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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, 10:00
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This question is more of a play of words.
The crux is to gather the correct numbers.

Castle requires 2W , 6S , 1M
Mansion requires 6W , 4S , 2M

Player has : 18S , 12W , 9M

So maximum number of Castles that can be formed is 3.

So maximum number of Mansions that can be formed is 2.
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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 10:13
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Deriving from the statements:

Castle requires 2 units of wood, 6 units of stone and 1 unit of metal.

Mansion requires 6 units of wood, 4 units of stone and 2 unit of metal.

Max Castles 3 since we have only 18 stones as per statement.

Max Mansions 2 since we have only 6 units of wood as per statement.

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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, 10:18
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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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From the given information, we can derive,

Stone: 18
Wood: 12
Metal: 9

So now we need to know the min requirements to build castle and mansion.

Castle :
Stone = 6
Wood = 2
Metal = 1

Hence, 3 Castles are possible with the resources.

Similarly, for mansion :

Stone = 4
Wood = 6
Metal = 2

Hence, 2 mansions are possible.

IMO Castle :3
Mansion: 2
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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 10:18
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Castle Requirements:

Wood = 2 units
Stone = 3*Wood = 6 units
Metal = Wood/2 = 1 units

Mansion Requirements

Wood = 6 units
Stone = in ratio 2:3 with Woods = 4 units
Metal = in ratio 1:5 w.r.t Woods & Stones = 2 units

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

Wood = 12 units
Stone = 18 units
Metal = 9 units

Maximum number of castles that can be build ?

A castle will require 2 units of woods, 6 units of stone and 1 unit of metal

Stone will be the limiting unit when building castle, therefore number of stone units will decide maximum number of castles that can be build

stone units we have = 18 units
castle requires 6 units

number of castles that can be build = 18/6 = 3 castles

Maximum number of mansions that can be build ?

A mansion will require 6 units of woods, 4 units of stone and 2 unit of metal

Wood will be the limiting unit when building mansion, therefore number of woods units will decide maximum number of mansions that can be build

wood units we have = 12 units

number of mansions that can be build = 12/6 = 2 mansions
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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, 10:24
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Approaching this problem we can first of all start by converting the word problem into numerical value. For each castle we need the following resources: 2 wood, 6 stone and 1 metal. For each mansion we need the following resources: 6 wood, 4 stone and 2 metal. The player has 12 Wood, 18 Stone and 9 Metal.

If the player wants to build the maximum amount of castles the first resource that will run out will be the stones which allow the player to build up to 3 castles.
If the player wants to build the maximum amount of mansions the first resource that will run out will be the wood which allows the player to build up to 2 mansions.

Regards,
Lucas
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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, 10:26
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lets make table of the information given:

woodstonemetal
Castle261
Mansion642
Available12189

clearly we can make 3 castles and 2 mansions
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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 10:49
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A Castle requires:
2 woods, 6 Stones and 1 Metal

A Mansion requires:
6 woods, 4 Stones and 2 Metal

Player has:
18 stones, 12 woods and 9 Metal (After basic calculation given in conditions)

Max Castle:
Here max requirement is of Stones, so we will check with stones.
Stones = 18/6 =3
woods and metal also fulfill.

Therefore, Maximum Castle= 3

Max Mansion:
Here max requirement is of woods, so we will check with woods
Woods = 12/6 =2
stones and metal also fulfill.

Therefore, Maximum Mansion= 2
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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 11:12
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Requiredwoodstonemetal
Castle ratio241
Mansion ratio321


Player haswood stonemetal
Ratio12189

1) maximum number of complete castles the player can build

Stone is maximum: 4*4=16. Therefore, 4


1) maximum number of complete masions the player can build

wood is maximum: 3*4=12. Therefore, 4
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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, 11:16
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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.
Castle requires 2 unit of wood, 6 units of stone and 1 unit of metal
Mansion requires 6 units of wood, 4 units of stone and 2 units of metal

The player has 18 units of stone, along with two-thirds as much wood and half as much metal as stone.
Total 12 units of wood, 18 units of stone & 9 units of metal are available

Maximum number of castles = min (12/2, 18/6, 9/1) = min (6,3,9) = 3
Maximum number of mansions = min(12/6, 18/4, 9/2) = min (2,4.5,4.5) = 2

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.

