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.

Difficulty: Easy

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).

More Questions from Data Sufficiency

Discussion & Comments

No comments yet. Be the first to comment!
Join Discussion