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

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yashsharma1

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14 Jul 2026, 20:17

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Container 1 - Gold:Green:White - x:3x:2x
Container 2 - Gold:Green:White - 4a:a:3a

Question says x+4a = 3x+a or a = 2x/3

This means, for container 2, the ratio becomes - 4(2x/3): 2x/3: 3(2x/3) - 8x/3: 2x/3: 6x/3

Multiply both C1 and C2 ratios by 3

C1 - 3x:9x:6x (total 18x)
C2 - 8x:2x:6x (total 16x)
Hence C1:C2 - 18x:16x or 9:8. The answers have to be in this ratio. If for C1 we take 72, C2 becomes 72/9*8 = 64. Thus C1 = 72 and C2 = 64.

rockstar09rulez

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14 Jul 2026, 21:08

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C1 ratios: x, 3x, 2x - Total 6x
C2 ratios: 4y, y, 3y - Total 8y

Given gold = green across both
So. x + 4y = 3x + y -> gives 3y = 2x

will use ratios for easily finding solution
C1/C2 = 6x/8y = 6/8 * 3/2 = 9/8

If C1 has 81, C2 can have 72
If C1 has 72, C2 can have 64

2 solutions possible but C1 should also be a multiple of 6 and 81 is not a multiple of 6
so C1= 72, C2 = 64

alamin8

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14 Jul 2026, 21:21

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Container 1. The sum of the ratio = 1+3+2 = 6
Let's test the answer choices, 54 and 72 are only numbers who can be divisible by 6 for container 1.
If 54, Gold = 9, Green = 27, White = 18
If 72, Gold = 12, Green = 36, White = 24 (Answer for C1)

Container 2. The sum of the ratio = 4+1+3 = 8
Answer choices 40, 64, and 72 can be divided by 8.
If 40, Gold = 20, Green = 5, White = 15 (Combining 54(C1) and 40(C2), since Gold and Green must be equal, G=29 and Gr = 32, not matched)
If 64, G = 32, Gr = 8, W = 24 (Combining 72 for C1 and 64 for C2, G = 44, Green = 44)! (Answer for C2)

Container 1 = 72
Container 2 = 64

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14 Jul 2026, 22:16

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Container 1
Gold:Green:White = 1:3:2
Total = x+3x+2x =6x

Container 2
Gold: Green: White = 4:1:3
Total = 4y+y+3y = 8y

We have total gold = total green
x + 4y = 3x + y
3y = 2 x
x = 3y/2

Total beads in container 1 = 6 x = 6 (3y/2) = 9y

So, beads in container 1 /beads in container 2 = 9y/8y = 9/8

So,

Container 1 must be a multiple of 6
container 2 must be a multiple of 8
Ratio of total beads in both container = 9:8

In given choices,

only 54 & 72 are multiple of 6
only 64 & 72 are multiple of 8

Among both, only 72 & 64 satisfy the ratio condition of 9:8

Answer :
Container 1 = 72
Container 2 = 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.

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.

SwethaReddyL

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14 Jul 2026, 22:26

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given that the combined gold is equal to green we have,
x+4y = 3x+y which simplifies as 2x=3y; x/y = 3/2
they asked for total in those containers,
C1:C2 = 6x:8y, which we can simplify as 3x/4y, substitute x and y you get, 9/8
the only values the fit in the ratios for C1 and C2 are 72 and 64

thanks,
Swetha

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.

vartikg

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14 Jul 2026, 22:43

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consider the total beads in container 1 as 6x, and container 2 as 8y. as per the question now, x+4y=3x+y; y=2/3x. use this to convert container 2's quantity of beads and we get the answer. DO NOT find x in terms of y it will lead to multiple answers. try and go with a fractional answer because it will minimize your answer possibilities.

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.

GamePine

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14 Jul 2026, 22:45

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Container 1's ratio is 1:3:2 which is 6 parts, so the number of beads must be a multiple of 6. Container 1 = 6x where x is the number of gold beads

Container 2's ratio is 4:1:3 so the number of beads is a multiple of 8. Container 2 beads = 8n where n is the number of green beads.

If the number of gold and green are equal, x + 4y = y + 3x. This represents that the total amount of beads outside of green and gold are equal.

when you solve you get x = 3y/2. y must be an even number because it must be divisible by 2 for x to be an integer. So I set y to equal 2z and therefore x = 3z based on the formula we solved for.

