25. Based on accounts of various ancient writers, scholars have painted a sketchy picture of the activities of an all-female cult that, perhaps as early as the sixth century B.C., worshipped a goddess known in Latin as Bona Dea, “the good goddess.” (A) Based on accounts of various ancient writers, (B) Basing it on various ancient writers’ accounts, (C) With accounts of various ancient writers used for a basis, (D) By the accounts of various ancient writers they used, (E) Using accounts of various ancient writers, Logical predication; Rhetorical construction Th e underlined phrase is a modifi er; it functions as an adjective to describe the noun that immediately follows it. In this case, the phrase incorrectly modifi es scholars, which does not make any sense. What are the scholars doing? When the modifi er begins with using, it correctly links the scholars with the modifi er that describes their activity. A Based on … incorrectly modifi es scholars. B Th e pronoun it does not have a clear reference. C Th is choice is wordy and awkward. D Th is choice is wordy and awkward. E Correct. In this sentence, using accounts of various ancient writers correctly modifi es scholars in a clear and concise expression of their activity.
In a certain population, there are 3 times as many people aged 21 or under as there are people over 21. The ratio of those 21 or under to the total population is (A) 1 to 2 (B) 1 to 3 (C) 1 to 4 (D) 2 to 3 (E) 3 to 4 Algebra Applied problems Let x represent the people over 21. Th en 3x represents the number of people 21 or under, and x + 3x = 4x represents the total population. Th us, the ratio of those 21 or under to the total population is 3 4 3 4 x x = , or 3 to 4.
86. Machine A produces 100 parts twice as fast as Machine B does. Machine B produces 100 parts in 40 minutes. If each machine produces parts at a constant rate, how many parts does Machine A produce in 6 minutes? (A) 30 (B) 25 (C) 20 (D) 15 (E) 7.5 Arithmetic Operations on rational numbers If Machine A produces the parts twice as fast as Machine B does, then Machine A requires half as much time as Machine B does to produce 100 parts. So, if Machine B takes 40 minutes for the job, Machine A takes 20 minutes for the job. Th is is a rate of 100 parts 20 minutes = 5 parts per minute. At this rate, in 6 minutes Machine A will produce 5(6) = 30 parts. Th e correct answer is A.
116. Each ? in the mileage table above represents an entry indicating the distance between a pair of the five cities. If the table were extended to represent the distances between all pairs of 30 cities and each distance were to be represented by only one entry, how many entries would the table then have? (A) 60 (B) 435 (C) 450 (D) 465 (E) 900
Arithmetic Interpretation of tables In a table with 30 cities, there are 30(30) = 900 boxes for entries. However, since a city does not need to have any entry for a distance to and from itself, 30 entries are not needed on the diagonal through the table. Th us, the necessary number of entries is reduced to 900 – 30 = 870 entries. Th en, it is given that each pair of cities only needs one table entry, not two as the table allows; therefore, the table only needs to have 870 2 = 435 entries. Th e correct answer is B.
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