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655-705 (Hard)|   Math Related|         
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Aarushi225
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GMAT Club Olympics 2024 (Day 5): A camp needs to be organized for 14 Jul 2024, 11:55
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­Does DI of focus contain geometry? was it just removed from quant?
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GMAT Club Olympics 2024 (Day 5): A camp needs to be organized for 15 Jul 2024, 00:28
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­Does DI of focus contain geometry? was it just removed from quant?
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­The GMAT no longer tests specific knowledge of geometry. However, not everything involving shapes, areas, or volumes is considered geometry. This question, in particular, is not a geometry question because it does not require specialized knowledge in geometry to be solved. The formula for the volume is provided, so all you need to do is plug in the values and calculate. It's more of an arithmetic problem than a geometry one.
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GMAT Club Olympics 2024 (Day 5): A camp needs to be organized for 16 Aug 2025, 08:16
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GMAT Club Olympics 2024 (Day 5): A camp needs to be organized for 24 Nov 2025, 21:49
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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 \(\pi\)\(rl\), 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.
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GMAT Club Olympics 2024 (Day 5): A camp needs to be organized for 26 Nov 2025, 01:38
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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 \(\pi\)\(rl\), 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.
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SMALL conical tent:

Host : 2 participants per tent.

Radius: 3 feet

Slant height : 5 feet

Cost of material: $2 per square feet.

Additional Charges: $20 per tent.

LARGER conical tent:

Host : 10 participants per tent.

Radius: 7 feet

Slant height : 9 feet

Cost of material: $2 per square feet.

Additional Charges: $50 per tent.

To accommodate 100 participants : we need 50 Smaller Tents, and 10 Larger Tents.


Surface area of a conical tent is given by the formulae:

\(\pi\)\(rl\),

where \(r\) is the radius of the cone, and

\(l\) is the slant height.

Surface area of the smaller cone = (22/7)* 3*5 = approx 47 square feet.

We know the cost for 1 sq ft is $2.

Therefore, the cost for 47 square feet = $47*2 = $94

Total cost incurred for smaller tent = $94 + $20 = $114

For 1 Smaller tent that can accommodate 2 persons , the cost is $114.

To accommodate 100 persons, we need 50 such smaller tents.

The cost incurred for accommodations of 100 persons = 50*$114 = $5700.


Surface Area of the Larger Cone = (22/7)* 7*9 = 198 square feet.

We know the cost for 1 sq ft is $2.

Therefore, the cost for 198 square feet = 198*2 = $396

Total cost incurred for Larger tent = $396 + $50 = $446

As we know , 1 Larger tent can accommodate 10 persons.

We need 10 Larger tents to accommodate 100 persons.

Cost incurred for accommodating 100 persons = 10 * $446 = $4460.

The closest possible answer is $4500.

Answer:

Smaller tent = $5700.

Larger tent = $4500.
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