GMAT Club Olympics 2024 (Day 5): A camp needs to be organized for

Question

A camp needs to be organized for sheltering 100 participants for an adventure sports event. The organizers have a choice of putting small conical tents that can host 2 participants each; else, they can put larger conical tents that can accommodate 10 participants each. The estimated radius of each smaller tent is 3 feet while the estimated radius of each larger tent is 7 feet. The slant height of the smaller tent is estimated to be 5 feet while the slant height of the larger tent is estimated to be 9 feet. The cost of material for building these tents is $2 per square feet of the fabric used for tent, and an additional $20 per smaller tent and $50 per larger tent for the installation and labor. The surface area of a cone is πrl

total participant is 100
small tents 2 person each ; 50 required
radius of small ; 3, h is 5
cost $2 per ft^2 + 20 per small tent
net cost
50 * 3 * 5 * 3.14 *2 + (20*50) ; 5710 ; ~ $5700

large tent
10 each ; 10 required
radius ; 7 height is 9
cost is $2 per ft^2 + $50 * 10
net cost
10*3.14*7*9*2 + 500 ; $4456 ~ $4500

small tent $ 5700 & large tent $4500

In the table, select the values that, approximately, indicate the total cost of setting up the smaller and larger tents for accommodating all 100 participants. Make only two selections, one in each column.

Bunuel · Answer

Experts' Global Explanation:

To set up smaller tents, material needed per tent:  π*r*l = π*3*5 = 15π  square feet

This material will cost  2*15π = $30π  per tent

For 50 tents:  $1,500π =~4,700

\frac{100}{2} = 50  such tents shall be needed

Installation cost:  20*50 = $1000  extra.

Total cost of smaller tents  = $1,000 + $4,700 = $5,700 
______________________________

To set up larger tents, material needed per tent:  π*r*l = π*7*9 = 63π  square feet

This material will cost  2*63π = $126π =~$400

\frac{100}{10} = 10  such tents shall be needed. Hence, the cost of material = $4,000

Installation cost  = $50*10 = $500  extra.

Total cost of larger tents  = $,4000 + $500 = $4,500 
______________________________

Hence, for the  Setting up the smaller tents  column, D is the correct answer choice.
And, for the  Setting up the larger tents  column, B is the correct answer choice.

A_Nishith · Answer

To determine the total cost of setting up the smaller and larger tents for accommodating all 100 participants, we will calculate the costs for each type of tent separately and then sum the costs.

Step 1: Calculate the cost of setting up the smaller tents
Surface area of each smaller tent:

Surface Area=π×r×l

Surface Area=π×3×5

Surface Area=15π square feet

Surface Area≈15×3.14=47.1 square feet

Cost of material for each smaller tent:

Cost of material=47.1×2=$94.2

Installation and labor cost for each smaller tent:

Installation and labor cost=$20

Total cost for each smaller tent:

Total cost per smaller tent=94.2+20=$114.2

Number of smaller tents needed to accommodate 100 participants:

Number of smaller tents= 100/2 =50

Total cost for all smaller tents:

Total cost for smaller tents=50×114.2=$5710

Step 2: Calculate the cost of setting up the larger tents
Surface area of each larger tent:

Surface Area=π×r×l

Surface Area=π×7×9

Surface Area=63π square feet

Surface Area≈63×3.14=197.82 square feet

Cost of material for each larger tent:

Cost of material=197.82×2=$395.64

Installation and labor cost for each larger tent:

Installation and labor cost=$50

Total cost for each larger tent:

Total cost per larger tent=395.64+50=$445.64

Number of larger tents needed to accommodate 100 participants:

Number of larger tents= 100/10 =10

Total cost for all larger tents:

Total cost for larger tents=10×445.64=$4456.4

Step 3: Select the appropriate costs from the table
Setting up the smaller tents: Approx. $5700 (closest value to $5710)
Setting up the larger tents: Approx. $4500 (closest value to $4456.4)

Therefore, the selections are:

