Diagram displays the percent of population that is obese...

[I_need_a_700plus]

The following question was in a CAT Exam IR section.

I follow where you get 3,000,000, but I do not understand "To change the denominator to 100,000 people, we divide by 30, so we must do the same to the top, yielding 5.33..."

Can someone explain? Many thanks!

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This diagram displays the percent of population that is obese versus the number of active farmers markets for 35 states and territories in the US. The size of the bubble gives a visual representation of the population of each state or territory. The smallest bubble represents a population of approximately 600,000, while the largest represents a population of approximately 13 million.

Question:
Under the simplification that the 5 smallest states all have about the same population, together they must have approximately ___ farmers markets per 100,000 people.

Answer:
Statement 1: 5. If the five smallest states are estimated (under the given simplification) to have the same population each, then they have about 600,000 people each (according to the text), or 3,000,000 altogether. From there, we have to approximate the number of farmers markets.

The five smallest dots are all to the left on the graph. Two have about 35 farmers markets each; one has about 25 markets; one has about 10; and the last has about 55. Together, that adds up to 160 markets for 3,000,000 people. To change the denominator to 100,000 people, we divide by 30, so we must do the same to the top, yielding 5.33..., or approximately 5 farmers markets per 100,000 people. Notice that if you misidentify one of the states (say, picking one of the cluster around 70-80 markets each), it will not make a real difference, since the answer choices all differ by powers of ten.

[tim]

It looks like there are 160 markets for 3,000,000 people. Since we want to know how many markets there are per 100,000, we need to divide both 160 and 3,000,000 by 30. 160/30 is 5.3333... Does that help?