Question: The length, width, and height of a rectangular box, in centimeters, are L, W, and H. If the volume of this box is V cubic centimeters and the total area of the 6 sides of this box is A square centimeters, what is the value of \(\frac{V}{A}\)?

1. Atleast 2 of L, W, and H are equal to 5
2. L, W, and H all have the same value

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.

Correct Answer: C

Approach Solution (1):

We are told that the length, width, and height of a rectangular box, in centimeters, are L, W, and H respectively, the volume of this box is V cubic centimeters and the total surface area of the 6 sides of the box is A square centimeters. We are asked for the value of \(\frac{V}{A}\). This question is based around some standard Geometry formulas for the solids and can be solved by Testing Values.

To start, volume of a rectangular solid is V = (L) (W) (H) and the total surface area is SA = 2 (L) (W) + 2 (L) (H) + 2 (w) (H)

(1) Atleast 2 of L, W and H are equal to 5.

Fact 1 tells us that 2 (or perhaps all 3) of the dimensions are equal to 5, but still leads to a number of different answers to the questions.
If…

L = 5, W = 5, H = 5, then the volume = (5) (5) (5) = 125 and total surface area = (2) (5) (5) + (2) (5) (5) + (2) (5) (5) = 150

So the answer to the question is \(\frac{125}{150}=\frac{5}{6}\)

L = 5, W = 5, H = 1, then the volume = (5) (5) (1) = 25 and total surface area = (2) (5) (5) + (2) (5) (1) + (2) (5) (1) = 70

So the answer to the question is \(\frac{25}{70}=\frac{5}{14}\)

Fact 1 is Insufficient

(2) L, W, and H all have the same value.

Fact 2 tells us that we are actually dealing with a cube, but the answer to the question will still vary depending on the side length

If…

L = 5, W = 5, H = 5, then the volume = (5) (5) (5) = 125 and total surface area = (2) (5) (5) + (2) (5) (5) + (2) (5) (5) = 150

So the answer to the question is \(\frac{125}{150}=\frac{5}{6}\)

L = 1, W = 1, H = 1, then the volume = (1) (1) (1) = 1 and total surface area = (2) (1) (1) + (2) (1) (1) + (2) (1) (1) = 6

So the answer to the question is \(\frac{1}{6}\)

Fact 2 is Insufficient

Combined, we know:

Atleast 2 of L, W, and H are equal to 5.

L, W, and H all have the same value.

When combining the two facts, it’s clear that we are dealing with a cube with a side length of 5, so the answer to the question is \(\frac{5}{6}\)

Combined, Sufficient

“The length, width, and height of a rectangular box, in centimeters, are L, W, and H. If the volume of this box is V cubic centimeters and the total area of the 6 sides of this box is A square centimeters, what is the value of \(\frac{V}{A}\)?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements.

