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GMAT Quantitative Practice, Data Sufficiency

Question 5

80 linear feet of fencing material is used to construct a rectangular enclosure. What is the area of the enclosure?

(1)  The length of one particular side of the enclosure is 10 feet.

(2)  It is possible to divide the enclosure into three square enclosures of equal size.

  1. Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is NOT sufficient.
  2. Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is NOT sufficient.
  3. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
  4. Each statement ALONE is sufficient to answer the question.
  5. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question.

Explanatory Answer

To determine the area of a rectangular enclosure, you must first know both its length and width (A = lw). Statement (1) alone suffices to answer the question. Given a perimeter of 80 feet, two sides must each run 10 feet in length, while the other two sides must each run 30 feet in length. Given the enclosure's length (30) and width (10), you can answer the question. The enclosure's area is (30)(10) = 300 feet.

Statement (2) alone also suffices to answer the question. Given a perimeter of 80, in order to divide the enclosure into three squares of equal size, the ratio of length to width must be 3:1 (1:1 for each square). The only possible dimensions are 30 feet and 10 feet. Thus, the only possible area is 300. The correct response is (D).