infiniti007 wrote:Does anyone know of any other ways to solve this problem besides using what my book suggest (a group formula: Total = Group 1 + Group 2 - Both + Neither)?
If 75% of all Americans own an automobile, 15% of all Americans own a bicycle, and 20% of all Americans own neither an automobile nor a bicycle, then what percent of Americans own both an automobile and a bicycle?
A) 0%
B) 1.33%
C) 3.75%
D) 5%
E) 10%
This is an EITHER/OR group problem.
Every American EITHER has an auto OR does not.
Every American EITHER has a bike OR does not.
For an EITHER/OR group problem, we can use a GROUP GRID (also known as a double-matrix) to organize the data.
Let A = auto, NA = no auto, B = bike, NB = no bike.
Let the total number of Americans = 100.
Here is the grid:
In a group grid, the entries in any given row or column must add up to the TOTAL of that row or column.
75% of all Americans own an automobile, 15% of all Americans own a bicycle.
The following grid is yielded:
20% of all Americans own neither an automobile nor a bicycle.
Completing the grid, we get:
In the resulting grid, both auto and bike = 10.
The correct answer is
E.
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