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30 May 2026, 10:45
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A delivery fleet currently has 108 vehicles of two types: vans and trucks. Are more than 75 percent of the vehicles vans?
(1) If the fleet added 12 trucks, then 30 percent of the vehicles would be trucks.
(2) \(\frac{7}{9}\) of the vehicles in the fleet are electric vans.
(1) If the fleet added 12 trucks, then 30 percent of the vehicles would be trucks.
(2) \(\frac{7}{9}\) of the vehicles in the fleet are electric vans.
30 May 2026, 10:45
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Official Solution:
A delivery fleet currently has 108 vehicles of two types: vans and trucks. Are more than 75 percent of the vehicles vans?
(1) If the fleet added 12 trucks, then 30 percent of the vehicles would be trucks.
Let \(t\) be the original number of trucks. Then statement (1) implies
\(\frac{t + 12}{108 + 12} = 0.3\)
This equation determines \(t\) uniquely, so the original number of trucks is fixed. Therefore, the original number of vans is also fixed, \(108 - t\), and we can determine whether more than 75 percent of the vehicles are vans. Sufficient.
(2) \(\frac{7}{9}\) of the vehicles in the fleet are electric vans.
\(\frac{7}{9} = 0.777...\), which is already greater than 0.75. So more than 75 percent of all the vehicles are electric vans. Because electric vans are a subset of vans, it follows that more than 75 percent of all the vehicles are vans. Sufficient.
Answer: D
A delivery fleet currently has 108 vehicles of two types: vans and trucks. Are more than 75 percent of the vehicles vans?
(1) If the fleet added 12 trucks, then 30 percent of the vehicles would be trucks.
Let \(t\) be the original number of trucks. Then statement (1) implies
\(\frac{t + 12}{108 + 12} = 0.3\)
This equation determines \(t\) uniquely, so the original number of trucks is fixed. Therefore, the original number of vans is also fixed, \(108 - t\), and we can determine whether more than 75 percent of the vehicles are vans. Sufficient.
(2) \(\frac{7}{9}\) of the vehicles in the fleet are electric vans.
\(\frac{7}{9} = 0.777...\), which is already greater than 0.75. So more than 75 percent of all the vehicles are electric vans. Because electric vans are a subset of vans, it follows that more than 75 percent of all the vehicles are vans. Sufficient.
Answer: D
