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11 May 2026, 09:54
Kudos
Bookmarks
This was a really good question, Catch being - To minimize the overlap think like two brothers doing a work & they don`t like to work together. So the faster one works all time & asks the slower brother to only join for the work that`s left & elder one couldn`t do.
That helped me remember this concept better!
Hit Kudos if you like the analogy!
That helped me remember this concept better!
Hit Kudos if you like the analogy!
03 Jun 2026, 00:23
Kudos
Bookmarks
Fast GMAT Approach
H = 3 dozen/hr
K = 4 dozen/hr
Total time period = 14 hours
Total production = 77 dozen
---------------------------
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.
----------------------------
Check
K: 14 × 4 = 56 dozen
H: 7 × 3 = 21 dozen
Total:
56 + 21 = 77 dozen
------------------
## 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.
H = 3 dozen/hr
K = 4 dozen/hr
Total time period = 14 hours
Total production = 77 dozen
---------------------------
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.
----------------------------
Check
K: 14 × 4 = 56 dozen
H: 7 × 3 = 21 dozen
Total:
56 + 21 = 77 dozen
------------------
## 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.
05 Jun 2026, 23:34
Kudos
Bookmarks
I applied two concepts here - WorkRatetime and Averages
- 77 units produced in 14 hours means avg pace is 5.5
- To minimise the time both machines work, need to maximise the output from the along working one. Therefore the one that works at the speed of 4 (K).
One machine and both machines
- K (4) and H+K (3+4=7)
- Now 5.5 is the middle value. That means the working ratio is 1:1 ( we can use allegation method, Even if it were not the middle value we would have found the ratio. (5.5-4 : 5.5-7, 1.5:1.5, 1:1)
- 14 hours into 1:1 ratio ((14/2) *1) = 7 hours
7 hours
- 77 units produced in 14 hours means avg pace is 5.5
- To minimise the time both machines work, need to maximise the output from the along working one. Therefore the one that works at the speed of 4 (K).
One machine and both machines
- K (4) and H+K (3+4=7)
- Now 5.5 is the middle value. That means the working ratio is 1:1 ( we can use allegation method, Even if it were not the middle value we would have found the ratio. (5.5-4 : 5.5-7, 1.5:1.5, 1:1)
- 14 hours into 1:1 ratio ((14/2) *1) = 7 hours
7 hours
nick13
