OG 2020: Question No. 333
The figure above represents a box that has the shape of a cube. What is the volume of the box?
- PR = 10 cm
- QT = 5√6 cm
| Source | OG 2020 |
| Type | Data Sufficiency |
| Topic | Geometry |
| Sub-Topic | Rectangular Solids |
| Difficulty | Medium |
Solution
Steps 1 & 2: Understand Question and Draw Inferences
In this question, we are given
- The diagram of a box, which is in the shape of a cube.
- PR represents the face diagonal of the cube, whereas QT represents the body diagonal of the cube.
We need to determine
- The volume of the box.
As the box is in the form of a cube, the volume of the box = (length of each side)3
Hence, to get the answer, we need to know the side length of the cube.
With this understanding, let us now analyse the individual statements.
Step 3: Analyse Statement 1
As per the information given in statement 1, PR = 10 cm
- √2 (side of the cube) = 10
Or, side of the cube = 10/(√2) cm
As we can determine the side length of the cube, we will also be able to determine the volume.
Hence, statement 1 is sufficient to answer the question.
Step 4: Analyse Statement 2
As per the information given in statement 1, QT = 5√6 cm
- √3 (side of the cube) = 5√6
Or, side of the cube = (5√6)/√3 cm
As we can determine the side length of the cube, we will also be able to determine the volume.
Hence, statement 2 is sufficient to answer the question.
Step 5: Combine Both Statements Together (If Needed)
Since we can determine the answer from either of the statements individually, this step is not required.
Hence, the correct answer choice is option D.