Setting up the smaller tents: $5700
Setting up the larger tents: $4500

parag08 · Answer

A camp needs to be organized for sheltering 100 participants for an adventure sports event. The organizers have a choice of putting small conical tents that can host 2 participants each; else, they can put larger conical tents that can accommodate 10 participants each. The estimated radius of each smaller tent is 3 feet while the estimated radius of each larger tent is 7 feet. The slant height of the smaller tent is estimated to be 5 feet while the slant height of the larger tent is estimated to be 9 feet. The cost of material for building these tents is $2 per square feet of the fabric used for tent, and an additional $20 per smaller tent and $50 per larger tent for the installation and labor. The surface area of a cone is πrl

total participant is 100
small tents 2 person each ; 50 required
radius of small ; 3, h is 5
cost $2 per ft^2 + 20 per small tent
net cost
50 * 3 * 5 * 3.14 *2 + (20*50) ; 5710 ; ~ $5700

large tent
10 each ; 10 required
radius ; 7 height is 9
cost is $2 per ft^2 + $50 * 10
net cost
10*3.14*7*9*2 + 500 ; $4456 ~ $4500

small tent $ 5700 & large tent $4500

In the table, select the values that, approximately, indicate the total cost of setting up the smaller and larger tents for accommodating all 100 participants. Make only two selections, one in each column.

Small Camp Tent: 
Accomodate: 2
Radius: 3
Slant Height: 5
Area: 3*5*3.14 = 47.1
Cost of setup: 20
Cost of one camp: 47.1 * 2 + 20 = 114.2
Cost of 50 (100 participants/2 per camps) camps : 5710 i.e. 5700

Large Camp Tent: 
Accomodate: 10
Radius: 7
Slant Height: 9
Area: 7*9*3.14 = 197.82
Cost of setup: 50
Cost of one camp: 197.82 * 2 + 50 = 445.64
Cost of 10 (100 participants/10 per camps) camps :4456.4 i.e. 4500

meet459 · Answer

A camp needs to be organized for sheltering 100 participants for an adventure sports event. The organizers have a choice of putting small conical tents that can host 2 participants each; else, they can put larger conical tents that can accommodate 10 participants each. The estimated radius of each smaller tent is 3 feet while the estimated radius of each larger tent is 7 feet. The slant height of the smaller tent is estimated to be 5 feet while the slant height of the larger tent is estimated to be 9 feet. The cost of material for building these tents is $2 per square feet of the fabric used for tent, and an additional $20 per smaller tent and $50 per larger tent for the installation and labor. The surface area of a cone is πrlπ𝑟𝑙, where r𝑟 is the radius of the cone and l𝑙 is the slant height.

Let's summarise the information:

Area of core: pi*rl
Number of small tents possible: 50
Number of large tents possible: 10

Area of each small tent: pi*3*5 = 15pi
Cost of each small tent's fabric = 2*15pi = 30pi

Total cost for small tents = 50 * (30pi + 20) = 5710 (approx) ~ 5700 [assume pi = 3.14]

Area of each large tent: pi*7*9 = 63pi
Cost of each small tent's fabric = 2*63pi = 126pi

Total cost for large tents = 10 * (126pi + 50) = 4460(approx) ~ 4500 [assume pi = 22/7]

Let's summarise the information:

Area of core: pi*rl
Number of small tents possible: 50
Number of large tents possible: 10

Area of each small tent: pi*3*5 = 15pi
Cost of each small tent's fabric = 2*15pi = 30pi

Total cost for small tents  = 50 * (30pi + 20) = 5710 (approx) ~  5700

Area of each large tent: pi*7*9 = 63pi
Cost of each small tent's fabric = 2*63pi = 126pi

Total cost for large tents  = 10 * (126pi + 50) =  4460(approx) ~  4500

Kinshook · Answer

A camp needs to be organized for sheltering 100 participants for an adventure sports event. The organizers have a choice of putting small conical tents that can host 2 participants each; else, they can put larger conical tents that can accommodate 10 participants each. The estimated radius of each smaller tent is 3 feet while the estimated radius of each larger tent is 7 feet. The slant height of the smaller tent is estimated to be 5 feet while the slant height of the larger tent is estimated to be 9 feet. The cost of material for building these tents is $2 per square feet of the fabric used for tent, and an additional $20 per smaller tent and $50 per larger tent for the installation and labor. The surface area of a cone is πrl

total participant is 100
small tents 2 person each ; 50 required
radius of small ; 3, h is 5
cost $2 per ft^2 + 20 per small tent
net cost
50 * 3 * 5 * 3.14 *2 + (20*50) ; 5710 ; ~ $5700

large tent
10 each ; 10 required
radius ; 7 height is 9
cost is $2 per ft^2 + $50 * 10
net cost
10*3.14*7*9*2 + 500 ; $4456 ~ $4500

small tent $ 5700 & large tent $4500

In the table, select the values that, approximately, indicate the total cost of setting up the smaller and larger tents for accommodating all 100 participants. Make only two selections, one in each column

