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655-705 (Hard)|   Math Related|         
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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 18:59
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Castel = 2W + 6S + M
Mansion = 6W + 4S + 2M

Player
12W
18S
9M

You have to divide the players resources by the building costs, and the limiting resource gives you the maximum for each.

Castle = 3 (Stone is the limit)
Mansion = 2 (Wood is the limit)

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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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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 20:29
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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."

Let S = Stone, W = Wood, and M = Metal

A castle requires 2 units of wood, along with three times as much stone as wood, and twice as much wood as metal.
W = 2
S = 3*2 = 6
M = 1/2 * 2 = 1

Castle's ratio (individual cost):
S:W:M
6:2:1

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 = 2/3 * 6 = 4
M = ( 6 + 4 ) / 5 = 10 / 5 = 2

Mansion's ratio (individual cost):
S:W:M
4:6:2


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

S = 18
W = 2/3 * 18 = 36/3 = 12
M = 1/2 * 18 = 9

Available resources:
S:W:M
18:12:9

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.

Castle -> Stone: 18/6 = 3, Wood: 12/2 = 6, Metal: 9/1 = 9 -> Castle: Min(3, 6, 9) = 3
Mansion -> Stone: 18/4 = 4.5, Wood: 12/6 = 2, Metal: 9/2 = 4.5 -> Castle: Min(2, 4.5) = 2

Answer:
Castle: 3
Mansion: 2
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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 20:56
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mansion = 6Wood + 4Stone + 2Metal - per stem
castle = 2Wood + 6Stone + 1Metal

the Player has 18 stone, 12 wood, and 9 stones

the limiting input on mansions will be wood; he can make at most 2 mansions per the wood requirement -- despite the excess in other inputs.

the limiting input on the castles will be the stone; he can make at most 3 castles per the stone requirement -- despite the excess in other inputs.

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This question was provided by GMAT Club
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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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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 21:04
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The player has 18 stone, with wood and metal given by 2/3 and 1/2 of stone, so 12 wood and 9 metal.

Castle: For each castle: wood = 2 units, stone = 3×wood = 6 units, metal = wood ÷ 2 = 1 unit; dividing resources by these shows stone limits castles to 3.

Mansion: For each mansion: wood = 6 units, stone = (2/3)×6 = 4 units, metal = 1 per 5 total wood + stone (6+4=10), so metal = 2 units; wood limits mansions to 2.

Since castles are limited by stone and mansions by wood, the maximum complete castles and mansions are 3 and 2 respectively.

Answer: 3 castles and 2 mansions.
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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 21:37
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NOTES:
Specific ratio of stone, wood, metal

castle requires 2 units of wood, along with three times as much stone as wood, and twice as much wood as metal
2 Wood, 6 stone, 1 metal

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.
6 Wood, 4 Stone, 2 metal

player has 18 units of stone, along with two-thirds as much wood and half as much metal as stone.
18 stone,12 wood, 9 metal
12 Wood, 18 stone, 9 metal

SOLVE:
Max number of complete castles.
Max number of mansions

Castle - stone is biggest factor of 6. so we can do 3 for 18 stone. Then we need 6 wood and 3 metal thats enough. 3 total!

Mansion- Wood is the big factor at 6. so 2 total that works for stone and metal also. 2 total

CASTLE: 3
MANSION: 2
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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 22:22
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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.

Total materials with player
Stone=18
Wood=2/3*18=12
metal=1/2*18=9

Castle requirements
Wood=2
Stone=2*3=6
Metal=1/2*2=1

Total castles that can be made=
Wood = 12/2=6
Stone=18/6=3
Metal=18/1=18

So max castles can be 3

Mansion requirements
Wood=6
Stone=2/3*6=4

Metal=1/5*(6+4)=2

Max mansions that can be made
wood=12/6=2
Stone=18/4=4.5
Metal=9/2=4.5

Max mansions that can be made is 2
Max castles =3
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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 22:43
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Castle Requires:

Wood, \(w=2\)
Stone, \(s= 3w=6\)
Metal, \(2m=w; m=\frac{w}{2}=1\)

Mansion Requires:

\(w=6\)

\(\frac{s}{w}=\frac{2}{3}\); \(s=4\)

\(\frac{m}{s+w}=\frac{1}{5}; \frac{m}{10}=\frac{1}{5}\); \(m=2\)

WoodStoneMetal
Castle261
Mansion642

Available units:

\(s=18\)
\(w=\frac{2}{3}s=12\)
\(m=\frac{s}{2}=9\)

WoodStoneMetal
Castle261
Mansion642
Available18129

Maximum no of Castles:

WoodStoneMetal
Castle, \(c\)261
Available, \(a\)18129
\(\frac{a}{c}\)929

Min of \(\frac{a}{c}\) is \(2\). Max \(2\) castles can be built

Maximum no of Mansions:

