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- Tue Jul 19, 2016 10:33 am
#27270
Complete Question Explanation
Must Be True-#%. The correct answer choice is (B)
This question belongs to a subcategory of Must Be True questions known as Proportion questions. In a Proportion question, the test makers provide you with partial information regarding one or more ratios. In this case, the two ratios described are the average number of students per teacher in Queenston’s school system in 1990 and the average number of students per teacher for the same school system in 1993.
The stimulus tells us that this ratio remained the same over this time period, despite the fact that the total number of teachers increased by 30%. Many students will immediately recognize that a constant ratio means that any change in one factor must be accompanied by a congruent change in the other factor; that is, if the ratio is the same between 1990 and 1993 and there are more teachers, there must be more students, as well. This conclusion matches answer choice (B).
Two points are noteworthy about this problem: first, this problem can be solved without ever determining the actual number of teachers or students in Queenston’s school system. Specific numbers are unnecessary. Remember that the test makers generally provide the absolute minimum information required to justify an answer choice and giving specific numbers might further simplify the problem. This leads us to the second point: the information regarding the school system’s operating budget is completely irrelevant. Well-prepared test takers should recognize this question type and immediately distinguish between useful and superfluous information. Test takers who lack this skill frequently select Attractive Distractors.
Answer choice (A): This is an Opposite answer. Students who note that the student-teacher ratio was constant from 1990 to 1993 may select this answer choice, but even a basic understanding of proportionality should prevent this error. If the information in the stimulus is true, this answer choice must be false.
Answer choice (B): This is the correct answer choice. Students who are less comfortable with abstract ratios may find it useful to “solve” the problem with hypothetical numbers. Always ensure that such numbers fit the given criteria and are easy to manipulate.
The criteria for this problem are a constant student-teacher ratio and a 30% increase in the total number of teachers between 1990 and 1993. The following chart includes suitable hypothetical numbers:
Of course there are an infinite set of numbers which could meet these criteria and solve this problem. But all of them will prove that “the total number of students enrolled in Queenston’s school system increased between 1990 and 1993.” Therefore, answer choice (B) is correct.
Answer choice (C): The stimulus tells us that the operating budget increased by an unspecified amount. Although the number of teachers increased by 30 percent, many other factors are included in the school system’s operating budget such as administrative expenses, facilities costs, supplies, and average teacher salary. We have no basis for concluding that the budget increase precisely matched the increase in the total number of teachers.
Answer choice (D): Based on the information given, we cannot prove that most of the teachers remained in the school system between 1990 and 1993. Therefore, we cannot justify this answer choice.
Answer choice (E): Several studies purport an inverse relationship between class size and quality of education. However, even if this were true, the ratio here remains unchanged and therefore we cannot conclude that the quality of education has improved.
Must Be True-#%. The correct answer choice is (B)
This question belongs to a subcategory of Must Be True questions known as Proportion questions. In a Proportion question, the test makers provide you with partial information regarding one or more ratios. In this case, the two ratios described are the average number of students per teacher in Queenston’s school system in 1990 and the average number of students per teacher for the same school system in 1993.
The stimulus tells us that this ratio remained the same over this time period, despite the fact that the total number of teachers increased by 30%. Many students will immediately recognize that a constant ratio means that any change in one factor must be accompanied by a congruent change in the other factor; that is, if the ratio is the same between 1990 and 1993 and there are more teachers, there must be more students, as well. This conclusion matches answer choice (B).
Two points are noteworthy about this problem: first, this problem can be solved without ever determining the actual number of teachers or students in Queenston’s school system. Specific numbers are unnecessary. Remember that the test makers generally provide the absolute minimum information required to justify an answer choice and giving specific numbers might further simplify the problem. This leads us to the second point: the information regarding the school system’s operating budget is completely irrelevant. Well-prepared test takers should recognize this question type and immediately distinguish between useful and superfluous information. Test takers who lack this skill frequently select Attractive Distractors.
Answer choice (A): This is an Opposite answer. Students who note that the student-teacher ratio was constant from 1990 to 1993 may select this answer choice, but even a basic understanding of proportionality should prevent this error. If the information in the stimulus is true, this answer choice must be false.
Answer choice (B): This is the correct answer choice. Students who are less comfortable with abstract ratios may find it useful to “solve” the problem with hypothetical numbers. Always ensure that such numbers fit the given criteria and are easy to manipulate.
The criteria for this problem are a constant student-teacher ratio and a 30% increase in the total number of teachers between 1990 and 1993. The following chart includes suitable hypothetical numbers:
Of course there are an infinite set of numbers which could meet these criteria and solve this problem. But all of them will prove that “the total number of students enrolled in Queenston’s school system increased between 1990 and 1993.” Therefore, answer choice (B) is correct.
Answer choice (C): The stimulus tells us that the operating budget increased by an unspecified amount. Although the number of teachers increased by 30 percent, many other factors are included in the school system’s operating budget such as administrative expenses, facilities costs, supplies, and average teacher salary. We have no basis for concluding that the budget increase precisely matched the increase in the total number of teachers.
Answer choice (D): Based on the information given, we cannot prove that most of the teachers remained in the school system between 1990 and 1993. Therefore, we cannot justify this answer choice.
Answer choice (E): Several studies purport an inverse relationship between class size and quality of education. However, even if this were true, the ratio here remains unchanged and therefore we cannot conclude that the quality of education has improved.
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