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GMAT Club World Cup 2026 (Day 7): Clara was assembling display trays

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sonit1987

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14 Jul 2026, 10:21

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Conatainer-1 Gold(Go): Green(Gr): White(W) are 1:3:2 lets say Go= Y then Gr= 3Y and W=2Y total 6Y
Conatiner-2 Go:Gr:W are 4:1:3 lets say Go= 4X Gr= X W=3X Total 8X

combined both containers Go(total= Gr(total)

Hence 4x+y= 3y+x 3x=2y hence x=2/3y ratio of beads in container1/container2= 6Y/8X since X=3/2Y then ratio becomes 9:8

check one by one 40 can't make 9:8 with any other number in the option
Only two pair out of all options make this ratio possible 45:40 and 72:64

How to decide which should be the answer. Total in container-1 is 6Y if 6Y=45 then Y=45/6 which makes Y not a whole number rule out

6Y=72 Y=12 only possible solution and 8X=64 X=8

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container 1) 72 , 1/6 of 12 =9 , 1/2 of 72 is 36

2 )64 4/8 of 64 = 32 1/8 of 64 = 8

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Container 1 --> Gold: Green:White -> (1:3:2) -> (1A:3A:2A)

--> Gold: A and Green: 3A

Container 2 --> Gold: Green:White -> (4:1:3) -> (4B:1B:3B)

--> Gold = 4B and Green = B

Since total number of gold beads is equal to green beads --> A + 4B = 3A +B
--> 3B = 2A
--> A:B = 3:2

Then: Container 1 = 6A = 18K and Container 2 = 8B = 16K

From the options:
Container 1 = 72 (18*4)
Container 2 = 64 (16*4)

Answer:
Container 1 = 72
Container 2 = 64

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We are given that Container 1 (C1) has beads in the ratio gold:green:white = 1:3:2
Container 2 (C2) has beads in the ratio gold:green:white = 4:1:3

Let x and y be the constants for the ratios of C1 and C2 respectively. Thus, the number of beads can be expressed as follows:

(Please ignore the above table if you can see it, I am unable to figure out how to delete it:eh:

	Gold	Green	White	Total
C1	x	3x	2x	6x
C2	4y	y	3y	8y
C1+C2	x+4y	3x+y	2x+3y	6x+8y

We are also given that total number of gold beads is equal to the total number of green beads when beads in both containers are combined.
Hence,

x+4y = 3x+y
Or, 2x = 3y
Or, x/y = 3/2 ___(1)

We can also see from the above table that the (total beads in C1)/(total beads in C2) = (6*x)/(8*y) = (6/8)*(x/y) = (6/8)*(3/2) = 9/8

Thus, we know that the total number of beads in C1 and C2 have to be in the ratio of 9/8
We have three such combinations of (C1, C2) (ordered) possible as follows:
(45, 40), (72, 64), (81, 72)

In order to pick the correct option, we can again visit the table. Total number of beads in C1 = 6x
That means this number has to be a multiple of 6.
Only (72, 64) satisfies that condition.

Hence, Total number of beads in C1 is 72 and in C2 is 64

anushree01

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Let the total in C1 be p & C2 be q
Using gold equals greens combined we get -
p+q\4 = p\3+q
8p=9q
Thus 9 : 8 ratio

Bunuel

Clara was assembling display trays using gold, green, and white beads from two containers.

In Container 1, the ratio of gold beads to green beads to white beads was 1 : 3 : 2.

In Container 2, the ratio of gold beads to green beads to white beads was 4 : 1 : 3.

Across the two containers combined, the total number of gold beads was equal to the total number of green beads.

Select for Container 1 the possible total number of beads in Container 1, and select for Container 2 the possible total number of beads in Container 2, that would be jointly consistent with the given information. Make only two selections, one in each column.

AviNFC

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Container 1:
gold=x
green=3x
white=2x
total=6x

Container 2:
gold=4y
green=y
white=3y
total=8y

x+4y=3x+y
3y=2x

container 2 total is multiple of 8. this satisfies 40, 64,72..but only 64 is correct as rest produces non integer value of x. so y=8, and x=9

container 1=72
container 2=64

Nkathiyawadi

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Container 1 contains : Gold = 1x; Green = 3x; White = 2x
Container 2 contains : Gold = 4y; Green = y ; White = 3y

As per question stem Total Gold = Total Green i.e. 1x+4y = 3x + y Then 3y = 2x hence x =3y/2

Total beads in Container 1 = 1x + 3x + 2x = 6x =6*3y/2 = 9y i.e. it should be divisible by 6 as well as 9.
Total beads in container 2 = 4y + y + 3y = 8y i.e. it should be divisible by 8. And total beads in container 1 is greater than in container 2.

