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16 Sep 2014, 01:17
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A potter places his pots in two types of boxes: big boxes that hold 24 pots each, and small boxes that hold 6 pots each. If the potter stored 126 pots ensuring every box he used was filled to capacity, how many big boxes did he use?
(1) The potter used fewer than 4 small boxes.
(2) The potter used more than 4 big boxes.
(1) The potter used fewer than 4 small boxes.
(2) The potter used more than 4 big boxes.
16 Sep 2014, 01:17
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Official Solution:
A potter places his pots in two types of boxes: big boxes that hold 24 pots each, and small boxes that hold 6 pots each. If the potter stored 126 pots ensuring every box he used was filled to capacity, how many big boxes did he use?
Let \(b\) be the number of big boxes used and \(s\) be the number of small boxes used. We can express this situation with the equation \(24b + 6s = 126\), which can be simplified to \(4b + s = 21\).
(1) The potter used fewer than 4 small boxes.
Now, since \(s < 4\) and \(b=\frac{21-s}{4}\), we can determine that \(s=1\) (otherwise, \(21-s\) would not be a multiple of 4), which in turn gives us \(b=\frac{21-s}{4}=5\). Sufficient.
(2) The potter used more than 4 big boxes.
Since \(b > 4\), we can conclude that \(b=5\) as otherwise \(4b\) would exceed 21. Sufficient.
Answer: D
A potter places his pots in two types of boxes: big boxes that hold 24 pots each, and small boxes that hold 6 pots each. If the potter stored 126 pots ensuring every box he used was filled to capacity, how many big boxes did he use?
Let \(b\) be the number of big boxes used and \(s\) be the number of small boxes used. We can express this situation with the equation \(24b + 6s = 126\), which can be simplified to \(4b + s = 21\).
(1) The potter used fewer than 4 small boxes.
Now, since \(s < 4\) and \(b=\frac{21-s}{4}\), we can determine that \(s=1\) (otherwise, \(21-s\) would not be a multiple of 4), which in turn gives us \(b=\frac{21-s}{4}=5\). Sufficient.
(2) The potter used more than 4 big boxes.
Since \(b > 4\), we can conclude that \(b=5\) as otherwise \(4b\) would exceed 21. Sufficient.
Answer: D
22 Oct 2023, 13:02
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I've revised the question and solution, incorporating additional details for improved clarity. I trust this makes it more comprehensible.