The total cost of setting up the smaller tents: - 
The number of participants per tent = 2
The number of tents required = 100/2 = 50
Radius = r = 3 feet
Slant height = l = 5 feet
Surface area of fabric used for a small tent = πrl = 15π = 15*3.14 = 47.1 sq ft
The cost for setting up 1 small tent = 47.1*2 + 20 = $114.2 
 The total cost for setting up 50 small tents to accomodate all 100 participants = $5710 (approx $5700)

The total cost of setting up the smaller tents: - 
The number of participants per tent = 10
The number of tents required = 100/10 = 10
Radius = r = 7 feet
Slant height = l = 9 feet
Surface area of fabric used for a small tent = πrl = 63π = 63*3.14 = 197.82 sq ft
The cost for setting up 1 larger tent = 197.82*2 + 50 = $445.64
 The total cost for setting up 10 large tents to accomodate all 100 participants = $4456.4 (approx $4500)

Archit3110 · Answer

A camp needs to be organized for sheltering 100 participants for an adventure sports event. The organizers have a choice of putting small conical tents that can host 2 participants each; else, they can put larger conical tents that can accommodate 10 participants each. The estimated radius of each smaller tent is 3 feet while the estimated radius of each larger tent is 7 feet. The slant height of the smaller tent is estimated to be 5 feet while the slant height of the larger tent is estimated to be 9 feet. The cost of material for building these tents is $2 per square feet of the fabric used for tent, and an additional $20 per smaller tent and $50 per larger tent for the installation and labor. The surface area of a cone is πrl

total participant is 100
small tents 2 person each ; 50 required
radius of small ; 3, h is 5
cost $2 per ft^2 + 20 per small tent
net cost
50 * 3 * 5 * 3.14 *2 + (20*50) ; 5710 ; ~ $5700

large tent
10 each ; 10 required
radius ; 7 height is 9
cost is $2 per ft^2 + $50 * 10
net cost
10*3.14*7*9*2 + 500 ; $4456 ~ $4500

small tent $ 5700 & large tent $4500

total participant is 100
small tents 2 person each ; 50 required
radius of small ; 3, h is 5
cost $2 per ft^2 + 20 per small tent
net cost 
50 * 3 * 5 * 3.14 *2 + (20*50) ; 5710 ;  ~ $5700

large tent 
10 each ; 10 required
radius ; 7 height is 9
cost is $2 per ft^2 + $50 * 10
net cost
10*3.14*7*9*2 + 500 ; $4456  ~ $4500

small tent $ 5700 & large tent $4500

AthulSasi · Answer

Small tent  
Number of tent needed = 100/2  = 50
Area of a tent = 3.14 * 3 * 5 = 47.1
Cost of 50 tent = 50 * (47.1*2 + 20)
= 5710 
  Closest answer 5700

Large tent  
Number of tent needed = 100/10  = 10
Area of a tent = 3.14 * 7 * 9 = 197.8
Cost of 10 tent = 10 * (197.8*2 + 50)
= 4456
  Closest asnwer 4500

Abhijeet24 · Answer

Small Tents: 
- Each small tent can host 2 participants.
- For 100 participants, we need 100/2 = 50 small tents.
- The radius  r  of each small tent is 3 feet.
- The slant height l of each small tent is 5 feet.
- The surface area  A   of a small tent is given by pi r l = pi * 3 * 5 = 15 pi square feet.
- The material cost per small tent is $ 15\pi \times 2 = 30\pi $ dollars.
- The total material cost for 50 small tents is $ 50 \times 30\pi \approx 50 \times 94.25 = 4712.5 $ dollars (since $ \pi \approx 3.14 $).
- The installation/labor cost per small tent is $20.
- The total installation/labor cost for 50 small tents is $ 50 \times 20 = 1000 $ dollars.
- The total cost for small tents is $ 4712.5 + 1000 = 5712.5 $ dollars.