Out of all the options 72 is divisible by 6 as well as 9(8*9). Hence, possible number of beads in container 1.
Out of all the options 64 is divisible by 8 and is 8*(9-1) = 64. Hence, possible number of beads in container 2.

Bunuel

Clara was assembling display trays using gold, green, and white beads from two containers.

In Container 1, the ratio of gold beads to green beads to white beads was 1 : 3 : 2.

In Container 2, the ratio of gold beads to green beads to white beads was 4 : 1 : 3.

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In Container 1, the ratio of gold beads to green beads to white beads was 1 : 3 : 2.
Total= 1a+3a+2a= 6a beads

In Container 2, the ratio of gold beads to green beads to white beads was 4 : 1 : 3
Total= 4b+1b+3b= 8b beads
Total gold= Total green
a+4b= 3a+b ; a/b = 3/2
a=3k and b=2k
Total beads in container 1= 6a=6(3k)= 18k
A multiple of 18

Total beads in container 2= 8b= 8(2k) =16k
A multiple of 16.

From options, it is 72 for container 1 and 64 for container 2.

72 & 64

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C1: x, 3x, 2x = 6x; C2: 4y, y, 3y = 8y = 16x/3
x + 4y = 3x + y
3y = 2x; y = 2x/3; C2 = 8x/3, 2x/3, 2x
so the option should satisfy, 6x and 16x/3 relation which is only satisfied by 72 and 64.

jefferyillman

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Container 1
Gold 1: Green 3 : White 2

Container 2
Gold 4 : Green 1 : White 3

Total gold = Total green

Container 1 must be a multiple of 1 + 3 + 2 = 6 so either 54 or 72. Let multiplier be A. Green must be half or 3 of 6 = 3A and Gold is A

Container 2 must be a multiple of 4 + 1 + 3 = 8 so either 40, 64, or 72. Let multiplier be B. Green must be 1 of 8 = B and Gold is 4B

Total gold is equal to total green

A + 4B = 3A + B
so 2A = 3B

So if container 1 has 72 total then A = 72/6 which is 12
2 (12) = 24 = 3B

to B = 8

and container 2 total is 8B =64

Container 1
gold 12
green 36

Container 2
gold 32
green 8

Totals
gold is 12 + 32 = 44
green 36 + 8 = 44

Therefore Container 1 = 72, and container 2 = 64

puncuz

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gold: green: white
1x: 3x: 2x (Container 1)
4y: 1y: 3y (Container 2)

also, 1x+4y=3x+1y
4y-y=3x-x
x/y=3/2
(3: 9: 6. Container 1) Total = 18
(8: 2: 6. Container 2) Total = 16

number 64 caught my eye so I multiplied both with 4 and got
72 for container 1 and 64 for container 2.

RudrAkshat7

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	Gold	Green	White
Container 1	a	3a	2a
Container 2	4b	b	3b

Given, a + 4b = 3a + b, so 2a = 3b, or b = 2a/3

now, Container 1 total = 6a = 6a * 3 = 18a = 9a
and, Container 2 total = 8b = 8*2a/3 * 3 = 16a = 8a

finding the appropriate value, we get Con 1 = 81 (9a, a=9), and Con 2 = 72 (8a, a=9)

BunuelClara was assembling display trays using gold, green, and white beads from two containers.

In Container 1, the ratio of gold beads to green beads to white beads was 1 : 3 : 2.

In Container 2, the ratio of gold beads to green beads to white beads was 4 : 1 : 3.

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Bunuel

Clara was assembling display trays using gold, green, and white beads from two containers.

In Container 1, the ratio of gold beads to green beads to white beads was 1 : 3 : 2.

In Container 2, the ratio of gold beads to green beads to white beads was 4 : 1 : 3.

Container 1 : G : R : W = x : 3x : 2x
Container 2 : G : R : W = 4y : y : 3y

x + 4y = 3x + y

3y = 2x

y/x = 2/3

Total beads in Container 1 : c1 = 6x
Total beads in Container 2 : c2 = 8y

From options c1 = 54
x = 9

y = 2/3*x = 6

c2 = 6*8 = 48

No c2 is present

c1 = 72

x = 12

y = 2/3*12 = 8

c2 = 8 * 8 = 64

valid

Container 1 = 72
Container 2 = 64

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Now in this problem, there are 6 parts in Container 1 and 8 in 2. Formulate this equation, and we get the ratio of Total 1 to total 2 as 9:8, which is through T1/6+T2/2=T1/2+T2/8 which gives us 9T2:8T1. Now look for options having 9 and 8 as divisors, and the only pair which is consistent with a common factor is 72,64 respectively. Which is our answer.

