A Rectangular Solid has Length, Width, and Height of L cm, W cm, and H cm, Respectively GMAT Data Sufficiency

Question: A rectangular solid has length, width, and height of L cm, W cm, and H cm, respectively. If these dimensions are increased by x%, y%, and z%, respectively, what is the percentage increase in the total surface area of the solid?
(1) L, W, and H are in the ratios of 5:3:4.
(2) x = 5, y = 10, z = 20

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

“A rectangular solid has length, width, and height of L cm, W cm, and H cm, respectively.”- 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. GMAT data sufficiencycomprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation:

Approach Solution 1:

There is only one approach to solve the problem statement.

Given:

• A rectangular solid has length, width, and height of L cm, W cm, and H cm, respectively.

Condition:

• If these dimensions are increased by x%, y%, and z%, respectively

Find Out:

• The percentage increase in the total surface area of the solid

Approach:
Since the length, width and height are given, we will check each statement separately to find if they are sufficient. Then we will combine both the statements and check if they are sufficient.
length = L
width = W
height = H
length increased by x % = L (1+x/100)
width increased by y % = W (1+y/100)
height increased by z % = H (1+z/100)
What is the percentage increase in the total surface area?
Total surface area before increase = 2LW + 2WH + 2LH
Total surface area after increase:
2LW(1+x/100)(1+y/100) + 2WH (1+y/100)(1+z/100) + 2LH (1+x/100)(1+z/100)
Percentage increase in the total surface area:
\(\frac{Total surface area AFTER increase - Total surface area BEFORE increase}{Total surface area BEFORE increase} \)* 100
Now, let us check each statement separately:
Statement 1:
L,W, and H are in the ratios of 5:3:4
L=5k
W=3k
H=4k
We know nothing about x,y, and z to calculate the percentage increase in the total surface area.
Hence, the statement is Insufficient
Statement 2:
x = 5, y = 10, z = 20
We know nothing about L,W, and H to calculate the percentage increase in the total surface area. Hence, the statement is Insufficient.
Combining 1 and 2:
Now we have all required variables for calculation. We need to understand abovementioned formulas to exactly know at least which variables should be IDENTIFIED for the formula to work. In this case ALL of them are required. If the VOLUME were asked, knowing only
x,y, and z would be enough and that was the trap most people fall into choosing B under time pressure.

Correct Answer: C

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