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03 Aug 2026, 08:17
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During two 7-day promotional weeks, Week 1 and Week 2, a bike-share service tracked the total number of bicycles rented. If in Week 1, 20 percent of the bicycles rented were rented on Sunday, while in Week 2, 15 percent of the bicycles rented were rented on Sunday, were more bicycles rented in Week 2 than in Week 1?
(1) On each day from Monday through Saturday in Week 2, the number of bicycles rented was at least 7 percent higher than the number rented on the corresponding day in Week 1.
(2) The number of bicycles rented on Sunday in Week 2 was greater than 76 percent of the number rented on Sunday in Week 1.
(1) On each day from Monday through Saturday in Week 2, the number of bicycles rented was at least 7 percent higher than the number rented on the corresponding day in Week 1.
(2) The number of bicycles rented on Sunday in Week 2 was greater than 76 percent of the number rented on Sunday in Week 1.
03 Aug 2026, 08:17
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Official Solution:
During two 7-day promotional weeks, Week 1 and Week 2, a bike-share service tracked the total number of bicycles rented. If in Week 1, 20 percent of the bicycles rented were rented on Sunday, while in Week 2, 15 percent of the bicycles rented were rented on Sunday, were more bicycles rented in Week 2 than in Week 1?
Let \(W_1\) be the total number of bicycles rented in Week 1, and let \(W_2\) be the total number rented in Week 2.
Since 20 percent of Week 1 rentals were on Sunday, Sunday rentals in Week 1 were \(0.20W_1\).
So Monday through Saturday rentals in Week 1 were \(0.80W_1\).
Since 15 percent of Week 2 rentals were on Sunday, Sunday rentals in Week 2 were \(0.15W_2\).
So Monday through Saturday rentals in Week 2 were \(0.85W_2\).
We need to determine whether \(W_2 > W_1\).
(1) On each day from Monday through Saturday in Week 2, the number of bicycles rented was at least 7 percent higher than the number rented on the corresponding day in Week 1.
So the total for Monday through Saturday in Week 2 was at least \(1.07\) times the total for Monday through Saturday in Week 1.
Thus,
\(0.85W_2 \geq 1.07(0.80W_1)\)
\(0.85W_2 \geq0.856W_1\)
\(\frac{W_2}{W_1} \geq \frac{0.856}{0.85}\)
So \(W_2 > W_1\).
Sufficient.
(2) The number of bicycles rented on Sunday in Week 2 was greater than 76 percent of the number rented on Sunday in Week 1.
So,
\(0.15W_2 > 0.76(0.20W_1)\)
\(0.15W_2 > 0.152W_1\)
So \(W_2 > W_1\).
Sufficient.
Answer: D
During two 7-day promotional weeks, Week 1 and Week 2, a bike-share service tracked the total number of bicycles rented. If in Week 1, 20 percent of the bicycles rented were rented on Sunday, while in Week 2, 15 percent of the bicycles rented were rented on Sunday, were more bicycles rented in Week 2 than in Week 1?
Let \(W_1\) be the total number of bicycles rented in Week 1, and let \(W_2\) be the total number rented in Week 2.
Since 20 percent of Week 1 rentals were on Sunday, Sunday rentals in Week 1 were \(0.20W_1\).
So Monday through Saturday rentals in Week 1 were \(0.80W_1\).
Since 15 percent of Week 2 rentals were on Sunday, Sunday rentals in Week 2 were \(0.15W_2\).
So Monday through Saturday rentals in Week 2 were \(0.85W_2\).
We need to determine whether \(W_2 > W_1\).
(1) On each day from Monday through Saturday in Week 2, the number of bicycles rented was at least 7 percent higher than the number rented on the corresponding day in Week 1.
So the total for Monday through Saturday in Week 2 was at least \(1.07\) times the total for Monday through Saturday in Week 1.
Thus,
\(0.85W_2 \geq 1.07(0.80W_1)\)
\(0.85W_2 \geq0.856W_1\)
\(\frac{W_2}{W_1} \geq \frac{0.856}{0.85}\)
So \(W_2 > W_1\).
Sufficient.
(2) The number of bicycles rented on Sunday in Week 2 was greater than 76 percent of the number rented on Sunday in Week 1.
So,
\(0.15W_2 > 0.76(0.20W_1)\)
\(0.15W_2 > 0.152W_1\)
So \(W_2 > W_1\).
Sufficient.
Answer: D
