Last visit was: 18 Nov 2025, 14:08 It is currently 18 Nov 2025, 14:08
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
 1   2   3   4   
655-705 Level|   Math Related|         
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 Nov 2025
Posts: 105,355
Own Kudos:
778,062
 [5]
Given Kudos: 99,964
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,355
Kudos: 778,062
 [5]
GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 08:00
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide Answer
Hide
Show
History
Castle: 3 Mansion: 2
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

65% (hard)

Question Stats:

68% (02:37) correct 32% (02:58) wrong based on 487 sessions

History

Date
Time
Result
Not Attempted Yet
 


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.
Castle Mansion
2
3
4
5
6
8
Submit Answer
Start the Timer above, select the radio buttons, and click "Submit" to add this question to your Error log.
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 Nov 2025
Posts: 105,355
Own Kudos:
778,062
Given Kudos: 99,964
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,355
Kudos: 778,062
GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 08:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
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

­

GMAT Club Official Explanation:



Available resources:

Stone = 18 units
Wood = 12 units (two-thirds of 18)
Metal = 9 units (half of 18)

Castle requirements:

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

Total per castle: 6 stone, 2 wood, 1 metal

Maximum castles:
Stone: 18/6 = 3
Wood: 12/2 = 6
Metal: 9/1 = 9

Limiting factor: stone
Maximum castles = 3

Mansion requirements per unit:

Wood = 6 units
Stone = 2/3 * 6 = 4 units

Total wood + stone = 6 + 4 = 10
Metal = 10/5 = 2 units

Total per mansion: 4 stone, 6 wood, 2 metal

Maximum mansions:
Stone: 18/4 = 4.5
Wood: 12/6 = 2
Metal: 9/2 = 4.5

Limiting factor: wood
Maximum mansions = 2
General Discussion
User avatar
Mohak01
User avatar
Joined: 05 Sep 2020
Last visit: 12 Nov 2025
Posts: 104
Own Kudos:
64
 [1]
Given Kudos: 70
Location: India
Schools: ISB '26 NUS '26 (A)
GMAT Focus 1: 695 Q83 V87 DI83
GPA: 8
Schools: ISB '26 NUS '26 (A)
GMAT Focus 1: 695 Q83 V87 DI83
Posts: 104
Kudos: 64
 [1]
GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 09:01
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Given that following are requirements for construction,

Castle = 2W+6S+1M
Mansion = 6W+4S+2M

Available resources = 18S, 12W,9M

Maximum castle = 3 (limited by available number of stone)
Maximum Mansion = 2 (Limited by available number of wood)
User avatar
A_Nishith
User avatar
Joined: 29 Aug 2023
Last visit: 12 Nov 2025
Posts: 455
Own Kudos:
199
Given Kudos: 16
Posts: 455
Kudos: 199
GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 09:06
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
User avatar
Heix
User avatar
Joined: 21 Feb 2024
Last visit: 18 Nov 2025
Posts: 361
Own Kudos:
153
Given Kudos: 63
Location: India
Concentration: Finance, Entrepreneurship
Schools: Ross MM "26 NUS Columbia '27
GMAT Focus 1: 485 Q76 V74 DI77
GPA: 3.4
WE:Accounting (Finance)
Products:
My Reviews
Schools: Ross MM "26 NUS Columbia '27
GMAT Focus 1: 485 Q76 V74 DI77
Posts: 361
Kudos: 153
GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 09:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
User avatar
Jarvis07
User avatar
Joined: 06 Sep 2017
Last visit: 18 Nov 2025
Posts: 295
Own Kudos:
236
Given Kudos: 160
GMAT 1: 750 Q50 V41
GMAT 1: 750 Q50 V41
Posts: 295
Kudos: 236
GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 09:12
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
 


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
User avatar
Archit3110
User avatar
Major Poster
Joined: 18 Aug 2017
Last visit: 18 Nov 2025
Posts: 8,423
Own Kudos:
4,979
 [1]
Given Kudos: 243
Status:You learn more from failure than from success.
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1: 545 Q79 V79 DI73
GMAT Focus 2: 645 Q83 V82 DI81
GPA: 4
WE:Marketing (Energy)
GMAT Focus 2: 645 Q83 V82 DI81
Posts: 8,423
Kudos: 4,979
 [1]
GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 09:17
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
 


