In a certain region, the number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps. The number who have been vaccinated against both is twice the number who have been vaccinated only against mumps. If 5000 have been vaccinated against both, how many have been vaccinated only against rubella?
2500 : 7500 : 10000 : 15000 : 17500
This is an EITHER/OR group problem.
Every child EITHER has been vaccinated against mumps OR has not.
Every child EITHER has been vaccinated against rubella OR has not.
For an EITHER/OR group problem, we can use a GROUP GRID (also known as a double-matrix) to organize the data.
Let M = mumps, NM = not mumps, R = rubella, NR = not rubella.
In the grids below, the entries in any given row or column must add up to the TOTAL of that row or column.
The number who have been vaccinated against both is twice the number of who have been vaccinated against only mumps:
The number who have been vaccinated against rubella is twice the number who have been vaccinated against mumps:
5000 have been vaccinated against both:
According to the grid, both = 2x = 5000 and only rubella = 4x = 10,000.
The correct answer is
C.
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