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PQID: DS50351.01 | OG 2020: Question No. 371

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  V/A?

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

Source	OG 2020
PQID	DS50351.01
Type	Data Sufficiency
Topic	Geometry
Sub-Topic	Rectangular Solids
Difficulty	Hard

Solution

Steps 1 & 2: Understand Question and Draw Inferences

In this question, we are given

• The length, width, and height of a rectangular box, in centimeters, are L, W, and H.
• The volume of this box is V cubic centimeters and the total area of the 6 sides of this box is A square centimeters.

We need to determine

• The value of V/A.

As the given box is a rectangular one, we can say

• Volume V = LWH
• Total area of 6 sides = A = 2(LW + LH + WH)

With this understanding, let us now analyse the individual statements.

Step 3: Analyse Statement 1

As per the information given in statement 1, at least 2 of L, W, and H are equal to 5.

• However, we do not know the exact values of each of them.

Hence, statement 1 is not sufficient to answer the question.

Step 4: Analyse Statement 2

As per the information given in statement 2, L, W, and H all have the same value.

If we assume each of them is equal to ‘a’, then we can write

• V/A = a³/2(3a²)  = a³/6a² = a/6
• Therefore, we need to know the value of ‘a’ to get the answer.

Hence, statement 2 is not sufficient to answer the question.

Step 5: Combine Both Statements Together (If Needed)

Combining information from both statements, we can say

• L = W = H = 5.

As we know the value of each of them, we can determine the value of V/A.

Hence, the correct answer is option C.

Takeaways

1. Any rectangular box having dimensions l, w, and h has the same shape as a cuboid. So,
   1. Volume of the box = l*w*h
   2. Total surface area of the box = 2(lw + wh + lh)