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805+ (Hard)|   Math Related|         
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Reon
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GMAT Club World Cup 2026 (Day 9): A plant uses the same group of 16 Jul 2026, 10:34
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Let, total number of workers= 27x
Day 1,
Morning= 27x
Evening= 0
Day 2, (1/3) of morning shift are assigned to evening shift.
Morning=27x-27x/3= 18x
Evening= 9x
Day 3, (1/3) morning shift workers on day 2 are assigned to evening shift.
Morning= 18x-6x= 12x
Evening= 9x+6x= 15x
Day 4, (1/3) morning shift workers on day 3 are assigned to evening shift.
Morning= 12x-4x =8x
Evening= 15x+4x =19x

Evening shift works on all 4 days= 0+9x+15x+19x= 43x
Total workers working on all 4 days= 27x+27x+27x+27x= 108x
If x=2,
Evening shift= 43(2)=86 .......... Both shifts= 108(2)=216
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GMAT Club World Cup 2026 (Day 9): A plant uses the same group of 16 Jul 2026, 10:37
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Over a course of 4 days 1/3rd workers each day move to evening shifts.
So its like: say 27 people working in morning shifts in day 1 will be 18 in morning and 9 in evening and on the 4th day it will be 9 in morning and 19 in evening.
thats the min number we can assume for the total no of workers = 27.
day 1 : M: 27, E:0, day 2- M: 18, E:9. Day 3, M: -12, E 15, Day 4 : M 8, E 19.
1 unit of work per worker : Total evening units: 0 +9 + 15 + 19 = 43x
Total units = 27 x 4 = 108x
From the options 86 is a multiple of 43 and 216 is a multiple of 108 so ans is 86 for evening and 216 for morning
Bunuel
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.
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GMAT Club World Cup 2026 (Day 9): A plant uses the same group of 16 Jul 2026, 11:09
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Here's my solution for this question
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Screenshot_2026-07-16-23-37-31-31_40deb401b9ffe8e1df2f1cc5ba480b12.jpg
Screenshot_2026-07-16-23-37-31-31_40deb401b9ffe8e1df2f1cc5ba480b12.jpg [ 922.73 KiB | Viewed 163 times ]

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GMAT Club World Cup 2026 (Day 9): A plant uses the same group of 16 Jul 2026, 11:15
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If we assume Day 1 morning shift to be 27x, the remaining values will move as shown in the attached photo. Hence, the total number of units produced has to be a multiple of 108. There are two such options, 108 and 216. However, if the answer for both shifts is 108, then answer for evening shift has to be 43 (since Both:evening is 108x:43x as per the photo attached) which is not in options. When both becomes 216, evening has to be 86 (which is available in the option) and hence this is the final answer.
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GMAT Club World Cup 2026 (Day 9): A plant uses the same group of 16 Jul 2026, 11:19
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The 4 Day Production Team of Workers each work 1 Shift;

Shift can be divided into : (i) Morning; (ii) Evening

We can use a matrices table to tabulate the information given and calculate accordingly.

Day 1Day 2Day 3Day 4
MorningAll (x)

Assume it as 27 Total		\(\frac{2x}{3}\)

[18]
\(\frac{2}{3 X 2x/3 = 4x / 9}\)

[12]
[8]
EveningZero\(\frac{x}{3}\)

[9]
\(\frac{1x}{3 + [1/3 X 2x/3]}\) = \(\frac{1x}{3 + 2x / 9}\)

[9] + [6] = [15]		[\(\frac{1}{3 X 4x/9 = 4x/27}\)] = [4]

Total = 9 + 6 + 4 = 19

Now in the evening shift, the total number of workers are 9 + 15 + 19 = 43

If each worker did 2 units of work, then the applicable option would be 86. Hence Option No. 3


Moving onto Both,

27 + 18 + 12 + 8 = 65 in the Morning Shift
43 in the Evening Shift

Both Units = 65 + 43 = 108
Since we assumed 2 units of work for Evening, 108 X 2 = 216 - Hence Option No. 5 is the answer.
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GMAT Club World Cup 2026 (Day 9): A plant uses the same group of 16 Jul 2026, 11:37
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Let's assume the total number of workers at the beginning is 27
Morning workersEvening workers
D1270
D2189
D3129+6=15
D4815+4=19
If every worker did x unit of per day work
total morning works (M) = (27+18+12+8)x = 65x units
Total evening work (E) = (9+15+19)x units = 43x units
Total work (B) = 108x units
for x=2, E=86, B=216
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GMAT Club World Cup 2026 (Day 9): A plant uses the same group of 16 Jul 2026, 11:41
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Let total n workers & each work c unit per day per shift
Day 1: n & 0
Day 2: 2n/3 & n/3
Day 3: 4n/9 & (2n/9 + n/3)
Day 4: 8n/27 & (4n/27 + n/3 + 2n/9)