Large Tents: 
- Each large tent can host 10 participants.
- For 100 participants, we need $ \frac{100}{10} = 10 $ large tents.
- The radius $ r $ of each large tent is 7 feet.
- The slant height $ l $ of each large tent is 9 feet.
- The surface area $ A $ of a large tent is given by $ A = \pi r l = \pi \times 7 \times 9 = 63\pi $ square feet.
- The material cost per large tent is $ 63\pi \times 2 = 126\pi $ dollars.
- The total material cost for 10 large tents is $ 10 \times 126\pi \approx 10 \times 395.64 = 3956.4 $ dollars (since $ \pi \approx 3.14 $).
- The installation/labor cost per large tent is $50.
- The total installation/labor cost for 10 large tents is $ 10 \times 50 = 500 $ dollars.
- The total cost for large tents is $ 3956.4 + 500 = 4456.4 $ dollars.

- Total cost for smaller tents: 5712.5 dollars.
- Total cost for larger tents: 4456.4  dollars.

Therefore, the approximate total costs are:
- $5700 for smaller tents.
- $4500 for larger tents.

captain0612 · Answer

Total cost of setting up a smaller tent :  5700 
Total cost of setting up a larger tent   :  4500

Given:
1. Total number of participants: 100
2. Smaller tent specs:
    2.1 Max participants in a tent: 2
    2.2 Radius of tent (r) : 3
    2.3 Slant height of the tent (l) : 5
    2.4 Fixed cost per tent: 20
    2.5 Total number of tents required: 100/2 = 50
3. Smaller tent specs:
    3.1 Max participants in a tent: 10
    3.2 Radius of tent: 7
    3.3 Slant height of the tent: 9
    3.4 Fixed cost per tent: 150
    3.5 Total number of tents required: 100/10 = 10
Surface area of cone = πrl
Cost per square feet of fabric = 2

Total cost of setting up tents = (surface area of cone) * (total number of tents) * (cost per square foot of fabric) + (total number of tents) * (fixed cost of setup cost per tent)

Total cost of setting up smaller tent = ( πrl ) * ( 50 ) * ( 2 ) + ( 50 ) * ( 20 )
= ( 3.14 * 3 * 5 ) * ( 50 ) * ( 2 ) + ( 1000 )
= ~ ( 4700 ) + ( 1000 )
=  5700

Total cost of setting up larger tent = ( πrl ) * ( 10 ) * ( 2 ) + ( 100 ) * ( 50 )
= ( 3.14 * 7 * 9 ) * ( 10 ) * ( 2 ) + ( 1000 )
= ~ ( 4000 ) + ( 500 )
=  4500

DG1989 · Answer

A camp needs to be organized for sheltering 100 participants for an adventure sports event. The organizers have a choice of putting up small conical tents that can host 2 participants each; otherwise, they can put up larger conical tents that can accommodate 10 participants each. The estimated radius of each smaller tent is 3 feet while the estimated radius of each larger tent is 7 feet. The slant height of the smaller tent is estimated to be 5 feet while the slant height of the larger tent is estimated to be 9 feet. The cost of material for building these tents is $2 per square foot of the fabric used for the tent, an additional $20 per smaller tent, and $50 per larger tent for the installation and labor. The surface area of a cone is π𝑟𝑙, where 𝑟 is the radius of the cone and 𝑙 is the slant height.

In the table, select the values that, approximately, indicate the total cost of setting up the smaller and larger tents for accommodating all 100 participants. Make only two selections, one in each column.