Any quick ways to solve this?

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Ratios	Gold	Green	White
Container 1	1x	3x	2x
Container 2	4y	1y	3y

Answer: Container 1 = 72 and Container 2 = 64

Given = 4y +1x = 3x + 1y >> Y = 2/3 * X

Step 1:

Substitute 2/3 * X for each Y in container 2: 8/3 * x Gold, 2/3 * x Green, 6/3 * x White

Step 2: Sum each container ratios

Container 1: 6x

Container 2: 16/3 * x

Step 3: Evaluate possible totals:

Total Container 1 = 6x > Total Container 2 = 16/3 * x

Total has to be integers

From container 2 x is divisible by 3 and container 2 is divisible by 16 and is even

Container 1 is divisible by 2 and at least 9 form 6 = 3 * 2 and x is multiple of 3 and is even

Eliminate Odd answer choices

Container 1 is 72 and Container 2 is 64

Bunuel

Clara was assembling display trays using gold, green, and white beads from two containers.

In Container 1, the ratio of gold beads to green beads to white beads was 1 : 3 : 2.

In Container 2, the ratio of gold beads to green beads to white beads was 4 : 1 : 3.

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container1 :- 1x+3x+2x=6x
container2:- 4y+1y+3y=8y

also, 1/6x+4/8y = 3/6x +1/8y

3/8y =2/6x
8x=9y

container 1 total is 6x and x=9y/8 , so it has to be multiple of 6 and 8, so container 1 total is 72
Container 2 total is 8y and y=8/9x, so it has to be multiple of 8 & 9, so container 2 total is 64.

Bunuel

Clara was assembling display trays using gold, green, and white beads from two containers.

In Container 1, the ratio of gold beads to green beads to white beads was 1 : 3 : 2.

In Container 2, the ratio of gold beads to green beads to white beads was 4 : 1 : 3.

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Assuming container 1 beads are x, 3x and 2x respectively (total 6x), and container 2 beads as 4y, y, and 3y respectively (total 8y).

We know total gold beads = total green beads.
Therefore, x+4y = 3x+y
or, 2x=3y

We know total number of beads in container 1 is 6x. We can rewrite this as 9y.
Therefore, the total beads will be in the ratio 9:8.

Three options satisfy the above, (45,40), (72,64), (81,72).
Since the total beads in container 1 is 6x, the total beads have to be a multiple of 6 (otherwise number of beads will be in fractions).
The second option is the only one that satisfies: 72 total beads in container 1 and 64 total beads in container 2.

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Gold : Green : White
in Container 1 - 1:3:2
Let x be the variable so 1x + 3x + 2x = 6x - so the total number of beads in Container 1 is a multiple of 6
Similarly, for the Container 2 - 4:1:3, let the variable be y. So 4y + 1y + 3y = 8y - the total number of beads in Container 2 is a multiple of 8.

Now, we have been given that the total number of gold beads across the 2 containers is equal to the number of green beads across the 2 containers.
So, 1x + 4y = 3x + 1y

I applied a trial and error method where, for container 1, my candidates were 54 and 72
I first considered 54 for container 1 and then ran with all the possible outcomes for container 2 where the total number needs to be a multiple of 8 - so the likely candidates were 40, 64 and 72). However, 40 was too small a number for the given condition of gold and green beads to be equal. hence, I discarded it.
So consider 54 for Container 1 and 64 for container 2.
Applying the ratios you get
Gold beads = 41 (9 + 32) whereas green beads = 35 (27 + 8) - Does not satisfy the condition.

I ran 54 for Container 1 and 72 for Container 2 - does not satisfy

Then I considered 72 for container 1 and 64 for container 2
Gold Beads = (12 + 32) 44 and Green Beads = (36 + 8) = 44
This satisfied the condition.
Hence, Container 1 - 72 and Container 2 - 64

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I approach it by setting up the relationship between two containers.

Total gold beads = Total green beads

Assume a = the total number of beads in the first container, and b = the total number of beads in the second.

Then,

a/6 + 4b/8 = 3a/6 + b/8
9b = 8a

We know that a > b, or the first container has more beads than the second.

Next, I use this relationship to plug in a different number.

If the first has 81 beads, then the second must have 8 as the last digit.

Try a = 81, b = 72 -> 8a ≠ 9b
Next, a = 72, b = {64, 54} -> found one! a = 72, b = 64.