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26 Apr 2026, 13:12
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A bike share operator ran a four week pilot program and recorded the number of rides taken in each week. The average (arithmetic mean) number of rides per week for Weeks 1, 2, and 3 was 8,640. How many more rides were taken in Week 4 than in Week 1?
(1) The average (arithmetic mean) number of rides per week for Weeks 2, 3, and 4 was 9,120.
(2) The total number of rides taken in Weeks 1 and 2 was equal to the total number of rides taken in Weeks 3 and 4.
(1) The average (arithmetic mean) number of rides per week for Weeks 2, 3, and 4 was 9,120.
(2) The total number of rides taken in Weeks 1 and 2 was equal to the total number of rides taken in Weeks 3 and 4.
26 Apr 2026, 13:12
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Official Solution:
A bike share operator ran a four week pilot program and recorded the number of rides taken in each week. The average arithmetic mean number of rides per week for Weeks 1, 2, and 3 was 8,640. How many more rides were taken in Week 4 than in Week 1?
Given: the average for Weeks 1, 2, and 3 is 8,640, so:
\(\frac{W1 + W2 + W3}{3} = 8,640\)
\(W1 + W2 + W3 = 25,920\)
(1) The average arithmetic mean number of rides per week for Weeks 2, 3, and 4 was 9,120.
This gives:
\(\frac{W2 + W3 + W4}{3} = 9,120\)
\(W2 + W3 + W4 = 27,360\)
Subtract the two totals:
\((W2 + W3 + W4) - (W1 + W2 + W3) = W4 - W1 = 27,360 - 25,920 = 1,440\)
Sufficient.
(2) The total number of rides taken in Weeks 1 and 2 was equal to the total number of rides taken in Weeks 3 and 4.
This gives:
\(W1 + W2 = W3 + W4\), so \(W4 - W1 = W2 - W3\).
But \(W2 - W3\) is not fixed by \(W1 + W2 + W3 = 25,920\), so statement (2) is not sufficient.
Answer: A
A bike share operator ran a four week pilot program and recorded the number of rides taken in each week. The average arithmetic mean number of rides per week for Weeks 1, 2, and 3 was 8,640. How many more rides were taken in Week 4 than in Week 1?
Given: the average for Weeks 1, 2, and 3 is 8,640, so:
\(\frac{W1 + W2 + W3}{3} = 8,640\)
\(W1 + W2 + W3 = 25,920\)
(1) The average arithmetic mean number of rides per week for Weeks 2, 3, and 4 was 9,120.
This gives:
\(\frac{W2 + W3 + W4}{3} = 9,120\)
\(W2 + W3 + W4 = 27,360\)
Subtract the two totals:
\((W2 + W3 + W4) - (W1 + W2 + W3) = W4 - W1 = 27,360 - 25,920 = 1,440\)
Sufficient.
(2) The total number of rides taken in Weeks 1 and 2 was equal to the total number of rides taken in Weeks 3 and 4.
This gives:
\(W1 + W2 = W3 + W4\), so \(W4 - W1 = W2 - W3\).
But \(W2 - W3\) is not fixed by \(W1 + W2 + W3 = 25,920\), so statement (2) is not sufficient.
Answer: A
