Multiple choice

Directions: This data sufficiency problem consists of a question and two statements labelled (1) and (2). You have to decide whether the data given in the statements is sufficient for answering the question. Find the cost of flooring the rectangular hall if perimeter of hall is 320 m and cost of flooring is Rs. 120 per sq.m. (1) The length of rectangular hall is 66.67% more than the breadth of rectangular hall. (2) The area of rectangle hall is 6,000 sq.m.

  1. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

  3. Both statements (1) and (2) together are sufficient, but neither of them alone is sufficient.

  4. Both the statements alone are sufficient.

  5. Both statements (1) and (2) together are not sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Perimeter = 2(L+B) = 320, so L+B = 160. Statement 1: L = 1.6667B = 5/3 B. 5/3 B + B = 160 -> 8/3 B = 160 -> B=60, L=100. Area = 6000. Statement 2: Area = 6000. Both allow finding dimensions and thus cost.

AI explanation

To find the flooring cost we need the area of the rectangle, and using statement one we let the breadth be x so the length is 5x divided by 3 and the perimeter of 320 m means 2 times x plus 5x divided by 3 equals 320, which solves to give the dimensions and thus the area. Using statement two, the area is directly given as 6000 sq m, so multiplying it by the rate of 120 rupees gives the cost. Each statement independently provides a way to find the area and calculate the cost. The result is that both statements alone are sufficient.

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