PQID – PS95602.01 | OGQR 2020: Question No. 96
When a rectangular vat that is 3 feet deep is filled to (2/3) of its capacity, it contains 60 gallons of water. If 7 1/2 gallons of water occupies 1 cubic foot of space, what is the area, in square feet, of the base of the vat?
| Source | OGQR 2020 |
| Type | Problem Solving |
| Topic | Geometry |
| Sub-Topic | Rectangular Solids |
| Difficulty | Medium |
Solution
Given
In this question, we are given
- When a rectangular vat that is 3 feet deep is filled to 2/3 of its capacity, it contains 60 gallons of water.
- 7(½) gallons of water occupies 1 cubic foot of space.
To Find
We need to determine
- The area, in square feet, of the base of the vat.
Approach & Working
When the vat is filled to 2/3 of its capacity, it contains 60 gallons of water.
- Hence, the capacity of the vat = 60 * 3/2 = 90 gallons
- The space occupied, when the vat is fully filled = 90/7.5 = 12 cubic feet
If the area of the base is n, then we can say
- Area of the base * height = volume (or space occupied)
Or, n * 3 = 12
Or, n = 4
Hence, the correct answer is option A.
Takeaways:
- If 2/3rd of something is ‘X’, then total of that = X * 3/2
- Volume = Area of base * height
Did you know a 700+ GMAT Score can increase your chances to get into your dream business school? We can help you achieve that. Why don’t you try out our FREE Trial? We are the most reviewed online GMAT Preparation company in GMATClub with more than 2500 reviews as of February 2023.