Evening shift work = n + 4n/9 + 4n/27 = 43nc/27
Both shift work = 4 nc

so both shift work must be divisible by 4 such that nc is multiple of 27

if both shift =108, nc =27, evening work=43..not in option
if both shift = 216..nc=54..evening work = 86..YES

Ans 86 & 216
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GMAT Club World Cup 2026 (Day 9): A plant uses the same group of 16 Jul 2026, 11:54
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Let workers on day1 = x
all are in morning shift so evening shift = 0

day2: 1/3 of morning shifted to evening
evening = x/3
morning = x-x/3 = 2x/3

day3: 1/3 of morning shifted to evening
evening = x/3 + 1/3(2x/3) = x/3 + 2x/9 = 5x/9
morning = (2/3)(2x/3) = 4x/9

day: 1/3 of morning shifted to evening
evening = 5x/9 + 1/3(4x/9) = 5x/9 + 4x/27 = 19x/27
morning = (2/3)(4x/9) = 8x/27

total evening = x/3 + 5x/9 + 19x/27 = 43x/27
total morning = x+2x/3+4x/9+8x/27 = 65x/27
both shifts total = (43x+65x)/27 = 108x/27 = 4x

let's assume that each worker produces y unit in each shift so the total both shifts units = 4xy and total evening shift units = 43xy/27

let's check for both shifts value first , intuition says it is going to be larger number so we start looking 86 onwards for a multiple of 4. 108 and 216 are options.
test 108: xy = 108/4 = 27
evening = 43(27)/27 = 43 is not in options.
test 216: 216/4 = 54
evening = 43(54)/27 = 86 is in options.

both shifts = 216
evening = 86
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GMAT Club World Cup 2026 (Day 9): A plant uses the same group of 16 Jul 2026, 11:58
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Given info: 4 days of production run
two shifts working- morning and evening
each workers produce same number of units irrespective of shift they work
once a worker is shifted to evening shift, he will remain in that shift for remaining days


Day-1 of production: all workers in morning shift( assume total x workers)

Day-2 of production: 1/3 of the workers who worked on morning shift on day-2 are sent to evening shift.
(2/3)*x- remains in morning and (1/3)*x- evening
Day-3 of production: 1/3 of the workers who worked on morning shift on day-2 senet to evening shift
Remaining workers in morning shift= 2/3*(x)*2/3= (4/9)*x, Evening shift = (1/3)*x+ (2/3)*1/3*x= (1/3)*x+(2/9)*x=(5/9)*x
Day-4 of production: 1/3 of the workers in the morning shift on day-3 sent to evening shift
Remaining workers in morning shift= (4/9)*(2/3)*x= (8/27)*x , Evening shift = (5/9)*x+ (1/3)*(4/9)*x= (5/9)*x+(4/27)*x= (19/27)*x

Lets just add work human-power of all workers number present in morning and evening separately for 4 days of production

Morning shift= x+(2/3)*x+(4/9)*x+(8/27)*x= (27+18+12+8)/27*(x)= (65/27)*x ( number of units will be proportional to this)
Evening shift= 0+ (1/3)*x+(5/9)*x+( 19/27)*x= (0+9+15+19)/27*(x)= (43/27)*x ( number of units will be proportional to this)

Options are 20, 65, 86,108, 162, 216

lets say evening has 20 units produced then x= 20*27/43 (not possible as it won't yield integer)

so any possibility will be divisible by 43 for evening shift units to yield a integer

only options is 86.

for both shift option both shift should be proportional to ( 65/27)* x+ (43/27) *x = 108/27 *x

so option should be divisible by 108 for it to be integer,

only 216 is divisible by 108

we got our both answer.
Note:- we don't need to solve this, assuming number of units produced: just by smart assumption and proportionality consideration we can solve this question.
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GMAT Club World Cup 2026 (Day 9): A plant uses the same group of 16 Jul 2026, 12:32
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n=No. of workers
u= unit produced by 1 worker 1 shift.
T=n
workers on evening shift
day1=0
day2=n/3
day3=n/3+2n/9=5n/9
day4=5n/9+4n/27=19n/27
total=0+n/3+5n/9+19n+27=43n/27
evening sift produced 43n/27u=43/27t
both shifts=4n=4t
PITA for both shifts
if t-20=5
if t-108=27
if t-216=54
evening totals
if t is 5 =43/27(5) no
if t is 27= 43no
if t is 54 =86 yes

