GMAT Practice Question: In a certain region, the number of children who have been vaccinated against rubella is twice...
Question
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 5,000 have been vaccinated against both, how many have been vaccinated against rubella only?
- 2,500
- 7,500
- 10,000
- 15,000
- 17,500
Topics: word problems, translations, ratios, sets & groups
Solution
Step 1
We define variables for each group to avoid ambiguity.
M = \text{number vaccinated against mumps only}
Step 2
We define variables for each group to avoid ambiguity.
R = \text{number vaccinated against rubella only}
Step 3
We define variables for each group to avoid ambiguity.
B = \text{number vaccinated against both}
Step 4
We translate \textbf{\text{"The number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps."}} into an equation.
R + B = 2(M + B)
Step 5
We translate \textbf{\text{"The number who have been vaccinated against both is twice the number who have been vaccinated against mumps."}} into an equation.
B = 2M
Step 6
We substitute B = 5000 into the second equation and solve for M.
M = \frac{B}{2} = \frac{5000}{2} = 2500
Step 7
We substitute M = 2500 and B = 5000 into the first equation and solve for R.
R + 5000 = 2(2500 + 5000) = 2 \times 7500 = 15000 R = 15000 - 5000 = 10000
Answer
10000 (Option C): 10,000 children have been vaccinated against rubella only.