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
User avatar
Emkicheru
User avatar
Joined: 12 Sep 2023
Last visit: 12 Sep 2025
Posts: 119
Own Kudos:
22
Given Kudos: 11
Location: Kenya
Schools: Anderson (UCLA) Sloan (MIT) Columbia '27
GMAT 1: 780 Q50 V48
GRE 1: Q167 V164
GPA: 3.7
Schools: Anderson (UCLA) Sloan (MIT) Columbia '27
GMAT 1: 780 Q50 V48
GRE 1: Q167 V164
Posts: 119
Kudos: 22
GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 09:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
. 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
User avatar
Cana1766
User avatar
Joined: 26 May 2024
Last visit: 15 Nov 2025
Posts: 85
Own Kudos:
79
 [1]
Given Kudos: 11
Posts: 85
Kudos: 79
 [1]
GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 09:20
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
 


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
User avatar
Missinga
User avatar
Joined: 20 Jan 2025
Last visit: 16 Nov 2025
Posts: 393
Own Kudos:
261
Given Kudos: 29
Posts: 393
Kudos: 261
GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 09:22
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
User avatar
shashank17gupta
User avatar
Joined: 19 Jun 2025
Last visit: 29 Oct 2025
Posts: 19
Own Kudos:
12
 [1]
Given Kudos: 4
Posts: 19
Kudos: 12
 [1]
GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 09:28
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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)
User avatar
iCheetaah
User avatar
Joined: 13 Nov 2021
Last visit: 17 Nov 2025
Posts: 81
Own Kudos:
72
 [1]
Given Kudos: 1
Location: India
Posts: 81
Kudos: 72
 [1]
GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 09:30
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
User avatar
MinhChau789
User avatar
Joined: 18 Aug 2023
Last visit: 17 Nov 2025
Posts: 132
Own Kudos:
140
 [1]
Given Kudos: 2
Posts: 132
Kudos: 140
 [1]
GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 09:32
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
User avatar
hakzarif
User avatar
Joined: 31 May 2025
Last visit: 25 Oct 2025
Posts: 65
Own Kudos:
29
Given Kudos: 9
Products:
My Reviews
Posts: 65
Kudos: 29
GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 09:40
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
User avatar
AviNFC
User avatar
Joined: 31 May 2023
Last visit: 13 Nov 2025
Posts: 216
Own Kudos:
288
 [1]
Given Kudos: 5
Posts: 216
Kudos: 288
 [1]
GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 09:42
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
avatar
ManifestDreamMBA
avatar
Joined: 17 Sep 2024
Last visit: 18 Nov 2025
Posts: 1,282
Own Kudos:
784
 [1]
Given Kudos: 236
Products:
GMAT Club Tests
Posts: 1,282
Kudos: 784
 [1]
GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 09:51
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
SWMT
Castle6219
Mansion46212
Available total18129


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
 


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
User avatar
Dipan0506
User avatar
Joined: 24 May 2021
Last visit: 17 Nov 2025
Posts: 72
Own Kudos:
14
Given Kudos: 3
Products:
GMAT Club Tests
Posts: 72
Kudos: 14
GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 09:53
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
User avatar
Dav2000
User avatar
Joined: 21 Sep 2023
Last visit: 14 Sep 2025
Posts: 75
Own Kudos:
44
 [1]
Given Kudos: 69
Posts: 75
Kudos: 44
 [1]
GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 09:53
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
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.
User avatar
bart08241192
User avatar
Joined: 03 Dec 2024
Last visit: 17 Nov 2025
Posts: 75
Own Kudos:
64
 [1]
Given Kudos: 13
Posts: 75
Kudos: 64
 [1]
GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 09:54
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
we have
– Stone: 18 units
– Wood: (2/3)·18 = 12 units
– Metal: (1/2)·18 = 9 units


STONEWOODMETAL
CASTLE RECIPE 621
MASION RECIPE 462
WE HAVE 18129


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.
User avatar
Ryga
User avatar
Joined: 12 Aug 2023
Last visit: 19 Aug 2025
Posts: 68
Own Kudos:
51
 [1]
Given Kudos: 5
Location: India
Concentration: General Management, Leadership
Schools: INSEAD Jan '26 NUS '27 Stern '26
GMAT Focus 1: 695 Q90 V80 DI83
Schools: INSEAD Jan '26 NUS '27 Stern '26
GMAT Focus 1: 695 Q90 V80 DI83
Posts: 68
Kudos: 51
 [1]
GMAT Club Olympics 2025 (Day 9): In the computer game Stoneforge 10 Jul 2025, 09:58
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
 1   2   3   4   
Moderators:
Bunuel
Math Expert
105355 posts
kingbucky
496 posts