Solution: Total number of participants = 100
Cost of material building = $2 per sq. ft. plus

$20 per small tent
$50 per large tent

For setting up smaller tents
Small tents can hold 2 people each
Hence, the number of small tents required to accommodate all = 50
Radius r1 of 1 tent = 3ft
Slant height l1 = 5ft
Surface area of 1 small tent = π * r1 * l1
= 3.14 * 3 * 5
= 47 sq. ft (approx)

Total building cost for 50 such tents = $ (47 * 50 * 2 + 20 * 50) = $5700 (approx.)
Total cost for setting smaller tents = $ 5700

For setting up larger tents
Large tents can hold 10 people each
Hence, the number of large tents required to accommodate all = 10
Radius r2 of 1 tent = 7ft
Slant height l2 = 9ft
Surface area of 1 large tent = π * r2 * l2
= 3.14 * 7 * 9
= 198 sq. ft (approx)

Total building cost for 10 such tents = $ (198 * 10 * 2 + 50 * 10) = $4500 (approx.)
Total cost for setting larger tents = $ 4500

Show Spoiler

Attachment:

GMAT-Club-Forum-xr8dgrsx.png [ 48.25 KiB | Viewed 3716 times ]

GuadalupeAntonia · Answer

small tent 
2 per tent
r=3ft
slant=l=5 ft
Cost of material for building these tents= $2 per ft2
Additional cost per tent= $20

# tent requiered=100/2=50
The surface area of a cone is π*r*l=π*3*5=15π

Total cost for 50 tents= Additional cost per tent*(50)+builiding cost*(50)*surface are of cone (tent)=
Total cost for 50 tents=20*(50)+2*(50)*15π= 1000+100*15π= aprox 1000+4700= $5700

Larger tents 
10 per tent
r=7ft
slant=l=9 ft
Cost of material for building these tents= $2 per ft2
Additional cost per tent= $50

# tent requiered=100/10=10
The surface area of a cone is π*r*l=π*7*9=63π

Total cost for 50 tents= Additional cost per tent*(10)+builiding cost*(10)*surface are of cone (tent)=
Total cost for 50 tents=50*(10)+2*(10)*63π= 500+20*63π= aprox 500+3956=4456 aprox  $4500

Purnank · Answer

Given - A camp needs to be organized for sheltering  100 participants  for an adventure sports event. small conical tents or larger conical tents.
The cost of material for building these tents is  $2 per square feet of the fabric  used for tent
The surface area of a cone is  pi*r*l , where r is the radius of the cone and l is the slant height.

small conical tents details
 
 host  2  participants each 
  radius  of each smaller tent is  3 feet  
  The slant height  of the smaller tent is estimated to be  5 feet  
 an additional $20  per smaller tent  
 no. of smaller tents need = Participants / capacity per each tent = 100 / 2 = 50 
 Surface area of cone to calculate sq. feet fabric required =  pi*r*l  =  \frac{22}{7} * 3 * 5  = 47.142 sq.ft 
 Cost of fabric per small tent = 2*47.142 = 94.2857 
 Total cost per each small tent = fabric cost + additional cost = 94.2857 + 20 = 114.2857 
   Total cost for Setting up the smaller tents = 114.2857 * 50 = 5714.2857 (appx = 5700 Option D.)

larger conical tents details
 
 can accommodate  10  participants each 
  radius  of each larger tent is  7 feet  
  The slant height  of the larger tent is estimated to be  9 feet  
 an additional $50  per larger tent  
 no. of larger tents need = Participants / capacity per each tent = 100 / 10 = 10 
 Surface area of cone to calculate sq. feet fabric required =  pi*r*l  =  \frac{22}{7} * 7 * 9  = 198 sq.ft 
 Cost of fabric per larger tent = 2*198 = 396 
 Total cost per each larger tent = fabric cost + additional cost = 396 + 50 = 446 
   Total cost for Setting up the larger tents tents = 446 * 10 = 4460 (appx = 4500 Option B.)

jairovx · Answer

To calculate the total cost of setting up the smaller and larger tents for accommodating all 100 participants, we need to consider both the material cost and the installation and labor cost.

Step 1: Calculate the Surface Area of Each Tent

Smaller Tent
- Radius (r) = 3 feet
- Slant height (l) = 5 feet
- Surface area A = πrl
A_small = π × 3 × 5 = 15π square feet

Larger Tent
- Radius (r) = 7 feet
- Slant height (l) = 9 feet
- Surface area A = πrl
A_large = π × 7 × 9 = 63π square feet

Step 2: Calculate the Material Cost per Tent
- Cost per square foot = $2

Smaller Tent
Material cost per smaller tent = 15π × 2 = 30π dollars

Larger Tent
Material cost per larger tent = 63π × 2 = 126π dollars

Step 3: Calculate the Total Cost for Installation and Labor

Smaller Tent
Installation and labor cost per smaller tent = 20 dollars

Larger Tent
Installation and labor cost per larger tent = 50 dollars

Step 4: Calculate the Number of Tents Needed
- Each smaller tent accommodates 2 participants.
- Each larger tent accommodates 10 participants.

