Cost of flooring a rectangular hall — which statements suffice? I. Length : Breadth = 3 : 2. II. Length = 48 m; flooring rate = $850 per m^2. III. Perimeter = 160 m; flooring rate = $850 per m^2.
Verbal Reasoning
Data Sufficiency
Difficulty: Medium
Choose an option
Answer
Correct Answer: Any two of the three
Explanation
Introduction / Context:We need the total cost of flooring, which equals Area * Rate. Thus we must be able to determine the rectangle’s area and have the rate per m^2.
Given Data / Assumptions:
- I: L : B = 3 : 2.
- II: L = 48 m and rate = $850/m^2.
- III: Perimeter P = 160 m (so L + B = 80) and rate = $850/m^2.
Concept / Approach:Any pair that yields both L and B and includes the rate will suffice. With L and B known, Area = L * B, and cost follows directly using the provided rate.
Step-by-Step Solution:
I + II: Ratio + L ⇒ B = (2/3)*48 = 32 m ⇒ Area = 48*32 = 1,536 m^2 ⇒ Cost = 1,536 * 850.I + III: Ratio + (L + B) = 80 ⇒ L = 48, B = 32 ⇒ Area as above ⇒ Cost known since rate is in III.II + III: L = 48 and L + B = 80 ⇒ B = 32 ⇒ Area known; rate given in II or III ⇒ Cost computable.Verification / Alternative check:Each pair independently determines L and B, and includes a rate statement.
Why Other Options Are Wrong:
- Only I and II / Only I and III / Only II and III are each sufficient individually; therefore the most accurate selection is “Any two of the three”.
- All three together is unnecessarily strong.
Common Pitfalls:Forgetting that perimeter with a fixed ratio completely determines both dimensions.
Final Answer:Any two of the three