Washington High School randomly selected freshman, sophomore, junior, and senior students for a survey about potential changes to next year's schedule. Of the students selected for the survey, 1/4 were freshmen, and 1/3 were sophomores. Half of the remaining selected students were juniors. If 336 students were selected for the survey, how many were seniors?
Correct answer: D. 70
- A. 240
- B. 140
- C. 120
- D. 70
Explanation
Choice D is correct. It is given that the number of students surveyed was 336. Finding 1/4 of 336 yields (1/4)(336) = 84, the number of freshmen, and finding 1/3 of 336 yields (1/3)(336) = 112, the number of sophomores. Subtracting these numbers from the total number of selected students results in 336 − 84 − 112 = 140, the number of juniors and seniors combined. Finding half of this total yields (1/2)(140) = 70, the number of juniors. Subtracting this number from the number of juniors and seniors combined yields 140 − 70 = 70, the number of seniors.
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Quantitative reasoning applies arithmetic and basic algebra to numerical relationships, including percentages, ratios, averages, fractions, proportions, profit and loss, rates, time, work and measurement. Questions focus on translating words into equations, choosing an efficient method and checking whether the result is numerically reasonable.
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