Sudha’s present salary — which statements suffice? I. The salary increases every year by 15%. II. Her starting salary (at joining) was $10,000. III. She joined exactly 5 years ago.
Verbal Reasoning
Data Sufficiency
Difficulty: Easy
Choose an option
Answer
Correct Answer: All I, II and III
Explanation
Introduction / Context:We need to determine which statements allow computation of Sudha’s current salary under compound annual raises.
Given Data / Assumptions:
- I: Annual raise rate r = 15% per year, compounded yearly.
- II: Initial salary S0 = $10,000 at joining.
- III: Time elapsed t = 5 years.
Concept / Approach:Present salary S = S0 * (1 + r)^t. Therefore, we require S0, r, and t — i.e., all three statements together.
Step-by-Step Solution:
S0 = 10,000; r = 0.15; t = 5.S = 10,000 * (1.15)^5.Numerically, (1.15)^5 ≈ 2.011357 ⇒ S ≈ $20,113.57.Verification / Alternative check:Any missing element (rate, initial salary, or years) prevents a unique numeric answer.
Why Other Options Are Wrong:
- II and III only: Missing raise rate.
- I and II only: Missing time.
- I and III only: Missing base salary.
Common Pitfalls:Using simple interest instead of compounding for annual percentage raises; ignoring the exact number of years.
Final Answer:All I, II and III