Both shifts:216
Evening shift: 86
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GMAT Club World Cup 2026 (Day 9): A plant uses the same group of 16 Jul 2026, 12:47
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Let W be total number of workers

U be the units produced per worker per shift

Day 1
Day W. Evening 0

Day 2
Day 2/3 W. Evening 1/3 W

Day 3
1/3 or remaining morning workers move
1/3 x 2/3W = 2/9W

Day (1/3 of remaining). Evening
2/3W - 2/9W. = 4/9W. 1/3W + 2/9W = 5/9W


Day 4
1/3 move
1/3 x 4/9W = 4/27W

Day
4/9W - 4/27W = 12/27W - 4/27W = 8/27W

Evening
5/9W + 4/27W = (15 + 4)/27 W = 19/27W

Total evening production multiply by production U
Day 1: 0
Day 2: 1/3 W x U
Day 3: 5/9 W x U
Day 4: 19/27 W x U

Evening Total is W x U (1/3 + 5/9 + 19/27)

Evening Total is W x U (9/27 + 15/27 + 19/27) = 43/27 WxU

TOTAL BOTH SHIFTS

Day shift over 4 days is 4 W x U

Ratio of evening to total must hold

43/27 WU to 4WU must hold. Or ratio of 43 Evening to 108 Both must hold

Pair that work (43, 108) or (86,216)

43 is not a possibility in evening shift so answer is 86 evening and 216 total

ANSWER Evening 86 , Total both 216
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GMAT Club World Cup 2026 (Day 9): A plant uses the same group of 16 Jul 2026, 15:37
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Bunuel
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.
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Imagine having 27 workers where 1 worker is making one unit.

Day 1: Morning 27 workers making 27 units and Evening 0 workers making 0 products.
Day 2: Morning 18 workers (27*1/3 which is 9; 27-9) making 18 products and Evening 9 (0+9) workers making 9 products.
Day 3: Morning 12 workers (18*1/3 which is 6; 18-6) making 12 products and Evening 15 (9+6) workers making 15 products.
Day 4: Morning 8 workers (12*1/3; which is 4; 12-4) making 8 products and Evening 19 (15+4) workers making 19 products.

Evening Shift total is 43 (0+9+15+19), multiple of 43 - 86 (Answer)
Both shift is 108 (27*4), multiple of 108 - 216 (Answer)

Since we did not have 43 we choose the next multiple for both to find the answer.
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GMAT Club World Cup 2026 (Day 9): A plant uses the same group of 16 Jul 2026, 17:34
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Let the initial number of workers be W.
Each day, one-third of the workers on the morning shift move to the evening shift.

So, the no. of morning workers is:
  • Day 1 : W
    Day 2 : 2W/3
    Day 3 : 4W/9
    Day 4 : 8W/27

The evening shift has the remaining workers:
  • Day 1 : 0
    Day 2 : W/3
    Day 3 : 5W/9
    Day 4 : 19W/27
If each worker produces "U" units per shift, then:
  • Evening Production = (43/27) WU
  • Total production over both shifts = 4WU

So, the ratio of evening production to total production is --> 43:108

The only pair in this ratio is --> 86:216

Answer: Evening Shift: 86 and Both Shifts: 216
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GMAT Club World Cup 2026 (Day 9): A plant uses the same group of 16 Jul 2026, 18:34
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Day1 Morning Shift : n Evening Shift: 0
D2 Morning : 2n/3 Evening: n/3
D3 Morning: 4n/9 Evening: 2n/9+n/3
D4 Morning: 8n/27 Evening: 4n/27+2n/9+n/3

Evening shift total units produced are proportional to the number of people working: 43n/27
Looking at the options if n=54
then units produced= 43*54/27=86
Total units in the 4 days produced for both the shifts: 4n=54*4= 216
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GMAT Club World Cup 2026 (Day 9): A plant uses the same group of 16 Jul 2026, 19:29
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Let us assume each worker produces 1 unit of work per day as this does not change irrespective of shift.
Let us denote the total number of workers as x, and below I will be signifying the number of workers in morning and evening shifts on a particular day as (morning, evening).

