A survey of university researchers evaluated their usage of three high-performance computing resources: Cloud Containers (), GPU Accelerators (), and Distributed Storage (). Exactly researchers use none of these three resources. The survey revealed that equal numbers of researchers use Cloud Containers and GPU Accelerators (), while researchers use Distributed Storage (). Exactly researchers use all three resources. Furthermore, the number of researchers who use both and but not is equal to the number who use both and but not , and this quantity is exactly twice the number of researchers who use both and but not .
How many researchers use GPU Accelerators () ONLY?
- A32
- 72Answer
- C104
- D112
- E144
Answer
72 researchers use GPU Accelerators () only.
The total number of researchers using at least one resource is . Assigning to the region using Cloud Containers and Distributed Storage only, the regions for C-and-G-only and G-and-D-only are each . Applying the three-set inclusion-exclusion principle gives , which simplifies to , so . The exclusive overlapping regions containing GPU Accelerators are and . Subtracting these overlaps along with the triple intersection () from yields .
Step-by-Step Solution
Key Concept
3-Set Inclusion-Exclusion Principle and Venn Diagram Region Partitioning