you'd have to be ahead in the 40+ range.) But we know that isn't true. Merton County has the highest percentage of households earning 40,000+. C is the answer.

D) we only know about percentages, not absolute numbers. No good.

E) No way to know. Outliers can swing percentages. (Imagine someone in Merton County earned $100,000,000 last year, and no one in Sommer County earned more than 65,000.)

[alanforde800Maximus]

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. The percentage of households with an annual income between $40,000 and $60,000 is higher in Merton County than in Sommer County.
D. The total 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.

Boiled way down, we have two facts

Merton County: highest percentage of households earning 40,000+
Sommer County: highest percentage of households earning 60,000+

A) No way to know. It's possible that a large percentage of Sommer County households earning 60,000+ are just beyond the threshold, and thus make less than 80,000. A is out.

B) No way to know. It's possible that a large percentage of Merton County households earning 40,000+ are below 60,000. B is out

C) Looks good. Consider what would happen if this weren't the case. If Sommer County had a higher percentage of households earning between 40,000 and 60,000, and we already know that they have the highest percentage of households earning 60,000, then they'd have to have the highest percentage of households earning 40,000+. (In other words, if you're ahead in the 40-60 range and you're ahead in the 60+ range, you'd have to be ahead in the 40+ range.) But we know that isn't true. Merton County has the highest percentage of households earning 40,000+. C is the answer.

D) we only know about percentages, not absolute numbers. No good.

E) No way to know. Outliers can swing percentages. (Imagine someone in Merton County earned $100,000,000 last year, and no one in Sommer County earned more than 65,000.)

Hello David,

Can you share more insight on option C?