Pyramid Geometry Data Sufficiency Question

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infiniti007: Senior | Next Rank: 100 Posts; Posts: 37; Joined: Wed Feb 25, 2015 6:00 pm; Thanked: 1 times

by infiniti007 » Wed Jul 15, 2015 11:22 pm

Any help on how to solve the following problem would be appreciated.

A pyramid-shaped box to protect a plant is constructed with 4 lateral faces and an open bottom. What is the lateral area of the box?

1.) The base of the pyramid is a polygon with all sides of equal length and the perimeter of the base is 1 meter.

2.) The lateral faces are isosceles triangles that have the same size and shape.

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Source: Beat The GMAT — Data Sufficiency | Wed Jul 15, 2015 11:22 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Jul 16, 2015 3:27 am

infiniti007 wrote:Any help on how to solve the following problem would be appreciated.

A pyramid-shaped box to protect a plant is constructed with 4 lateral faces and an open bottom. What is the lateral area of the box?

1.) The base of the pyramid is a polygon with all sides of equal length and the perimeter of the base is 1 meter.

2.) The lateral faces are isosceles triangles that have the same size and shape.

Even when the statements are combined, the height of each triangle serving to form the pyramid is not constrained.
Each of the triangles could have a height of 1 meter or of 100 meters.
Since different heights are possible, the lateral area of the box cannot be determined.

The correct answer is E.

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Jim@StratusPrep: MBA Admissions Consultant; Posts: 2279; Joined: Fri Nov 11, 2011 7:51 amFollowed by: 266 members; Location: New York; Thanked: 660 times; GMAT Score:770

by Jim@StratusPrep » Thu Jul 16, 2015 3:56 am

I always try to think about what can be changed about shape. In this instance the height of the triangles is movable. If it is movable, aka it can be smaller or larger, then there are multiple values.

Also, you aren't likely to see the term 'lateral area' on the GMAT, but it is referring to the surface area.

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Mo2men: Legendary Member; Posts: 712; Joined: Fri Sep 25, 2015 4:39 amFollowed by: 5 members; Thanked: 14 times

by Mo2men » Thu Oct 08, 2015 12:19 am

GMATGuruNY wrote:
infiniti007 wrote:Any help on how to solve the following problem would be appreciated.

A pyramid-shaped box to protect a plant is constructed with 4 lateral faces and an open bottom. What is the lateral area of the box?

1.) The base of the pyramid is a polygon with all sides of equal length and the perimeter of the base is 1 meter.

2.) The lateral faces are isosceles triangles that have the same size and shape.
Even when the statements are combined, the height of each triangle serving to form the pyramid is not constrained.
Each of the triangles could have a height of 1 meter or of 100 meters.
Since different heights are possible, the lateral area of the box cannot be determined.

The correct answer is E.

HiGMATGuruNY,
I have a question, when we say that the pyramid has 4 lateral faces, does it mean that the bottom consists of polygon of 4 sides? or is there is another possibility?

Thanks

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Thu Oct 08, 2015 1:01 am

infiniti007 wrote:Any help on how to solve the following problem would be appreciated.

A pyramid-shaped box to protect a plant is constructed with 4 lateral faces and an open bottom. What is the lateral area of the box?

1.) The base of the pyramid is a polygon with all sides of equal length and the perimeter of the base is 1 meter.

2.) The lateral faces are isosceles triangles that have the same size and shape.

Question : Lateral Area = ?

Statement 1: The base of the pyramid is a polygon with all sides of equal length, and the perimeter of the base is 1 meter.
Since the Number of sides in base =4
Perimeter i.e. 4*Side = 1
i.e. Side = 1/4
But the height of the pyramid is unknown rendering to different values of lateral faces for different height of Pyramid. Hence,
NOT SUFFICIENT

Statement 2: The lateral faces are isosceles triangles that have the same size and shape.
But the height of the pyramid and Side of base quadrilateral are unknown rendering to different values of lateral faces for different height of Pyramid. Hence,
NOT SUFFICIENT

Combining the two statements
Side of Base = 1/4
All faces are Isosceles but the heights can be different rendering different values of Area of Lateral Surface Area. Hence,
NOT SUFFICIENT

Answer: option E

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Thu Oct 08, 2015 1:02 am

Mo2men wrote: I have a question, when we say that the pyramid has 4 lateral faces, does it mean that the bottom consists of polygon of 4 sides? or is there is another possibility?

Thanks

Yes, 4 lateral faces mean that the base is a quadrilateral.

You are right about it.

I hope this helps!

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