A pyramid-shaped box to protect a plant is constructed with 4 lateral

Question

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.

chetan2u · Answer

1) statement 1 tells us the base of all lateral faces and nothng else.. insuff..
2) th e faces aare iso triangle... no fruitful info...insuff

combined we know the lateral faces to be isosceles tri with base .25 m... not suff
E

GMATinsight · Answer

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

Mo2men · Answer

When there is 4 lateral faces, does not it mean that the base have 4 sides? if so, why sides are unkown? I can't imagine. For me E is the choice as in both statement height is unknown.

GMATinsight · Answer

I missed some information while reading question and this gives another message "Careless reading of questions is too dangerous unless you are lucky to get correct answer by luck" :wink:

Have made some changes in explanations. I hope You would find it appropriate now.

Mo2men · Answer

Thanks for your help. You are well respected person. For a moment, I suspect my knowledge about shapes. Or I thought I lost my imagination about shapes. You are highly responsive. :thanks

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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.

Looking at the original condition, there are numerous variables in a pyramid-shaped box (3 for triangles and 4 for squares), so we need that much number of equations. However, the conditions only provide us with 2 equations in total, giving a high chance that (E) is going to be the answer
Looking at the conditions, even if we combine the 2 conditions, we cannot know the length of an edge of any face, making the conditions insufficient and the answer becomes (E).

For cases where we need 3 more equation, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

Question Type: What Is the Value? This question asks for the lateral area of the pyramid-shaped box. The lateral area represents the area of the faces of the polygon added together.

Given information in the question stem or diagram: The box is pyramid shaped and constructed with four lateral faces and an open bottom.

Statement 1: The base is a polygon with all sides of equal length and the perimeter of the base is 1 meter. This statement does not provide enough information to determine the area of the faces of the pyramid. While you know that each side of the polygon at the base is .25 meters, you have no idea about the height of the pyramid and thus the height of each lateral face. This is not sufficient so you can eliminate choices A and D.

Statement 2: The lateral faces are isosceles triangles that have the same size and shape. This statement is clearly insufficient by itself, as you are given no hard numbers. The question, then, is whether this statement helps you when combined with Statement 1. The answer is C or E.

Together: Taken together, the information still does not give you any idea about the height of the pyramid. If Statement 2 said that the lateral faces were equilateral triangles, then the answer would be C. However, this pyramid could be 3 meters high, or 10 meters high, greatly changing the area of the faces. Note: This question is a good example of the “prove E” concept. If you are going to choose  answer E , as you should in this problem, do so because you can identify the missing information, not just because the problem seems difficult. Here you are still missing the height of the pyramid so the correct answer is indeed E.

bumpbot · Answer

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A pyramid-shaped box to protect a plant is constructed with 4 lateral

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