Step 5: Calculate the Total Cost
For simplicity, let's consider all possibilities. We can form all larger tents, all smaller tents.

Option 1: All Smaller Tents
x = 100 / 2 = 50
Total cost = 50 × (30π + 20) = 50 × (30π + 20) = 1500π + 1000

Option 2: All Larger Tents
y = 100 / 10 = 10
Total cost = 10 × (126π + 50) = 10 × 126π + 10 × 50 = 1260π + 500

Conclusion
- All smaller tents: 1500π + 1000 = 5,700
- All larger tents: 1260π + 500 = 4,500

aviraj1703 · Answer

Given, 
 
 100 participants 
 Small tent:
 
 Capacity = 2 participants/camp 
 Base Radius = 3 feet 
 Slant Height = 5 feet 
 Labour cost per tent = $20 
 Required tents = 100/2 = 50   
 Large tent:
 
 Capacity = 10 participants/camp 
 Base Radius = 7 feet 
 Slant Height = 9 feet 
 Labour cost per tent = $50 
 Required tents = 100/10 = 10   
 Cost per square feet of fabric used = $2 
 Area of the surface of tent =   πrl ;  r = Base Radius, l = Slant Height.  
1) Cost for  Small tents :
 
 Surface area =  πrl  
 Cost per tent with labour cost = ( πrl  x 2) + 20 
 Total cost for 50 tents = 50 x  πrl  x 2) + 20] 
  Total cost = $5712   
2) Cost for  Large tents :
 
 Surface area =  πrl  
 Cost per tent with labour cost = ( πrl  x 2) + 50 
 Total cost for 10 tents = 10 x  πrl  x 2) + 50] 
  Total cost = $4458   
 1st column: $5700
2nd column: $4500

Spectre26 · Answer

Participants: 100
Cost of material: $2 per sq. ft

For small tents,
 
No of tents required: 100/2 = 50 tents
Radius: 3 ft
Slant height: 5 ft
Surface Area:  \pi * 3 * 5 \approx{45} 
Material required: Surface Area * No of tents required = 45 * 50 = 2250
Material cost: 2250 * 2 = 4500
Cost of installation: $20 per tent
Total Cost of installation: 20 * 50 = 1000
Total Cost for smaller tents: 4500 + 1000 = 5500
Nearest Option: 5700
 
For larger tents,
 
No of tents required: 100/10 = 10 tents
Radius: 7 ft
Slant height: 9 ft
Surface Area:  \pi * 7 * 9 \approx{190} 
Material required: Surface Area * No of tents required = 190 * 10 = 1900
Material cost: 1900 * 2 = 3800
Cost of installation: $50 per tent
Total Cost of installation: 10 * 50 = 500
Total Cost for larger tents: 3800 + 500 = 4300
Nearest Option: 4500
 
 Setting up the smaller tents: 5700
Setting up the larger tents: 4500

rsrobin864 · Answer

Using Small Tents

Number of small tents needed:

100 participants/2 participants=50 small tents 
 Surface area of one small tent:

Surface area=π×r×l=π×3×5=15π square feet  
 Total surface area for 50 small tents:

50×15π=750π square feet 
 Material cost for 50 small tents:

750π×2 dollars/square feet=750×3.14×2≈4710 dollars 
 Installation and labor cost for 50 small tents:

50×20=1000 dollar 
 Total cost for 50 small tents:

4710+1000=5710  
  Large Tents Only

Number of large tents needed:

100 participants/10 participants/tent=10 large tents 
 Surface area of one large tent:

Surface area=π×r×l=π×7×9=63π square feet 
 Total surface area for 10 large tents:

10×63π=630π square feet 
 Material cost for 10 large tents:

630π×2 dollars/square feet=630×3.14×2≈3956.4 dollars 
 Installation and labor cost for 10 large tents:

10×50=500 dollar 
 Total cost for 10 large tents:

3956.4+500=4456.4≈4500 dollars  
 So Ans- For small tent-5700 $
For Larger tent- 4500 $

kavyavishnoi02 · Answer

Since there are a total of 100 participants and we need to accommodate all, and since small tents can accommodate only 2 per tent, total small tents required are 100/2 = 50. And since, large tents can accommodate 10 per tent, total large tents required are 100/10 = 10.
Now, let's calculate the cost for each of these tents individually.

