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16 Jul 2026, 08:00
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Evening Shift: 86
Both Shifts: 216
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
73% (02:49) correct
27%
(03:27)
wrong
based on 170
sessions
History
Date
Time
Result
Not Attempted Yet
A plant uses the same group of workers for a 4 day production run. Each worker works one shift per day, either the morning shift or the evening shift, and each worker produces the same number of units in any shift worked.
On Day 1, all workers work the morning shift. Once a worker is assigned to the evening shift, that worker remains on the evening shift for the rest of the production run. On Day 2, one third of the workers who worked the morning shift on Day 1 are assigned to the evening shift. On Day 3, one third of the workers who worked the morning shift on Day 2 are assigned to the evening shift. On Day 4, one third of the workers who worked the morning shift on Day 3 are assigned to the evening shift.
Select for Evening Shift the possible total number of units produced by the evening shift over the four days, and select for Both Shifts the possible total number of units produced by both shifts together over the four days, that would be jointly consistent with the given information. Make only two selections, one in each column.
On Day 1, all workers work the morning shift. Once a worker is assigned to the evening shift, that worker remains on the evening shift for the rest of the production run. On Day 2, one third of the workers who worked the morning shift on Day 1 are assigned to the evening shift. On Day 3, one third of the workers who worked the morning shift on Day 2 are assigned to the evening shift. On Day 4, one third of the workers who worked the morning shift on Day 3 are assigned to the evening shift.
Select for Evening Shift the possible total number of units produced by the evening shift over the four days, and select for Both Shifts the possible total number of units produced by both shifts together over the four days, that would be jointly consistent with the given information. Make only two selections, one in each column.
| Evening Shift | Both Shifts | |
| 20 | ||
| 65 | ||
| 86 | ||
| 108 | ||
| 162 | ||
| 216 |
ShowHide Answer
Official Answer
Evening Shift: 86
Both Shifts: 216
|
⚠️ Important: GMAT Club does not allow AI-generated posts. AI-generated solutions are not eligible for kudos, and users who post them may face moderation action, including a ban.
I31-46
16 Jul 2026, 09:00
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GMAT Club Official Solution:
A plant uses the same group of workers for a 4 day production run. Each worker works one shift per day, either the morning shift or the evening shift, and each worker produces the same number of units in any shift worked.
On Day 1, all workers work the morning shift. Once a worker is assigned to the evening shift, that worker remains on the evening shift for the rest of the production run. On Day 2, one third of the workers who worked the morning shift on Day 1 are assigned to the evening shift. On Day 3, one third of the workers who worked the morning shift on Day 2 are assigned to the evening shift. On Day 4, one third of the workers who worked the morning shift on Day 3 are assigned to the evening shift.
Select for Evening Shift the possible total number of units produced by the evening shift over the four days, and select for Both Shifts the possible total number of units produced by both shifts together over the four days, that would be jointly consistent with the given information. Make only two selections, one in each column.
Since one third of the morning-shift workers are moved on each of Days 2, 3, and 4, the original number of workers must allow three successive divisions by 3.
After Day 2, 2/3 of the original workers remain on the morning shift.
After Day 3, 2/3 * 2/3 = 4/9 of the original workers remain on the morning shift.
After Day 4, 2/3 * 2/3 * 2/3 = 8/27 of the original workers remain on the morning shift.
So let the original group have 27x workers.
Since the full group works one shift per day for 4 days, the total output of both shifts together is proportional to:
4 * 27x = 108x
So the Both Shifts value must be a multiple of 108. From the options, it could be 108 or 216.
Now find the evening-shift output.
Day 1: 0 workers are on the evening shift.
Day 2: 1/3 of 27x = 9x workers are on the evening shift.
Day 3: 18x workers remained on the morning shift after Day 2, and 1/3 of them, or 6x workers, are moved to the evening shift. So the evening shift now has 9x + 6x = 15x workers.
Day 4: 12x workers remained on the morning shift after Day 3, and 1/3 of them, or 4x workers, are moved to the evening shift. So the evening shift now has 15x + 4x = 19x workers.
Thus, the total evening-shift output over the four days is proportional to:
0 + 9x + 15x + 19x = 43x
Therefore:
Evening Shift : Both Shifts = 43x : 108x = 43 : 108
From the options, 86 and 216 are in the ratio 43 : 108.
Answer:
Evening Shift: 86
Both Shifts: 216
GMAT-Club-Forum-7ttfl7d0.png [ 13.93 KiB | Viewed 1446 times ]
A plant uses the same group of workers for a 4 day production run. Each worker works one shift per day, either the morning shift or the evening shift, and each worker produces the same number of units in any shift worked.