CastleMansion
32
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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 11:27
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Wood(w), Stone(s), Metal(m)

Material required:
Caste: 2w + 6s + 1m
Mansion: 6w + 4s + 2m

Material available: 12w +18s + 9m

For maximum Castle: (2w + 6s + 1m)*3 =6w + 18s + 3m, which is maximum available stone
Therefore max. 3 castles.

For maximum Mansion: (6w + 4s + 2m)*2= 12w + 8s + 4m, which is maximum available wood
Therefore max. 2 mansions.

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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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 11:39
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Stone. Wood Metal
Castle 6 2 1
Mension 4 6. 2

Total 18 12 9

Highest possible for castle, max 6 stone and total 18, then 3

Highest possible for castle, Max 6 wood, then max wood 12, then capacity 2
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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 11:40
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Bunuel
 


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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The computer game Stoneforge Dominion , a player can use the available resources to build Castles and Mansions.

To build such a structure, we need specific components like Stone , Wood and Metal, but at some specific ratio.

Castle requires :

2 units of wood.

3* 2 units of wood = 6 units of Stone.

1 unit of metal.

Ratio of Wood : Stone : Metal = 2: 6: 1

Mansions requires :

6 units of Wood.

4 units of Stone.

2 units of Metal.

Ratio of Wood : Stone : Metal = 6: 4: 2

The Resource available is 18 stone, (2/3)*18 = 12 wood, and (1/2)*18 = 9 metal.

Ratio of Wood : Stone : Metal = 12: 18: 9

Maximum castles that can be built with the available resource is :


Ratio of Wood : Stone : Metal = 2x : 6x : 1x . For x =3, we get wood : stone : metal = 6:18:3

Maximum number of castle = 3

Maximum mansions built using the resources is Ratio of Wood : Stone : Metal = 6y: 4y : 2y . For y= 2, the ratio of wood: Stone : Metal = 12: 8 : 4

This has utilised 100% of wood. So, the maximum mansions built is 2.

Maximum castle = 3

Maximum Mansion = 2
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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 12:08
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Bunuel
 


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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A Castle need: 2 units of Wood , S=3W=3*2=6 units, W=2M => M=1/2W=2/2=1 unit
A Mansion need: 6 units of Wood, each 2S for every 3W => S=6/3*2=4 units, 1M for every 5 of (S+W) => S+W=10 => M=10/5=2 units.

The player has 18 units of Stone, W=2/3S=18*2/3=12 units, M=1/2S=18/2=9 units.

The maximum Castle that the player can build is 3 (each Castle needs 6 units of stone, and the player has 18 units total)
The maximum Mansion that the player can build is 2 (each Mansion needs 6 units of wood, and the player has 12 unit total)

=> Answer: Castle 3 Mansion 2
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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 12:28
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For 1 castle we need: 2 wood, 6 stones, 1 metal
For 1 Mansion we need: 6 wood, 4 stones, 2 metal

We have 18 stones, 12 woods, 9 metals

So max number of castles, we need to identify limiting material
wood => 12/2 = 6
Stones => 18/6 = 3
Metals => 9/1 = 9

Hence stone is limiting and we can build max 3 castles

For max mansions, we need to identify limiting material
wood => 12/6 = 2
Stones => 18/4 = 4.5
Metals => 9/2 = 4.5
So limiting material is wood and we can build 2 mansion

Hence Answer is:
Castle 3
Mansion 2
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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, 12:58
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Bunuel
 


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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Castle

Wood: 2 units
Stone: 6 units
Metal: 1 unit

Mansion

Wood: 6 units
Stone: 4 units
Metal: 2 unit

Player has:

Wood: 12 units
Stone: 18 units
Metal: 9 unit

Number of Castle the player can create

Wood: 12/2 = 6 units
Stone: 18/6 =3 units
Metal: 9/1 = 4.5 unit

Min = 3

Number of Mansion the player can create

Wood: 12/6 = 2 units
Stone: 18/4 =4.X units
Metal: 9/2 = 4.X unit

Min = 2

Castle = 3
Mansion = 2
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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 13:34
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First, we simplify the information to see how much of each resource each castle and mansion needs, along with the available resources.

