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03 Jul 2018, 18:28
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
75% (03:22) correct
25%
(02:59)
wrong
based on 346
sessions
History
Date
Time
Result
Not Attempted Yet
A group of children start a mowing and raking team called Gardening Guys that services one neighborhood house a day for 21 days. Each day, Gardening Guys receives $50 for their services and divides it equally between all the children who serviced the house that day. For one week (7 days), 3 children on the team go to camp and can’t work on the team, but they work every day they are not in camp. Everyone else works on the team every day. If there are k total children in Gardening Guys, where k > 3, how much will Lamar, who does not go to camp, make from working on the team?
A. \(\frac{1050}{k(k-2)(k-3)}\)
B. \(\frac{1050k}{(k-3)}\)
C. \(\frac{1050(k-3)}{k(k-2)}\)
D. \(\frac{1050}{k(k-3)}\)
E. \(\frac{1050(k-2)}{k(k-3)}\)
A. \(\frac{1050}{k(k-2)(k-3)}\)
B. \(\frac{1050k}{(k-3)}\)
C. \(\frac{1050(k-3)}{k(k-2)}\)
D. \(\frac{1050}{k(k-3)}\)
E. \(\frac{1050(k-2)}{k(k-3)}\)
05 Jul 2018, 16:16
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dabaobao
Let k=4. implying a total of 4 children.
On the 14 non-camp days when all 4 children work, Lamar earns \(\frac{1}{4}\) of the total earnings.
Since $50 is earned for each of these 14 days, we get:
Lamar's share = \(\frac{1}{4} * 50 * 14 = 175\).
On the 7 camp days when 3 of the 4 children attend camp and Lamar works alone, Lamar earns the entire $50 per day, for a 7-day total of $350.
Thus:
Total earned by Lamar = \(175+350=525\).
The correct answer must yield $525 when k=4.
Only E works:
\(\frac{1050(k-2)}{k(k-3)} = \frac{1050(4-2)}{4(4-3)} = 1050(\frac{2}{4}) = 1050(\frac{1}{2}) = 525\)
General Discussion
03 Jul 2018, 20:01
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50*14/k+350/(k-3)
IMO answer E
Is really 700 level question?
IMO answer E
Is really 700 level question?
