OFFICIAL EXPLANATION (1) Identify the Question Type
The problem explicitly asks for an assumption, so this is a Find Assumption question.
(2) Deconstruct the Argument
The argument presents a statistical discrepancy: 80 percent of high schools in Cantville's District 1 have sent at least ten female students to the state science exposition, yet only 63 percent of high schools in the city's District 2 have done the same. The argument uses this statistic to conclude that high schools in District 1 are more active than those in District 2 in encouraging young women to pursue science.
(3) State the Goal
The reasoning in the argument is based on the idea that the difference in these percentages signifies a corresponding difference in the schools' encouragement of their female science students. For that to be the case, there must not be any other viable explanation for the discrepancy. The argument thus must assume that anything that would provide a different explanation for the discrepancy is false.
(4) Work from Wrong to Right
(A) If true, this statement would help explain the discrepancy in a way unrelated to the schools' encouragement of students: namely, because the students in District 1 have more free time, they are more likely to be able to pursue science irrespective of the level of encouragement they receive at school. Therefore, not only is this statement not an assumption, but the argument must in fact assume that it is not true.
(B) The overall populations of the districts are not useful in evaluating the argument, since nothing about the number of students in either district may be reliably inferred from such information. For instance, it could be the case that one district has a much larger proportion of senior citizens than does the other.
(C) Negative statements are often easier to look at through negation. If the average school in District 2 does have more students than the average school in District 1, then it should be even easier for schools in District 2 to find 10 female students to compete in the science fair. That would make it more likely that District 1 does a better job of encouraging girls to pursue science. Because the negation of the statement supports the argument, the original wording must not support the argument. Hence, it cannot be an assumption that the argument relies upon.
(D) CORRECT. This statement is required by the argument. If it is false -- i.e., if District 2 has significantly more all-male high schools -- then we would have an alternate explanation for the difference in statistics, because the all-male schools would be unable to qualify for the award.
(E) The argument does assume that school plays a role in encouraging (female) students to pursue science, but does not require the notion that school is the primary source of that encouragement.