Stone Wood Metal
Castle 621
Mansion 462
Available resources 18129

So, based on the resources, the player can make at most 3 castles, with stone being the resource limit for more.
And, he can make 2 mansions, with wood being the resource limit for more.

So the answer is 3 for the castle and 2 for the mansion.

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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pappal
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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 14:05
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lets denote castle-C, mansion-M, wood-w, stone-s, metal-m
C&M are built with specific ratio of s:w:m
1. for C-> s:w:m=6:2:1 (simple ratio formulation)
2. for M-> s:w:m=4:6:2 (simple ratio formulation)
player has s=18, w=2/3*s=12, m=1/2*s=9
he can build Cmax=3(restriction from stone 6*3)
& Mmax=2(restriction from wood 6*2)
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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 14:38
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Given data,

A castle requires 2 units of wood, along with three times as much stone as wood, and twice as much wood as metal.
=> Wc = 2, Sc = 2Wc = 6, Mc= 2Wc = 4

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.
=> Wm = 6, Sm = (2/3)Wm = 4 , Mm = (1/5)(Wm+Sm) = 2

The player has 18 units of stone, along with two-thirds as much wood and half as much metal as stone.
=>Sp = 18, Wp =(2/3)S = 12, Mp = (1/2)Sp = 9

Now lets solve for
(a) Castle the maximum number of complete castles the player can build
Stone = Sp/ Sc = 18 /6 = 3
Wood = Wp/Wc = 12/ 2 = 6
Metal = Mp/Mc = 9/1 = 9

from above values, we can understand only 3 complete castles can be build

Therefore castle = 3

(b) Mansion the maximum number of complete mansions the player can build
Stone = Sp/ Sm = 18/4 = 4.5
Wood = Wp / Wm = 12/6 = 2
Metal = Mp / Mm = 9/2 = 4.5

from above values, we can understand only 2 complete mansions can be build

Therefore mansion = 2
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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 16:02
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So what we know =
For Castle =>
2 unit wood,
3*2= 6 unit stone
2*2=4 unit metal

For Mansion =>
6 unit = wood,
2 units of stone for every 3 units of wood so 6/3 * 2 = 4 unit stone,
1 unit of metal for every 5 units of total wood and stone combined so 6 + 4 = 10 unit so for 10 units 1 unit metal

Now available things are:
18 units of stone, along with two-thirds as much wood and half as much metal as stone.
2/3 * 18 = 12 unit of wood.
18/2 = 9 unit of metal

so for Max Castle => lets see with 18 stone we can make max 3(18/6=3) castle, with 6 wood we can make 3(12/2=6) castle, 9 metal we can make 2(9/4 = 2.25) castle. but with combining this we can only make max 2 castles. due to metals

now for Max Mansion = >
with 12 wood / 6 per mansion = 2 mansions we can make
with 18 stone / 4 per mansion = 4.5 mansions we can make
with 9 metal / 1 per mansion = 9 mansions we can make
So all in all we can make only 2 mansions. hence 2

hence ans 2 for both
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GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 18:14
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Strategy: Ratio Tables
Variable(s)- Wood = "W"; Stone = "S"; Metal = "M"; Ratio Multiplier for Castle = "x"; Ratio Multiplier for Mansion = "y"

1) Use the Scale factor to go from ratio units to actual units, which provides the max # of each
i) Castle Ratio Table

Scale Factor WSMSUM
2X3*(2X)=6X(1/2)*(2X)=X9X
(2/3)*(18)=1218(1/2)*(18)=936
(4/X)(4/X)*(9x)=36

ii) Mansion Ratio Table
Scale Factor WSMSUM
2y3y(1/5)*(2y+3y)=1y6y
1218936
(6/y)(6/y)*(6y)=36

Answer: Castle = 4, Mansion = 6
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