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A carrier audits 500 shipments. 70% arrive on time. Of the late shipments, 60% are late by under an hour. Of the shipments late by an hour or more, 25% are lost entirely. How many shipments are lost entirely?
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Correct answer
A
This problem narrows the group at each step, so work through it level by level rather than applying the final percent to the original 500 shipments. Start with the late shipments: 100% − 70% on time = 30% late, and 30% of 500 = 150. Next, narrow to the shipments late by an hour or more: 60% of the 150 late shipments are late by under an hour, so the remaining 40% are late by an hour or more, which is 0.40 × 150 = 60. Finally, apply the last percent to that narrowed group: 25% of those 60 shipments are lost entirely, so 0.25 × 60 = 15.
As an independent check, multiply all three fractions in one chain against the original 500: 0.30 × 0.40 × 0.25 × 500 = 0.03 × 500 = 15. Both routes agree, choice A.
The key discipline is re-anchoring each "of the..." clause to the group it actually refers to: late shipments, then shipments late by an hour or more, then lost shipments, each one a subset of the one before it.
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