On Day 1, all workers work the morning shift. Once a worker is assigned to the evening shift, that worker remains on the evening shift for the rest of the production run. On Day 2, one third of the workers who worked the morning shift on Day 1 are assigned to the evening shift. On Day 3, one third of the workers who worked the morning shift on Day 2 are assigned to the evening shift. On Day 4, one third of the workers who worked the morning shift on Day 3 are assigned to the evening shift.
Select for Evening Shift the possible total number of units produced by the evening shift over the four days, and select for Both Shifts the possible total number of units produced by both shifts together over the four days, that would be jointly consistent with the given information. Make only two selections, one in each column.
Since one third of the morning-shift workers are moved on each of Days 2, 3, and 4, the original number of workers must allow three successive divisions by 3.
After Day 2, 2/3 of the original workers remain on the morning shift.
After Day 3, 2/3 * 2/3 = 4/9 of the original workers remain on the morning shift.
After Day 4, 2/3 * 2/3 * 2/3 = 8/27 of the original workers remain on the morning shift.
So let the original group have 27x workers.
Since the full group works one shift per day for 4 days, the total output of both shifts together is proportional to:
4 * 27x = 108x
So the Both Shifts value must be a multiple of 108. From the options, it could be 108 or 216.
Now find the evening-shift output.
Day 1: 0 workers are on the evening shift.
Day 2: 1/3 of 27x = 9x workers are on the evening shift.
Day 3: 18x workers remained on the morning shift after Day 2, and 1/3 of them, or 6x workers, are moved to the evening shift. So the evening shift now has 9x + 6x = 15x workers.
Day 4: 12x workers remained on the morning shift after Day 3, and 1/3 of them, or 4x workers, are moved to the evening shift. So the evening shift now has 15x + 4x = 19x workers.
Thus, the total evening-shift output over the four days is proportional to:
0 + 9x + 15x + 19x = 43x
Therefore:
Evening Shift : Both Shifts = 43x : 108x = 43 : 108
From the options, 86 and 216 are in the ratio 43 : 108.
Answer:
Evening Shift: 86
Both Shifts: 216
Attachment:
GMAT-Club-Forum-7ttfl7d0.png [ 13.93 KiB | Viewed 1446 times ]
General Discussion
16 Jul 2026, 08:21
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i am going with 86 for evening shift and with 216 for both shifts.
as both shifts = 216 as total production over 4 days is always 4\times (workers x units) = 108xy.
among the options only 216 = 108\times 2 fits.
evening shift = 86 as evening shift accumulates 43 workers days over the 4 days = 43xy. with xy=2 (from 216), = 43\times 2 = 86.
as both shifts = 216 as total production over 4 days is always 4\times (workers x units) = 108xy.
among the options only 216 = 108\times 2 fits.
evening shift = 86 as evening shift accumulates 43 workers days over the 4 days = 43xy. with xy=2 (from 216), = 43\times 2 = 86.
16 Jul 2026, 08:23
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given
Day | MS | ES
1 | x | 0
2 | 2x/3 | x/3
3 | 4x/9 | 1/3 (2x/3) = 2x/9 + x/3 (old batch remains as per question) = 5x/9 (4x/9+5x/9 = X, satistifes)
4 | 2/3 (4x/9) = 8x/27 | 1/3 (4x/9) = 4x/27 + 5x/9 = 19x/27
above i first consider x as total number of workers, let us now consider x workers produce x units
so ES produces in 4 days = 0+x/3 + 5x/9 + 19x/27 = (9x + 15x + 19x)/27 = 43x/27
and Total units produced in 4 days is x+x+x+x = 4x
as number of workers or number of units should be an integer
x should be divisible by 27
trying x = 27 -> ES = 43, which is not there in the options skip
x = 54, ES = 86, looks promising, if x = 54, 4(54) = T =216 good
so are the answers
Day | MS | ES
1 | x | 0
2 | 2x/3 | x/3
3 | 4x/9 | 1/3 (2x/3) = 2x/9 + x/3 (old batch remains as per question) = 5x/9 (4x/9+5x/9 = X, satistifes)
4 | 2/3 (4x/9) = 8x/27 | 1/3 (4x/9) = 4x/27 + 5x/9 = 19x/27
above i first consider x as total number of workers, let us now consider x workers produce x units
so ES produces in 4 days = 0+x/3 + 5x/9 + 19x/27 = (9x + 15x + 19x)/27 = 43x/27
and Total units produced in 4 days is x+x+x+x = 4x
as number of workers or number of units should be an integer
x should be divisible by 27
trying x = 27 -> ES = 43, which is not there in the options skip
x = 54, ES = 86, looks promising, if x = 54, 4(54) = T =216 good
so are the answers