Suggested GMAT Data Sufficiency Samples

• A rectangular solid has length, width, and height of L cm, W cm, and H cm, respectively GMAT Data Sufficiency
• The Cardinality of a Finite Set is the Number of Elements in the Set., GMAT Data Sufficiency
• What is the Radius of the Circle above with Center O?, GMAT Data Sufficiency
• Is the Average of a Set of 5 Distinct Positive Integers {a, b, 6, 4, 2} Greater than the Median?, GMAT Data Sufficiency
• If \(\sqrt{3+\sqrt{x-1}}=4\) , what is the value of x?, GMAT Data Sufficiency
• If There are 78 People Working at an Office, How Many of Them are Women Older than 40?, GMAT Data Sufficiency
• From a Group of M Employees, N Will be Selected, at Random, GMAT Data Sufficiency
• If L \(\neq\) 0, is \(\frac{18K}{L}\) an Integer?
• If 0 < x < 53, What is the Value of Integer x? GMAT Data Sufficiency
• P and Q are Prime Numbers Less than 70. What is the Units Digit of P*Q?, GMAT Data Sufficiency
• Is P – 1 Even?, GMAT Data Sufficiency
• Buster Leaves the Trailer at Noon and Walks Towards the Studio at a Constant Rate of B Miles Per Hour., GMAT Data Sufficiency
• If ab = ac is b = 2?, GMAT Data Sufficiency
• The symbol ∆ Denotes One of The Four Arithmetic Operations GMAT DATA Sufficiency, GMAT Data Sufficiency
• Is Quadrilateral ABCD a Rectangle?, GMAT Data Sufficiency
• If \(x^2\)=\(2^x\), What is the Value of x ?, GMAT Data Sufficiency
• A Pentagon With 5 Sides Of Equal Length And 5 Interior Angles Of Equal measure is Inscribed in a Circle, GMAT Data Sufficiency
• If m is a positive integer, is \(\sqrt{m}>25\) ? , GMAT Data Sufficiency
• What is the value of \(6x^2+9y^2\)?, GMAT Data Sufficiency
• If x and y are integers and \(x=\frac{y}{5}+2\) , is xy even?, GMAT Data Sufficiency
• If xy = - 6, What is the Value of xy(x + y)? GMAT Data Sufficiency
• A Drawer Contains 8 Socks, and 2 Socks are Selected at Random Without Replacement GMAT Data Sufficiency
• The Average Price of Three Stocks is $25 per Share GMAT Data Sufficiency
• Given k is a Nonzero Integer, is k>0? GMAT Data Sufficiency
• If J≠0, What Is The Value Of J? GMAT Data Sufficiency
• Paint X Costs $15 per Gallon, and Paint Y Costs $20 per Gallon GMAT Data Sufficiency
• What is the total value of Company H's stock? GMAT Data Sufficiency
• Is PQ > 1? GMAT Data Sufficiency
• How Many of the Students in a Certain Class are Taking Both a History and a Science Course? GMAT Data Sufficiency
• The Set S of Numbers has the following Properties GMAT Data Sufficiency
• A Contractor Combined x Tons of a Gravel Mixture that Contained 10 percent Gravel G GMAT Data Sufficiency
• If Jeff has four movies, and must choose to watch either 1, 2, or 3 different movies GMAT Data Sufficiency
• What is the probability that a student randomly selected from a class of 60 students will be a male who has brown hair? GMAT Data Sufficiency
• Does The Equation y = (x – p)(x – q) Intercept The x-axis At GMAT Data Sufficiency
• S is a Set of n Consecutive Positive Integers. Is the Mean of the Set GMAT Data Sufficiency
• What is x? (1) |x| < 2 (2) |x| = 3x – 2 GMAT Data Sufficiency
• In the Picture Quadrilateral ABCD is a Parallelogram and Quadrilateral DEFG is a Rectangle GMAT Data Sufficiency
• What is the Remainder when 333^222 is Divided by 7? GMAT Data Sufficiency
• Is 1/(a - b) > b - a ? GMAT Data Sufficiency
• If x is the Product of Three Consecutive Positive Integers, Which of the Following Must be True? GMAT Data Sufficiency
• What is the value of 6x^2 + 9y^2 =? GMAT Data Sufficiency
• If x and y are integers and, is x=(y/5 +2) even? GMAT Data Sufficiency
• If m is a positive integer, is √m>25? GMAT Data Sufficiency
• If there are 78 people working at an office, how many of them are women older than 40? GMAT Data Sufficiency
• If ab = ac is b = 2? GMAT Data Sufficiency
• If x is a positive integer, what is the value of x? GMAT Data Sufficiency
• If 53 students are enrolled in both the CS103 (Algorithms and Data Structures) And M101 GMAT Data Sufficiency
• Buster leaves the trailer at noon and walks towards the studio at a constant rate of B miles per hour GMAT Data Sufficiency
• If sq rt{3+sq rt(x-1)} = 4, what is the value of x? GMAT Data Sufficiency
• What is the sum of a, b, and c? GMAT Data Sufficiency