50   Small tents:

Total Surface Area = 50 X πrl = 50 X 22/7 X 3 X 5 = 2,200 sq. feet (approx.)
Total cost of fabric = 2 X 2,200 =  $4,400 
Total cost of installation and labor = 20 X 50 =  $1,000

Thus, total cost for 50 tents = 4,400 + 1,000 =  $5,400

10 Large tents:

Total Surface Area = 10 X πrl = 10 X 22/7 X 7 X 9 = 1,980 sq. feet (approx.)
Total cost of fabric = 2 X 1,980 =  $3,960 
Total cost of installation and labor = 50 X 10 =  $500

Thus, total cost for 10 tents = 3,960 + 500 =  $4,460

Therefore, answer for   Setting up the  smaller tents    is $5,700  and for  Setting up the  larger tents    is $4,500 .

d_patel · Answer

Question stem gives us following details,
100 participants.
Small tent house 2 participants, radius is 3 feet and slant height is 5 feet. Additional $20 labor is charged for each smaller tent.
Large tent house 10 participants, radius is 7 feet and slant height is 9 feet. Additional $50 labor is charged for each large tent.

The cost of material for building these tents is $2 per square feet of the fabric used for tent.

We can see that options are very different from each other so we should be able to approximate.

Let's approximate  π = 3  rather than  π = 3.14.

Now, 
 For small tent  - 
surface area of 1 small tent=  πrl  =  3 * 3 * 5  =  45 feet^2 
cost of material for 1 small tent =  2 * 45  = $ 90 
And each small tent will also cost additional $ 20  for labor. 
Total cost for 1 small tent =  $ 90  + $ 20  = $ 110

And we will need  \frac{100}{2}  =  50  smaller tents for 100 participants.

Total cost for smaller tents =  50 * 110  = $ 5500  
As we took value of  π = 3 , approximate answer will be slightly less than correct one.   $ 5700     is the closest option. 
So, select it for  smaller tents.

For large tent  - 
surface area of 1 large tent=  πrl  =  3 * 7 * 9  =  189 feet^2 
cost of material for 1 large tent =  2 * 189  = $ 378 
And each large tent will also cost additional $ 50  for labor. 
Total cost for 1 large tent =  $ 378  + $ 50  = $ 428

And we will need  \frac{100}{10}  =  10  larger tents for 100 participants.

Total cost for larger tents =  10 * 428  = $ 4280  
As we took value of  π = 3 , approximate answer will be slightly less than correct one.   $ 4500     is the closest option. 
So, select it for  larger tents.

Lizaza · Answer

The general equation for each type of tents will look as follows:
 number * installation.cost + number * surface.area * price.per.sq.foot = number (installation.cost + surface.area * price.per.sq.foot)

The camp would need  100:2 = 50  smaller tents or  100:10 = 10  bigger tents.

So, let's calculate the values:
 
 Small tents  
 50(20 + π*3*5*2) = 50(20 + 90) = 50*110 = 5500 
 
 Large tents  
 10(50+π*7*9*2) = 10(50+378) = 4280

As I've calculated  π ~ 3  for simplicity of calculus, the values obtained are roughly 5% less than the proper ones.
Hence, from the answer options,   the smaller tents would cost approximatly $5700 (D)  , and   the larger ones would cost $4500 (B).

GMAT Club Olympics 2024 (Day 5): A camp needs to be organized for

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

Setting up the smaller tents	Setting up the larger tents	Total Cost
		$3700
		$4500
		$5000
		$5700
		$6700

GMAT Two-part Analysis (TPA) Questions

GMAT Club Olympics 2024 (Day 5): A camp needs to be organized for

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards