Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the answer:
To answer the question, we need to know the three dimensions of the box (although we don’t need to know which dimension is the length or width or height).
Statement (1): INSUFFICIENT. Since the dimensions of the box are integers, the possible dimensions of 2 of the sides are either (1, 9) or (3, 3). In the first case, the third dimension of the box must be either 1 or 9 (to make two of the dimensions the same). In the second case, the third dimension must be any positive integer other than 3 (to prevent all three dimensions from being equal). We do not know enough to get the third dimension, however.
Statement (2): INSUFFICIENT. Since the dimensions of the box are integers, the dimensions of 2 of the sides could be (1, 81), (3, 27), or (9, 9). In the first case, the third dimension of the box must be either 1 or 81; in the second case, the third dimension must be 3 or 27. In the third case, the third dimension must be any positive integer other than 9. Again, we do not know enough to get the third dimension.
Statements (1) & (2): INSUFFICIENT. Using the foregoing, we can construct two cases that satisfy all the criteria: (1, 9, 9) and (3, 3, 27). These two cases lead to different surface areas (9+9+9+9+81+81=198 sq. inches and 81+81+81+81+9+9=342 sq. inches).
The correct answer is E: even together, the statements are insufficient.