GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge : Two-part Analysis (TPA)

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10 Jul 2025, 09:06

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Here's a step-by-step calculation to determine the maximum number of castles and mansions the player can build:

1. Calculate Available Resources:

Stone: 18 units (given)

Wood: "two-thirds as much wood as stone" = (2/3) * 18 = 12 units

Metal: "half as much metal as stone" = (1/2) * 18 = 9 units

So, the player has:

Stone: 18

Wood: 12

Metal: 9

2. Calculate Resource Requirements per Castle:

Wood: 2 units

Stone: "three times as much stone as wood" = 3 * 2 = 6 units

Metal: "twice as much wood as metal" means Metal = Wood / 2 = 2 / 2 = 1 unit

So, one castle requires:

Stone: 6

Wood: 2

Metal: 1

3. Calculate Maximum Castles:

From Stone: 18 (available) / 6 (per castle) = 3 castles

From Wood: 12 (available) / 2 (per castle) = 6 castles

From Metal: 9 (available) / 1 (per castle) = 9 castles

The limiting factor is stone. Therefore, the maximum number of complete castles the player can build is 3.

4. Calculate Resource Requirements per Mansion:

Wood: 6 units

Stone: "2 units of stone for every 3 units of wood" = (2/3) * 6 = 4 units

Metal: "1 unit of metal for every 5 units of total wood and stone combined"

Total Wood and Stone for one mansion = 6 (wood) + 4 (stone) = 10 units

Metal = 10 / 5 = 2 units

So, one mansion requires:

Stone: 4

Wood: 6

Metal: 2

5. Calculate Maximum Mansions:

From Stone: 18 (available) / 4 (per mansion) = 4.5 -> cannot build 0.5, so 4 mansions

From Wood: 12 (available) / 6 (per mansion) = 2 mansions

From Metal: 9 (available) / 2 (per mansion) = 4.5 -> cannot build 0.5, so 4 mansions

The limiting factor is wood. Therefore, the maximum number of complete mansions the player can build is 2.

Final Answer:
Castle: 3
Mansion: 2

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10 Jul 2025, 09:08

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First, let's identify the available resources:
* Stone: 18 units
* Wood: 2/3 x 18 = 12 units
* Metal: 1/2 × 18 = 9 units
Now, let's determine the requirements for each structure:
For a castle:
* Wood: 2 units
* Stone: 3 x wood = 3 × 2 = 6 units
* Metal: wood ÷ 2 = 2 ÷ 2 = 1 unit
For a mansion:
* Wood: 6 units
* Stone: (2/3) × wood = (2/3) × 6 = 4 units
* Total wood and stone: 6 + 4 = 10 units
* Metal: (1/5) × total wood and stone = (1/5) × 10 = 2 units
Now I'll calculate how many of each structure can be built based on each resource limitation:
For castles:
* Based on stone: 18 ÷ 6 = 3 castles
* ⁠Based on wood: 12 ÷ 2 = 6 castles
* Based on metal: 9 ÷ 1= 9 castles
The limiting resource is stone, so the maximum number of castles is 3.
For mansions:
* Based on stone: 18 ÷ 4 = 4.5 mansions
* Based on wood: 12 ÷ 6 = 2 mansions
* Based on metal: 9 ÷ 2 = 4.5 mansions
The limiting resource is wood, so the maximum number of mansions is 2.
Therefore, the player can build a maximum of 3 castles or 2 mansions with the available resources.

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10 Jul 2025, 09:12

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In Stoneforge Dominion, the player starts with 18 units of stone. Based on the game’s resource rules, this means they also have 12 units of wood (which is two-thirds of the stone) and 9 units of metal (which is half the stone). To build a castle, the player needs a small amount of wood, but significantly more stone and a small portion of metal. Specifically, each castle needs three times more stone than wood, and the amount of wood required is twice as much as the metal. When calculating based on the available resources, the player can build a maximum of three complete castles before running out of stone, which is the limiting resource.
For mansions, each one requires a large amount of wood, a moderate amount of stone in proportion to the wood, and a small amount of metal based on the combined amount of wood and stone used. Given the available quantities, wood becomes the limiting factor. After checking how many full sets of wood, stone, and metal are needed per mansion, the player finds they can build a maximum of two complete mansions with the resources on hand.

Bunuel

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In the computer game Stoneforge Dominion, a player can use available resources to build castles and mansions. Each structure must be built using a specific ratio of three components: stone, wood, and metal.

A castle requires 2 units of wood, along with three times as much stone as wood, and twice as much wood as metal.
A mansion requires 6 units of wood, along with 2 units of stone for every 3 units of wood, and 1 unit of metal for every 5 units of total wood and stone combined.

The player has 18 units of stone, along with two-thirds as much wood and half as much metal as stone.

Select for Castle the maximum number of complete castles the player can build, and select for Mansion the maximum number of complete mansions the player can build, using the available resources. Make only two selections, one in each column.