Container 1 = 6x = 18z
Container 2 = 8y = 16z

I tested different values for z and when z equals 4, container 1 is 72 and container 2 is 64.

vasu1104

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15 Jul 2026, 00:27

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C-1 gold:green: white = 1:3:2= x:3x:2x = 6x

C-2 = gold:green:white = 4:1:3 = 4y:y:3y = 8y

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

need to find, 6x and 16x/3

use the choice and test them to get the ans.

when 6x= 72, x= 12 and 16x/3 = 64

so c-1 = 72
c-2= 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.

ajain31

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15 Jul 2026, 00:52

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cont 1
Gold:Green:White
1:3:2
Gold = x, Green = 3x and White = 2x
total 6x

cont 2:
Gold: Green: White
4:1:3

let multiiple be y

gold = 4y green = y white = 3y
total 8y

across both cons total gold equals total green x+4y = 3x+y

rearrange 3y=2x

x:y = 3:2

x = 3k y = 2k

total umber of beads are c

cont 1 = 6x = 6x3k = 18k
cont 2 = 8y = 8x2k = 16k

total 18:16 = 9:8

choices has 72:64 which boils down to 9:8

cont 1 72
cont 2 64

quick check: k = 4 x = 12 y = 8
combined gold and green both come to 44

CrazyBlender123

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15 Jul 2026, 01:19

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Container 1:54
Container 2:72
Because,
54/6=9
and 72/8=9 and it satisfies the condition.
T_Gold= 1/6
T_Green=1/8

remdelectus

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15 Jul 2026, 01:22

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The ratio of the number of beads is:
Container 1, G:GR:W=1:3:2
total=6X
gold=x
green=3x
Container 2, G:GR:W=4:1:3
total=8y
gold=4y
green=y

gold=green
x+4y=3x+y
4y-y=3x-x
3y=2x
x=3/2y
let y=2k and x=3k
cont 1=6x=18k
cont 2=8y=16k
TITA
18K is one of 40,45,54,64,72,81
16k is one of 40,45,54,64,72,81
k=3: 18k=54, 16k=48 no
k=4: 18k=72, 16k=64 yes

then the viable pair is:
container 1: 72
container 2: 64

noerd23

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15 Jul 2026, 01:50

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Let x be the scale factor for Container 1.

Container 1 ratio = 1 : 3 : 2 (total = 6)

Gold = x
Green = 3x
White = 2x
total beads = 6x.

From the options, Container 1 must be a multiple of 6: 54 or 72.

Let y be the scale factor for Container 2

Container 2 ratio = 4 : 1 : 3 (total = 8)

Gold = 4y
Green = y
White = 3y
total beads = 8y.

From the options Container 2 must be a multiple of 8:
40, 64, or 72.

Given: Total gold = Total green

-----> x + 4y = 3x + y

-----> 4y − y = 3x − x

-----> 3y = 2x

Now test the possible values.

Container 1 = 54 → x = 9
Then 2x = 18, so y = 6 (not an option).

Container 1 = 72 → x = 12
Then 2x = 24, so y = 8.

y = 8 gives Container 2 total = 8 × 8 = 64.

Therefore,
Container 1 = 72
Container 2 = 64

canopyinthecity

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15 Jul 2026, 02:14

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C1: 1x Go, 3x Gr, 2x W, 6x total
C2: 4y Go, 1y Gr, 3y W, 8y total
As per question, total green = total gold
1x + 4y = 3x + 1y
=> 3y = 2x
=> 9y = 6x

So C1: 9y and C2: 8y

I tried combinations in options and found 3 valid pairs: (45,40), (72,64), (81,72)

But since bead counts should be integer, I tested if dividing by 6 and 8 correspondingly comes an integer value, only 1 pair satisfied

Hence 72 and 64 is the answer

GulfTube

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15 Jul 2026, 02:32

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this is very interesting solution mixture word problem disguised very well. if you recognize that it becomes fairly easy.
let x & y be total number of beads in C1 & C2.
1/6 is ratio of gold in C1 which is analogous to percentage by weight in solution mixture problems. similarly 4/8 = 1/2 is ratio of gold in C2.
3/6 = 1/2 is ratio of green in C1. 1/8 is ratio of green in C2.

lets look at gold first:
treat it as weighted average:
1/6 & 1/2 are the statistics , and x & y are the weights.
(1/6)x+(1/2)y = (2x+6y)/12

lets look at green now:
1/2 & 1/8 are statistics , and x & y are weights.
(1/2)x+(1/8)y = (4x+y)/8

these are the ratios of gold & green beads in the overall display, not the raw counts of gold and green beads. to get that we will have to multiply each to the total number of beads in the display which is (x+y).
notice that since we are given that gold & green beads in display are equal, we will equate the two expressions & (x+y) will cancel out so we can ignore it.
(2x+6y)/12 = (4x+y)/8
x/y = 9/8
easiest way instead of now running through answer choices is to multiply the numerator & denominator by common number to reach the numbers that are given in answer choices.
if we multiply both by 8 we get x/y = 72/64. hence x = C1 = 72 & y=C2=64

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15 Jul 2026, 02:53

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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.

