GMAT Practice Question: On a certain transatlantic crossing, 20 percent of a ship's passengers held round-trip tickets...
Question
On a certain transatlantic crossing, 20 percent of a ship's passengers held round-trip tickets and also took their cars aboard the ship. If 60 percent of the passengers with round-trip tickets did not take their cars aboard the ship, what percent of the ship's passengers held round-trip tickets?
- 33 \frac{1}{3} \%
- 40 \%
- 50 \%
- 60 \%
- 66 \frac{2}{3} \%
Topics: word problems, percentages, translations, sets & groups
Solution
Step 1
We first create an unknown for the percentage of passengers who held round-trip tickets.
R=\text{percent of passengers with round-trip tickets}
Step 2
We translate \textbf{"60 percent of the passengers with round-trip tickets did not take their cars aboard the ship"}, which means that the remaining percent of those passengers did take their cars.
R-\frac{60}{100}R=\frac{40}{100}R
Step 3
We translate \textbf{"20 percent of the ship's passengers held round-trip tickets and also took their cars aboard the ship"} as the fraction of all passengers who both held round-trip tickets and took their cars.
\frac{40}{100}R=\frac{20}{100}
Step 4
We solve the linear equation for the unknown by isolating it.
\frac{40}{100}R=\frac{20}{100} R=\frac{\frac{20}{100}}{\frac{40}{100}} =\frac{20}{40} =\frac{1}{2}=50\%
Answer
50%
