What Is The Volume Of Rectangular Box R? GMAT Data Sufficiency

Question: What is the volume of rectangular box R?

(1) The total surface area of R is 12 square meters.
(2) The height of R is 50 centimeters.

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 TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

“What is the volume of rectangular box R” is a topic of the GMAT Quantitative reasoning section of GMAT. The GMAT Quant section includes 31 multiple-choice questions that need to be finished in 62 minutes.GMAT Data Sufficiency questions are followed by a problem statement that consists of two factual statements. This specific GMAT data sufficiency question evaluates the candidate’s mastery of solving calculative mathematical problems. The challenging portion of this type of question mainly comes from clever wording of the question that candidates overlook. GMAT data sufficiency contains 15 questions, two-fifths of the entire 31 GMAT quant questions.

Solution and Explanation:

Approach Solution 1:

The problem statement asks the candidate to find the volume of rectangular box R. So let’s assume the dimensions of a rectangular box be a, b and c.

Therefore, the volume (V) of the rectangular box will be = length x width x height = abc

The total surface area of the rectangular box = 2 (length x width + width x height x height x length) = 2 (ab + bc + ca)

1. The statement states that the total surface area of the rectangular box R is 12 meters.
   => 2 (ab + bc + ca) = 12 sq m
   => ab + bc + ca = 600 sq cm
   Therefore, the value of abc cannot be resolved from this statement. Hence the statement is not sufficient to find the volume of the rectangular box.
2. The statement suggests that the height of the rectangular box R is 50 centimetres.
   Therefore, anyone of the dimension of the rectangular box is 50cm.
   Suppose c = 50 c
   But the value of a and b are not given. So it is impossible to find the value of abc without getting the value of all the dimensions of the rectangle.
   Therefore, the statement is not sufficient to find the volume of the rectangular box.
   Combining both statements (1) and (2), we get,
   ab + 50b + 50a = 600 sq cm. (since the height of the rectangle as mentioned in the second statement is 50)
   Or, ab + 50 (a+ b) = 600 sq cm,
   Therefore, the value of abc cannot be determined from both statements.

Hence both statements (1) and (2) together are not sufficient.

Correct Answer: E

Approach Solution 2:

The question asked to find the volume of the rectangular box R. This means it is required to find the value of the product of the length, breadth and height i.e l*b*h of the rectangle.

1. The statement implies that the total surface area of the rectangle R is 12 square meters.
   As per the formula of the total surface area of a rectangle, we can say,
   2*(lb+bh+lh) = 12
   Or, lb+bh+lh = 6
   From this equation, The value of l, b and h can not be derived.
   Hence the statement is not sufficient to find the volume of the rectangular box.
2. The statement indicates that the height of the rectangular box R is 50 centimetres.
   That is we can say, 50 centimetres = 0.5 meters (since the value of 1 meter is 10 centimetres)
   The statement does not provide any information about the value of l and b.
   Hence the statement is not sufficient to find the volume of the rectangular box.
   Combining both statements, we get,
   lb+bh+lh = 6 and h = 0.5
   Or, we can say, lb+0.5(l+b) = 6

The value of l and b is not given. Hence statement (1) and statement (2) together are not sufficient to get the volume of the rectangular box R.

Correct Answer: E

Approach Solution 3:

The problem statement asked to find the volume of the rectangular box R.

That is it is required to calculate the product of the length, breadth and height i.e l*b*h of the rectangular box R.

1. The statement signifies that the total surface area of the rectangle R is 12 square meters.
   Applying the formula of the total surface area of a rectangle, we get,
   2(lb+bh+lh) = 12Or, (lb+bh+lh) = 6
   The value of l, b and h can not be deduced from this statement.
   Hence the statement is insufficient to find the volume of the rectangular box.
2. The statement exhibits that the height of the rectangular box R is 50 centimetres.
   i.e h= 50 cm = ½ m
   Though the value of the height of the rectangle is given, the value of the length and breadth of the rectangle cannot be determined from this statement.
   Hence the statement is insufficient to find the volume of the rectangular box.
   Combining the two statements we get,
   lb+ (½)b + (½)l = 6 (since lb+bh+lh = 6 and h = ½ m)
   Therefore, the volume of the rectangular box can not be deduced since no value of length and breadth of the rectangle is given in both statements.

Hence, statement (1) and statement (2) together are insufficient to get the volume of the rectangular box R.

Correct Answer: E

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