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10 Jul 2025, 09:17

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material used
stone , wood & metal

total unit available
stone =18
wood = 12
metal = 9

castle requires 2 units of wood, along with three times as much stone as wood, and twice as much wood as metal.

for castle
wood = 2
stone = 6
metal = 1

maximum castle which can be made

stone = 18/6 ; 3
wood = 12/2 ; 6
metal = 9/1 ; 9
stone is limited so 3 maximum castles can be built

for Mansion

A mansion requires 6 units of wood, along with 2 units of stone for every 3 units of wood, and 1 unit of metal for every 5 units of total wood and stone combined.

Wood = 6
Stone = 4
Metal = 2

Maximum mansion that can built
stone = 18/4 ; 4.5
wood = 12/6 ; 2
metal = 9/2 ; 4.5

wood is limited
2 maximum mansions can be built

3 maximum castles can be built & 2 maximum mansions can be built

3, 2 is correct option

Bunuel

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A castle requires 2 units of wood, along with three times as much stone as wood, and twice as much wood as metal.
A mansion requires 6 units of wood, along with 2 units of stone for every 3 units of wood, and 1 unit of metal for every 5 units of total wood and stone combined.

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10 Jul 2025, 09:18

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Bunuel

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A castle requires 2 units of wood, along with three times as much stone as wood, and twice as much wood as metal.
A mansion requires 6 units of wood, along with 2 units of stone for every 3 units of wood, and 1 unit of metal for every 5 units of total wood and stone combined.

. For castle there are 2 woods,6 stones, 4 metals . There are a total of 30 woods,18 stones,27 metals .Meaning maximum wood is 30/2=15,stone is 18/6=3,metal is 27/4=6.7 therefore we take 3 as the maximum castles

For mansion there are 6 wood,4 stones,2 metals .we have 1 metal for every 5 units of wood and stones .But we have 30 woods,18 stones,27 metals. 1 unit=2stones ,3 woods,1 metal.implies we have 30/6=5 units of wood,18/4 =4.2 stones,27/2=13.5 metals.Therefore maximum mansion is 4 stones implies 4*2=8 mansions

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10 Jul 2025, 09:20

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So for 1 castle
It needs 2 units of wood,6 units of stone and 1 unit of metal.
The player has 18 stone,12 wood,9 metal from question

Suppose if there were 6 castle using 12 wood from user,then it would need 36 stone,which is not there with user.
Suppose if there were 3 castles using 18 stone from user,it would need 6 wood(which is there with user), and 3 metal(which is also there with the user)
So the max castle he can build is 3(because we used all of the 18 stone the user had)

For the mansion it requires 6 wood and the user has 12 wood.So the user can make either 0, 1 or 2 manions.But there is no 1 or 0 as a option,so 2 should be the answer.
Hence max mansion he can build is 2.

Bunuel

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A castle requires 2 units of wood, along with three times as much stone as wood, and twice as much wood as metal.
A mansion requires 6 units of wood, along with 2 units of stone for every 3 units of wood, and 1 unit of metal for every 5 units of total wood and stone combined.

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10 Jul 2025, 09:22

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S= 18; W= 2/3*18=12; M=1/2*18=9

Castle: 2W ; W= 3S , so 2W=6S ; W=2M, so 2W=4M
C= 2W:6S:4M

Mansion: 6W ; 2S per 3W, for 6W we need 4S;
1M per 5 units of W+S , So 6W+4S =10 ; M=10/5= 2
M= 6W:4S:2M

We have W=12, S=18, M=9
Castles = (Try using 1,2,3,4..... units of all and find max)
= 2W:6S:4M (Max here we can make is 2 castles because we only 9 Metals and 4*2=8)
Max castle = 2

Mansion = 6W:4S:2M (Max here is 2, as we only have 12 woods and to build 1 mansion we need 6 wood)

C=2 and M= 2

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10 Jul 2025, 09:28

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Wood = w, stone=s, metal=m
Castle requirement : 2w, 6s, 1m
Mansion requirement : 6w, 4s, 2m
Player inventory : 12w, 18s, 9m
So the max castles can be built is 3 .....(beyond 3, player wont have sufficient stone)
the max mansions can be built is 2 .......(beyond 2, player wont have sufficient wood)

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10 Jul 2025, 09:30

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By translating the statements into variables, we can get the ratio of stone(S), wood(W), and metals(M) for both castles and mansions.
We are also given the absolute number of items for each category as:
S=18, W=12, M=9

For castles:

S:W:M = 6:2:1
We can say that, S=6x, W=2x, and M=x

Thus for any value of x, we will have the maximum number of stones, since that has the largest multiple associated with it (i.e. 6)
If x = 3,
We will have S=18, W=6, M=3

Notice that we cannot make any more castles (i.e., x cannot be greater than 3) since the number of stones is the bottleneck.

