Totals (Growth rates) — What is the total number of students in the school this year? Statements: I. The ratio of girls to boys is 2:3. II. The number of students grew by 5% this year and by 4% last year, starting from 2000 the year before last.
Verbal Reasoning
Data Sufficiency
Difficulty: Easy
Choose an option
Answer
Correct Answer: Statement II alone is sufficient; Statement I alone is not sufficient.
Explanation
Introduction / Context:We must compute this year’s total from chained percentage growth starting from a known baseline.
Given Data / Assumptions:
- Year before last: 2000 students.
- Last year growth: +4%.
- This year growth: +5% (on last year).
- Gender ratio 2:3 is irrelevant for totals.
Concept / Approach:Apply successive percentage growth multiplicatively.
Step-by-Step Solution:
Last year = 2000 * (1 + 4/100) = 2000 * 1.04 = 2080.This year = 2080 * (1 + 5/100) = 2080 * 1.05 = 2184.Verification / Alternative check:Order of application matches chronology; no rounding needed for an integer cohort when base is integral in this setup.
Why Other Options Are Wrong:
- A: A ratio without any count cannot yield a total.
- C/D/E: Statement II alone already yields a unique total.
Common Pitfalls:Adding percentages instead of compounding; mixing base years.
Final Answer:B — Statement II alone suffices (Total = 2184 students).