I31-46

Question

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.

Bunuel · Answer

Official Solution:

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,  \frac{2}{3}  of the original workers remain on the morning shift.
 
After Day 3,  \frac{2}{3} * \frac{2}{3} = \frac{4}{9}  of the original workers remain on the morning shift.
 
After Day 4,  \frac{2}{3} * \frac{2}{3} * \frac{2}{3} = \frac{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:  \frac{1}{3}  of  27x = 9x  workers are on the evening shift.
 
Day 3:  18x  workers remained on the morning shift after Day 2, and  \frac{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  \frac{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 .

Correct answer:

Evening Shift  "86"

Both Shifts  "216"

I31-46

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards