Final answer:
To find out how many GORPS are neither GOOPS nor GORGS, first, determine the total number of GORPS by adding those that are GOOPS (30) and those that are GORGS (20), getting 50 GORPS. Since no GORG is a GOOP, subtract the GORPS that are GORGS (20) from the total GORPS (50) to get 30 GORPS that are neither GOOPS nor GORGS.
Step-by-step explanation:
The question involves logical reasoning and is a typical problem found in mathematics. Given the relationships between GOOPs, GORPs, and GORGs, we need to determine the number of GORPs that are neither GOOPs nor GORGs. Let's break down the information provided:
- Every GOOP is a GORP.
- Half of all GORGS are GORPS.
- Half of all GORPS are GOOPS.
- There are 40 GORGS and 30 GOOPS.
- No GORG is a GOOP.
Since every GOOP is a GORP, there are at least 30 GORPs (since there are 30 GOOPS). Now, let's find out how many GORGS are GORPS. With 40 GORGS and half of them being GORPS, there are 20 GORGS that are GORPS. The total number of GORPS is the sum of GOOPS that are GORPS and GORGS that are GORPS. However, we must not double count any GORPs that could potentially fall into both categories.
Since no GORG is a GOOP, the sets of GOOPS and GORGS are disjoint. Therefore, we can simply add the number of GORPS from the GOOP set (which is 30) and the number of GORPS that are GORGS (which is 20) to get the total number of GORPS.
Total GORPS = GORPS that are GOOPS + GORPS that are GORGS = 30 + 20 = 50 GORPS.
Now we need to find out how many GORPS are neither GOOPS nor GORGS. Since all GOOPS are GORPS and no GORGS are GOOPs, the GORPS that are neither are simply the total GORPS minus the GORPS that are GORGS.
GORPS that are neither GOOPs nor GORGS = Total GORPS - GORPS that are also GORGS = 50 - 20 = 30.
So, there are 30 GORPS that are neither GOOPS nor GORGS.