Let Container 1 have ratio 1 : 3 : 2.

Total parts = 6,

so if the total is 18k,
then
Gold = 3k
Green = 9k

Container 2 has ratio 4 : 1 : 3.
Total parts = 8,

so if the total is 16k,
then: Gold = 8k
Green = 2k

Since total gold = total green:

3k + 8k = 9k + 2k which works when the totals are in the ratio:

Container 1 : Container 2 = 18 : 16 = 9 : 8

From the choices, the only matching pair is:

Container 1 = 72
Container 2 = 64

K812

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15 Jul 2026, 03:03

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Container 1:

Total beads = 6x
Gold : Green : W = x:3x:2x

Container 2:

Total beads = 8y
Gold: Green: W = 4y:y:3y

Equation given: x + 4y = 3x + y

From this, we get the relationship between x and y : x = 3/2 (y)

Inferences:
1. Total beads in container two should be a multiple of 8
So, possibilities from the options for second container = 40, 64, 72

2. y has to be even for x to be an integer

If 8y = 40, y =5- Not possible. Similarly, if 8y = 72, y =9 Not possible

If 8y= 64, y =8
x = 12

Put the values in the given equation for total gold and green beads: 12 + 32 = 36 + 8 (Satisfies)

Correct answer: Container 1 = 72, Container 2= 64

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15 Jul 2026, 03:26

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Let the total no. of beads be
Container 1 = 6x ( ratio 1:3:2)
Container 2 = 8y (ratio 4:1:3)
So,
Container 1 : Gold = x , Green = 3x
Container 2 : Gold = 4y , Green = y

Since Total Gold = Total Green
-> x+4y = 3x+y
-> 3y = 2x

Let x = 3k and y = 2k. Then

Container 1 total = 6(3k) = 18k
Container 2 total = 8(2k) = 16k

So totals must be in the ratio 18:16 = 9:8

From the options, the only pair in the ratio 9:8 is 72:64

Ans:
Container 1 : 72
Container 2 : 64

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15 Jul 2026, 03:30

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From the passage.
Cont. 1=> G|Grn|wh = 1|3|2 => x|3x|2x => total would be 6x
Cont. 2=> G|Grn|wh = 4|1|3 => 4y|y|3y => total would be 8y
we are given that x+4y = 3x + y => x/y = 3/2

Now the ratio of cont 1/cont 2 = 6x/8y =(6/8)*(3/2) = 9/8
we need to find a combination of numbers which satisfy above condition.
Cont 1. multiple of 6 => 54 and 72
Cont 2. Multiple of 8 => 40, 64 and 72.
Out of these, 72 and 64 would be closest to come to ration 9/8
Cont 1/ cont 2 = 72/64 (cancel by 8)= 9/8

So answer is container 1=72 and container 2= 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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15 Jul 2026, 04:35

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C1 1:3:2 = x+3x+2x=6x
C2:4:1:3= 4y+y+3y=8y
Given x+4y=3x+y= 2x=3y =x=1.5y
Meaning C1=9y(6x1.5y)
And C2 = 8y
Testing cases we could start with y=5 and get C1=45 and C2=40 but this fails the Gold=Green being equal case because 45 is not divisible by 6 as expected from ratio above
The next case y=8 (x=12) works perfectly
Meaning container 1 is 9x8= 72
Container 2= 8x8= 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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15 Jul 2026, 04:47

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c1 ratio = 1:3:2 ⇒ total = 6k1

g1 = k1, gr1 = 3k1

c2 ratio = 4:1:3 ⇒ total = 8k2

g2 = 4k2, gr2 = k2

given:

g1 + g2 = gr1 + gr2

k1 + 4k2 = 3k1 + k

3k2 = 2k1

k1 : k2 = 3 : 2

so,

c1 total : c2 total

= 6(3) : 8(2)

= 18 : 16

options:

c1 must be multiple of 18 - 54, 72

c2 must be multiple of 16 - 64

only pair with ratio 18:16

72 : 64 = 18 : 16

ans: c1 = 72, c2 = 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.