PrepTest 152, Section 4, Question 15

What we’re looking for

Working the answers

• A

  This infers a rise in average temperature from what most people believe about summers. The original uses a measured change in average weight, not a popular belief, as its evidence. A possible mistake in relying on people's impressions is different from the mathematical inference about an average and a proportion.

• B
  Correct

  This matches the original's inference about the proportion, even though it doesn't repeat the final description of the epidemic as a myth. The commentator argues from a small increase in average weight to no substantial increase in the proportion of obese children. B argues from a small increase in average salary to no substantial increase in the proportion earning very high salaries.

  A small change in an average doesn't determine how many people cross a particular threshold. Imagine four employees earning $10,000, $20,000, $90,000, and $120,000. Their average is $60,000, and only one earns more than $100,000. A year later, suppose the salaries are $5,000, $10,000, $110,000, and $119,000. The average rises only to $61,000, but the proportion above $100,000 doubles from one-quarter to one-half. Decreases elsewhere offset much of the increase across the threshold.

  The same mathematical possibility defeats the move from a small average-weight increase to a small increase in the proportion of obese children. My initial concern focused on an existing problem. B directs us to another flaw in the reasoning the commentator uses to dismiss that problem. An intermediate conclusion is still a conclusion supported by evidence, and its faulty inference can be the part a parallel answer matches.

• C

  This moves from the number of buildings converted to apartments to the proportion of all buildings that are apartments. That proportion also depends on the total and on other changes in the buildings. A substantial number of conversions needn't establish a substantial proportional increase. The original, however, moves from a change in an average to a change in the proportion above a threshold; C doesn't use an average at all.

• D

  Offering more high-calorie dishes doesn't establish that people eat them, or that average weight increases. People might choose other dishes or leave food uneaten. The gap is between menu offerings and actual consumption and weight, not between an average and the proportion exceeding a threshold. The shared subject of weight doesn't make the reasoning match.

• E

  A larger share of income spent on housing doesn't establish rising house prices. Income could fall while housing costs stayed the same, making the share larger. This inference moves from an expense-to-income proportion to average prices. It doesn't repeat the original's small average change being treated as a limit on the change in a high-end group's proportion.