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26 Apr 2026, 14:31
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Leo starts assembling gift boxes for a charity event. He starts working alone, and later Hugo joins him to help finish the job. If a total of 96 boxes are assembled altogether, with some assembled by Leo alone and the rest assembled by Leo and Hugo working together, how many boxes had Leo already assembled by the time Hugo started helping?
(1) Working together, Leo and Hugo assemble 24 boxes per hour.
(2) Leo and Hugo worked together for a total of three hours.
(1) Working together, Leo and Hugo assemble 24 boxes per hour.
(2) Leo and Hugo worked together for a total of three hours.
26 Apr 2026, 14:31
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Official Solution:
Leo starts assembling gift boxes for a charity event. He starts working alone, and later Hugo joins him to help finish the job. If a total of 96 boxes are assembled altogether, with some assembled by Leo alone and the rest assembled by Leo and Hugo working together, how many boxes had Leo already assembled by the time Hugo started helping?
(1) Working together, Leo and Hugo assemble 24 boxes per hour.
Knowing only the combined rate does not tell us how many hours they worked together, so we cannot determine how many boxes they assembled after Hugo joined, and therefore we cannot determine how many Leo had already assembled. Not sufficient.
(2) Leo and Hugo worked together for a total of 3 hours.
Knowing only that they worked together for 3 hours does not tell us their combined rate, so we cannot determine how many boxes were assembled during those 3 hours, and we cannot determine how many of the total 96 boxes Leo had already assembled before Hugo joined. Not sufficient.
(1)+(2) We know they worked together for 3 hours at 24 boxes per hour, so they assembled \(24 * 3 = 72\) boxes while working together. Since 96 boxes were assembled in total, Leo must have already assembled \(96 - 72 = 24\) boxes when Hugo started helping. Sufficient.
Answer: C
Leo starts assembling gift boxes for a charity event. He starts working alone, and later Hugo joins him to help finish the job. If a total of 96 boxes are assembled altogether, with some assembled by Leo alone and the rest assembled by Leo and Hugo working together, how many boxes had Leo already assembled by the time Hugo started helping?
(1) Working together, Leo and Hugo assemble 24 boxes per hour.
Knowing only the combined rate does not tell us how many hours they worked together, so we cannot determine how many boxes they assembled after Hugo joined, and therefore we cannot determine how many Leo had already assembled. Not sufficient.
(2) Leo and Hugo worked together for a total of 3 hours.
Knowing only that they worked together for 3 hours does not tell us their combined rate, so we cannot determine how many boxes were assembled during those 3 hours, and we cannot determine how many of the total 96 boxes Leo had already assembled before Hugo joined. Not sufficient.
(1)+(2) We know they worked together for 3 hours at 24 boxes per hour, so they assembled \(24 * 3 = 72\) boxes while working together. Since 96 boxes were assembled in total, Leo must have already assembled \(96 - 72 = 24\) boxes when Hugo started helping. Sufficient.
Answer: C
