GMAT Practice Question: There are five sales agents in a certain real estate office. One month Andy sold twice as many...
Question
There are five sales agents in a certain real estate office. One month Andy sold twice as many properties as Ellen, Bob sold 3 more than Ellen, Cary sold twice as many as Bob, and Dora sold as many as Bob and Ellen together. Who sold the most properties that month?
- Andy
- Bob
- Cary
- Dora
- Ellen
Topics: word problems, linear equations, translations, comparisons, ratios
Solution
Step 1
We first define clear variables for each agent to avoid ambiguity.
A = \text{number of properties Andy sold} E = \text{number of properties Ellen sold} B = \text{number of properties Bob sold} C = \text{number of properties Cary sold} D = \text{number of properties Dora sold}
Step 2
We translate \textbf{\text{"Andy sold twice as many properties as Ellen"}} into an equation.
A = 2E
Step 3
We translate \textbf{\text{"Bob sold 3 more than Ellen"}} into an equation.
B = E + 3
Step 4
We translate \textbf{\text{"Cary sold twice as many as Bob"}} into an equation.
C = 2B
Step 5
We translate \textbf{\text{"Dora sold as many as Bob and Ellen together"}} into an equation.
D = B + E
Step 6
We express each variable in terms of E by substituting previous equations.
A = 2E B = E + 3 C = 2(E + 3) = 2E + 6 D = (E + 3) + E = 2E + 3
Step 7
We compare the expressions to see which is largest.
2E + 6 > 2E 2E + 6 > 2E + 3 2E + 6 > E + 3
Answer
Cary