Each day starting from Day 2, 1/3 of workers working the morning shift the previous day - leaving 2/3 of workers in the morning shift so each day the morning shift workers gets multiplied by 2/3 and the rest are in the evening shift.
Day 1 -> (x,0)
Day 2 -> (2x/3,x/3)
Day 3 -> (4x/9,5x/9)
Day 4 -> (8x/27,19x/27)

As the number of units per day per worker is 1, the above values will be unchanged for units of work.
Total number of work units in evening shift = x/3 + 5x/9 + 19x/27 = 43x/27

Total work each day is x units so total work in 4 days is 4x units. We can rewrite this as 108x/27

So, x can only be in multiples of 27 as fractional units of work are not possible.
Taking x/27=1, we do not get the desired option for evening shift, i.e. 43.
Taking x/27=2, we get evening shift units = 86 and both shift units = 216.
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Here is the breakdown
Day Morning Evening
1. N 0
2. 2N/3 N/3
3. 4N/9 5N/9
4. 8N/27 19N/27
Morning: (27N+18N+12N+8N)/27 = 65N/27
Evening: (9N+15N+19N)/27 = 43N/27
Total worker = 65N + 43N = 108N
Evening worker will be 43*2 = 86 and Total worker 108*2 = 216

Therefore, the evening shift is 86, and both shifts are 216.
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Let,
Number of workers = n
Units produced by each worker per shift = x

Total production in 4 days = 4nx

Production in evening shift (4 days)
= 0+ n/3 + ( n/3 + 2n/9) + (5n/9 + 4n/27) = 43n/27

S0, n is the multiple of 27 & 43

Among the answer choices ( 20, 65, 86, 108, 162, 216), only multiple of 43 is 86.

So, evening shift = 86.

putting n = 27k, we have ,
86 = 43*(27k)*x/27 = 43kx
kx = 2

So, total production in 4 days = 4nx = 4*(27k)*x = 108*kx = 108*2 = 216

Answer:
Evening shift = 86
Both shifts = 216

Bunuel
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.
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GMAT Club World Cup 2026 (Day 9): A plant uses the same group of 16 Jul 2026, 22:42
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Ans - 86 for Evening shift
216 for Both shifts

Sol
4 days , Morning and Evening shifts , once assigned the shifts cannot be changed

Let N be total number of workers
Day 1 Day 2 Day 3 Day4
M - N M - 2/3N M- 4/9N M- 8/27N
E -0 E- 1/3 N E- 5/9 N E- 19/27N

Total shifts = Adding all = 108/27 N
Total Evening shifts = 43/27 N

Since workers can only be whole number so it must be divisible by 27
so checking different values of N

let N be 1 , 43 - not an option
Let N be 2 , 86 and 216 both are correct



Bunuel
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.
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nuwaaanda
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GMAT Club World Cup 2026 (Day 9): A plant uses the same group of 16 Jul 2026, 23:29
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What we are given is that there are a certain number of workers that work in a plant. They work across 4 days. Each worker could be working in the morning shift or the evening shift. And then we are given a whole lot of information about exactly how many workers worked in each the morning and the evening shift. I found it useful to just create a table of daywise number of workers working in each shift. Below is the same

Let there be x total workers in the plant. Regardless of the day and split between workers, this will remain constant
MorningEveningTotal
Day1x0x
Day22x/3x/3x
Day3(2x/3) - (2x/9) = (4x/9)(x/3)+(2x/9) = (5x/9)x
Day4(4x/9) - (4x/27) = (8x/27)(5x/9)+(4x/27) = (19x/27)x
Totalx+(2x/3)+(4x/9)+(8x/27)
=(27x/27)+(18x/27)+(12x/27)+(8x/27)
= (65x/27)		(x/3)+(5x/9)+(19x/27)
= (9x/27)+(15x/27)+(19x/27)
= (43x/27)		(65x/27)+(43x/27)
=(108x/27)
=4x

Now, we are give that each worker produces the same number of units (y units per worker per shift) in every shift worked
Thus, total units produced across 4 days = (no. of workers across 4 days)*(no. of units produced per worker per shift) = 4x*y

Also, total units produced = (total number of units produced in every morning shift)+(total number of units produced in every evening shift)
= (65x/27)*y + (43x/27)*y

Now we know that the number of workers and the number of units are supposed to be whole positive numbers, the term x*y will be a multiple of 27 (otherwise, the number of units produced in morning/evening shifts will become a fraction)
Thus, xy = 27c (c is some positive integer constant)
Thus, total number of units = 4xy = 4*27*c = 108*c = some multiple of 108
Total number of units in the evening shift = 43xy/27 = 43*27c/27 = 43c = sum multiple of 43

Now, the easiest way to do this is look at the options. We can see that only 86 is a multiple of 43 (43*2) in the given option choices. Thus, it is the only possible answer for evening shift units. Thus, 43c = 86 ==> c = 2
If c = 2, total units produced = 108*2 = 216

Therefore the correct answer choices are 86 and 216
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GMAT Club World Cup 2026 (Day 9): A plant uses the same group of 16 Jul 2026, 23:53
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M: n, 2n/3, 4n/9, 8n/27
E: 0, n/3, 5n/9, 19n/27 = 43n/27; multiple of 43 = 86, (n = 54)
total = 4n = 4*54 = 216
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