Fast GMAT Approach
H = 3 dozen/hr
K = 4 dozen/hr
Total time period = 14 hours
Total production = 77 dozen
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To minimize overlap, let the faster machine (K) work alone as much as possible.
If K works all 14 hours:
14 × 4 = 56 dozen
Need:
77 - 56 = 21 dozen more
The only way to get these extra 21 dozen is from H.
H produces 3 dozen/hr.
Therefore H must work:
21 ÷ 3 = 7 hours
To minimize overlap, these 7 hours must occur while K is already working.
Therefore overlap = 7 hours.
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Check
K: 14 × 4 = 56 dozen
H: 7 × 3 = 21 dozen
Total:
56 + 21 = 77 dozen
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## Answer: A. 7 hr
Ultra-Fast Shortcut
Maximum production in 14 hours using only the faster machine:
14 × 4 = 56
Shortfall:
77 - 56 = 21
H makes 3 dozen/hr
21 ÷ 3 = 7
Minimum overlap = 7 hours.