WoodStoneMetal
Mansion, \(m\)642
Available, \(a\)18129
\(\frac{a}{m}\)334.5

Min of \(\frac{a}{m}\) is \(3\). Max \(3\) mansions can be built


Castles: 2

Mansions: 3
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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 23:08
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Given Resources:
Stone(S) = 18 units
Wood(W) = (2/3) × 18 = 12 units
Metal(M) = (1/2) × 18 = 9 units

Castle:
W= 2 units
S= 3 times as much as wood = 3*2= 6 units
M= half as much as wood= (1/2)*2= 1 unit

Mansion:
W= 6units
For stone it is given S: W= 2:3
==> S= (2/3)*6 = 4units
Total W+S = 10units
1 unit of Metal for every 5 units of (W+S)
So, Metal = 10/5 = 2units

1 Castle requirement= 2W,6S,1M
From given resources max number castle that can be built-
Based on wood=12/2=6 castles
Based on stone = 18/6= 3 castles(limiting resource)
Based on metal= 9/1= 9 castles

Since stone is the limiting resource the max number of castles can be built is 3

1 Mansion requirement= 6W,4S,2M
From given resources max number Mansions that can be built-
Based on wood=12/6=2 Mansions(Limiting resource)
Based on stone = 18/4= 4.5= 4 Mansions
Based on metal= 9/2= 4.5= 4 Mansions

The limiting resource is wood so the max number of complete Mansions that can be built is 2
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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 11 Jul 2025, 00:30
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Bunuel
 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 



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.
Show more

A castle requires 2 units of wood, along with three times as much stone as wood, and twice as much wood as metal.
Wood = 2
Stone = 6
Metal = 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.
Wood = 6
Stone = 2*6/3 = 4
Metal = (6+4)/5 = 2

The player has 18 units of stone, along with two-thirds as much wood and half as much metal as stone.
Wood = 12
Stone = 18
Metal = 9

To build a castle we have the least amounts would be
Wood = 12/2 = 6
Stone = 18/6 = 3
Metal = 9/1 = 9
Least is 3 hence 3 full Castles can be made

To build a mansion we have the least amounts would be
Wood = 12/6 = 2
Stone = 18/4 = 4.5
Metal = 9/2 = 4.5
Least is 2 hence 2 full mansions can be made


Castle = 3
Mansion = 2
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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 11 Jul 2025, 00:39
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Castle
wood = 2 units
stone = 3(units of wood) = 6 units
metal = 0.5(wood) = 1 unit

Mansion
wood = 6 units
stone = 6*2/3= 4 units
metal = 10/5 = 2 units >>1 unit of metal for 5(wood + stone ), so 2 units of metal for 10 (6 wood + 4 stone )

Wood Stone Metal
Castle 2 6 1
Mansion 6 4 2

Since question requires us to build complete mansions, we cannot reduce the ratio for mansion from 6:4:2 to 3:2:1.
available resources : 12 units of wood, 18 units of stone, and 9 units of metal
For maximum castles
> here the maximum limit will depend on the resource which is the bigger out of the three, which is stone
> 6 units of stone are required for 1 mansion
> Available to us : 18 units of stone , 18/6 = 3 castles can be made using our resources
3 castles will use 6 units of wood, 18 units of stone and 3 units of metal in total

For maximum mansions
> here the maximum limit will depend on the resource which is the bigger out of the three, which is wood.
> 6 units of wood are required for 1 mansion
> Available to us : 12 units of wood, 12/2 = 2 mansions can be made using our resources
2 mansions will use 12 units of wood, 8 units of stone and 4 units of metal in total


Maximum 3 castles, 2 mansions
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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 11 Jul 2025, 00:40
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Bunuel
 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 



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.
Show more


Final Answer:

Castle: 3
Mansion: 2
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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 11 Jul 2025, 00:59
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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 (3*2 = 6 units of stone), and twice as much wood as metal (1 unit of metal).
  • A mansion requires 6 units of wood, along with 2 units of stone for every 3 units of wood (4 units of stone for 6 units of wood), and 1 unit of metal for every 5 units of total wood and stone combined (2 units of metal for combined (6+4) 10 units.

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

Stone 18 units, Wood 18 * 2/3 = 12 Units, and Metal 18 * 1/2 = 9.


Select for Castle the maximum number of complete castles the player can build:

(18 / 6 = 3 Stones, 12 / 2 = 6 Wood, 9/1 = 9 Metal) From here, only 3 castles can be formed, considering all the requirements.


and select for Mansion the maximum number of complete mansions the player can build:

(18/4 = 4 Stones, 12/6 = 2 wood, from here only 2 Manson can be formed without considering metal, now for metal wood + stone would be 12 + 8 = 20; 4 Metal) Hence, only 2 mansions can be formed considering all the requirements.
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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 11 Jul 2025, 01:02
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Bunuel
 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

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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.
Show more
A Castle requires 2 woods, 6 stones, 1 Metal unit.
A Mansion requires 6 woods, 4 stone, 2 Metal Unit.

