An office building has 8 floors, and each floor contains 5 offices of the same size. How many offices are...
GMAT Geometry & Trigonometry : (Geo_Trig) Questions
An office building has 8 floors, and each floor contains 5 offices of the same size. How many offices are in the building?
\(\mathrm{13}\)
\(\mathrm{35}\)
\(\mathrm{40}\)
\(\mathrm{48}\)
1. TRANSLATE the problem information
- Given information:
- 8 floors in the building
- 5 offices on each floor (same size offices)
- Need to find: total number of offices
- What this tells us: We have equal groups (each floor has the same number of offices)
2. Set up the calculation
- Since each floor has the same number of offices, we multiply:
- Number of floors × Offices per floor = Total offices
- \(8 \times 5 = 40\)
Answer: C (40)
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE reasoning: Students misinterpret the problem structure and add instead of multiply.
They might think: "8 floors and 5 offices, so \(8 + 5 = 13\) offices total." This completely misses that there are 5 offices on each of the 8 floors.
This leads them to select Choice A (13).
Second Most Common Error:
Basic arithmetic confusion: Students correctly identify that they need to multiply \(8 \times 5\) but make a calculation error or confuse the setup.
For example, they might calculate \(8 \times 5\) incorrectly or mix up numbers from the problem, potentially leading to Choice B (35) or Choice D (48).
The Bottom Line:
The key challenge is recognizing that this is a "groups of" situation where multiplication is needed, not simple addition. Students need to visualize 8 separate floors, each containing 5 offices, to understand why we multiply rather than add.
\(\mathrm{13}\)
\(\mathrm{35}\)
\(\mathrm{40}\)
\(\mathrm{48}\)