For mansion:

S:W:M = 4:6:2
We can say that, S=4x, W=6x, M=2x

Thus for any value of x, we will have the maximum number of wood, since that has the largest multiple associated with it (i.e. 6)
If x = 2,
We will have S=8, W=12, M=6

Notice that we cannot make any more castles (i.e., x cannot be greater than 2) since the number of wood is the bottleneck.

Answer -
Castle: 3
Mansion: 2

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10 Jul 2025, 09:32

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A castle requires 2 units of wood, along with three times as much stone as wood, and twice as much wood as metal --> so w = 2, s = 6, m = 1

A mansion requires 6 units of wood, along with 2 units of stone for every 3 units of wood, and 1 unit of metal for every 5 units of total wood and stone combined --> w = 6, s =4, m = 2

The play has s = 18, w = 12, m=9. Therefore, for castle, stone is the limit with 3 castles. For mansions, woods are the limit with 2 mansions.

Answer: Castle = 3, mansion = 2

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10 Jul 2025, 09:40

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The player has 18 units of stone, 12 units of wood (two-thirds of stone), and 9 units of metal (half of stone). Each castle requires 6 units of stone, 2 units of wood, and 1 unit of metal, so the limiting resource for castles is stone, allowing a maximum of 3 castles. Each mansion requires 4 units of stone, 6 units of wood, and 2 units of metal, with wood as the limiting resource, permitting a maximum of 2 mansions. Therefore, the player can build up to 3 castles and 2 mansions with the available resources.

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10 Jul 2025, 09:42

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Castle:
Wood=2
Stone=6
Metal=1

Mansion:
Wood=6
Stone=4
Metal=2

Available: Stone=18, Wood=12, Metal=9

Castle: Stone decides no. of castles=18/6=3
Mansion: Wood decides no. of castles=12/6=2

Ans 3 & 2

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10 Jul 2025, 09:51

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	S	W	M	T
Castle	6	2	1	9
Mansion	4	6	2	12
Available total	18	12	9

Max castle
S=18/6=3
W=12/2=6
M=9/1=9
Stone is the lowest/limiting resource, so it's 3

Max mansion
S=18/4=4
W=12/6=2
M=9/2=4
Wood is the lowest/limiting resource, so it's 2

Bunuel

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A castle requires 2 units of wood, along with three times as much stone as wood, and twice as much wood as metal.
A mansion requires 6 units of wood, along with 2 units of stone for every 3 units of wood, and 1 unit of metal for every 5 units of total wood and stone combined.

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10 Jul 2025, 09:53

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for castle, wood= 2 units, stone= 6 units, metal= 4 units
for mansion, wood = 6 ,stone= 4, metal =2.
total, he has , he cn build 4 mansion and 3 castles

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10 Jul 2025, 09:53

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Bunuel

This question was provided by GMAT Club
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A castle requires 2 units of wood, along with three times as much stone as wood, and twice as much wood as metal.
A mansion requires 6 units of wood, along with 2 units of stone for every 3 units of wood, and 1 unit of metal for every 5 units of total wood and stone combined.

Given: Castle takes 2 units woods, 6 units stones and 1 metal
and 1 mansion takes 6 units of wood, 4 units of stone and 2 metal

Player has 18 stone, 12 wood and 9 metals

Therefore the player can build castles => limiting factor is stones, hence with 18 units of stone it can build 3 castles maximum.
and the limiting factor in mansion is wood so with 12 woods there can be 2 mansions at max. Hence the answer.

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10 Jul 2025, 09:54

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we have
– Stone: 18 units
– Wood: (2/3)·18 = 12 units
– Metal: (1/2)·18 = 9 units

	STONE	WOOD	METAL
CASTLE RECIPE	6	2	1
MASION RECIPE	4	6	2

WE HAVE	18	12	9

CASTLE limit - let's see who runs out first!
3 CASTLEs, stone depleted at 18:6:3.
Building MASION.
2 MASIONs, wood gone at 8:12:4.

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10 Jul 2025, 09:58

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Given Resources:
Stone: 18 units
Wood: (2/3) × 18 = 12 units
Metal: (1/2) × 18 = 9 units

CASTLE Requirements:
2 units wood
3 × wood = 6 units stone
Wood is 2× metal → So, metal = 2 / 2 = 1 unit
So, 1 castle needs:
Stone: 6
Wood: 2
Metal: 1

Now calculate how many complete castles can be made from:
18 stone → 18 / 6 = 3
12 wood → 12 / 2 = 6
9 metal → 9 / 1 = 9
The limiting factor is stone → Max castles = 3

MANSION Requirements:
6 units wood
2 units stone per 3 units wood → (6 wood) → (6 × 2) / 3 = 4 units stone
1 unit metal for every 5 units of (wood + stone)
Total wood + stone = 6 + 4 = 10
Metal = 10 / 5 = 2 units
So, 1 mansion needs:
Wood: 6
Stone: 4
Metal: 2

Now calculate how many complete mansions can be made:
Wood: 12 / 6 = 2
Stone: 18 / 4 = 4.5
Metal: 9 / 2 = 4.5

The limiting factor is wood -> Max mansions = 2