Available units are 12 wood, 18 stone, 9 Metal Unit.

Maximum Castle that can be built are 3 since 3 castle requires 6 woods, 18 stones, 3 Metal unit. No stone unit is left to build anymore castle.
Maximum Mansion that can be built are 2 since 2 Mansion requires 12 woods, 8 stones, 4 Metal unit. No wood unit is left to build anymore Mansion.
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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 11 Jul 2025, 01:55
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Bunuel
 


This question was provided by GMAT Club
for the GMAT Club Olympics Competition

Win over $30,000 in prizes such as Courses, Tests, Private Tutoring, and more

 



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.
Show more
Show Spoiler
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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 11 Jul 2025, 03:38
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As per the stem, for the castle ratio of stone : wood : metal is 6:2:1
for the Mansion , ratio is 4:6:2
The total number of stone =18, wood=12 and metal=9. Hence 39 units are available.
Since castle needs 9 units to make a full castle and mansion needs 12 units to make a complete mansion, we can make 4 castles =36units, for Mansion we can make a maximum of 3=36.
Not sure if we need to find max taking both together.

Hence castle is 4
Mansion is 3
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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 11 Jul 2025, 03:47
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Castle: 2w, 6s, 1m
Mansion: 6w, 4s, 2m

player: 12w, 18s, 9m

For castle the limiting factor is stone, 3 castles using 6w, 18s, 3m
For mansion the limiting factor is wood, 2 castles using 12w, 8s, 4m

Castle=3 and Mansion=2
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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 11 Jul 2025, 03:47
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Materials required by Castle ->
Wood = 2 units

Three times as much stone as wood -> Stone = 3(Wood)
Stone = 3*2
Stone = 6 units

Twice as much wood as metal -> Wood = 2(Metal)
2 = 2(Metal)
Metal = 1 unit

Materials required by Mansion ->
Wood = 6 units

2 units of stone for every 3 units of wood -> There two groups of 3 units of wood ->
Stone = 4 units

1 unit of metal for every 5 units of total wood and stone combined -> 6 units of wood + 4 units of stone = 10 units of wood and stone combined. That is the same as two groups of 5 units of total wood and stone combined.
Metal = 2 units

Player material ->
Stone = 18 units

Two-thirds as much wood as stone -> Wood = (2/3)(Stone)
Wood = (2/3)(18)
Wood = 12 units

Half as much metal as stone -> Metal = (1/2)(Stone)
Metal = (1/2)(18)
Metal = 9 units

Max Castles that can be built ->
Castles allowed by Wood = available/required = 12/2 = 6
Castles allowed by Stone = available/required = 18/6 = 3
Castles allowed by Metal = available/required = 9/1 = 9

Limiting factor is Stone. Maximum Castles = 3

Max Mansions that can be built ->
Mansions allowed by Wood = available/required = 12/6 = 2
Mansions allowed by Stone = available/required = 18/4 = 4.5
Mansions allowed by Metal = available/required = 9/2 = 4.5

Limiting factor is Wood. Maximum Mansions = 2
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twinkle2311
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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 11 Jul 2025, 04:03
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Here's what the player currently has :
Stones = 18 ; Wood = (2/3) * 18 = 12 ; Metal = (1/2) * 18 = 9

A castle needs 2 wood, 6 stone (3x of wood) and 1 metal (0.5x of metal)
Max castles that he can build is 3 because of stone limitation (18/6 = 3)

A mansion needs 6 wood, 4 stone (2/3x of wood), and 2 metal (1/5 of wood+stone)
Max castles that he can build is 2 because of wood limitation (12/6 = 2).

Ans : Castles = 3 ; Mansions = 2
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Tanish9102
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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 11 Jul 2025, 04:15
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Correct Answer: Total Castle & total Mansion= 3 & 2
1) Materials Castle required

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

Wood= 2
Stone= 6
Metal= If wood is 2 then must be 1

2) Materials Mansion required

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

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

Wood= 12
Stone= 18
Metal= 9

Now let’s check maximum possible castle and mansion can be made using total material we have:

1) Maximum mansion can be made= 2 because we have total 12 units of woods and mansion needs minimum 6 units of woods for completing 1. So 2 mansion can be made using this raw materials.


2) Maximum castle can be made= 3, because we have total 18 units of stone and one castle needs minimum 6 units of stone for completing. So 3 castle can be made using this raw materials.
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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 11 Jul 2025, 04:25
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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.
C=2w+6s+4m
M=6w+4s+2m
given , w=18, s=12, m=6
So, for C at max, we can build 2 complete castles as we have only 12 stones, and for 1 unit, 6 is required
And for M at max, we can build 3 complete mansions as we have 18 w and 6 is required for each and 12 stones, 4 for each, and 6 metal, 2 for each.
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