A Pyramid-Shaped Box To Protect A Plant Is Constructed With 4 Lateral Faces GMAT Data Sufficiency

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.

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

“A pyramid-shaped box to protect a plant is constructed with 4 lateral faces” is a topic of the GMAT Quantitative reasoning section of GMAT. The questions of GMAT Data Sufficiency consist of a problem statement with two factual statements. This specific GMAT data sufficiency question estimates the basic aptitudes of mathematics of the candidate. The clever wording used in these questions is the critical and the toughest part that candidates usually overlook. The GMAT Quant exam constitutes 31 MCQs and the allotted time limit is 62 minutes. The GMAT data sufficiency incorporates 15 questions which are basically two-fifths of the entire 31 GMAT quant questions.

Solution and Explanation:

Approach Solution 1:

The problem statement informs that a pyramid-shaped box is constructed with 4 lateral faces and an open bottom.

The question asks to find out the lateral area of the box.

1. Statement (1) states that the base of the pyramid is a polygon with equal sides and the perimeter of the base is 1 meter.
   The number of sides in the base of the pyramid = 4
   As per the formula, Perimeter= 4*side
   That is we can say, 4* side= 1
   Therefore, side= ¼
   But the statement does say anything about the height of the pyramid. The height is unknown rendering various values of lateral faces for the various height of the pyramid.
   Hence statement (1) alone is not sufficient to find the lateral area of the box.
2. Statement (2) cites that the lateral faces are isosceles triangles that hold the same size and shape. But the statement does not mention any information about the height of the pyramid and the side of the base quadrilateral. The height of the pyramid and the side of the base is therefore not known rendering various values of lateral faces for the various height of the pyramid.
   Hence statement (2) alone is not sufficient to find the lateral area of the box.
   Combining two statements we get,
   Side of the base quadrilateral = ¼
   All the faces of the pyramid are isosceles triangles but the height can be distinct due to the distinct values of the area of lateral surface area.
   Hence, both statements together are not sufficient to find the lateral area of the box.

Correct Answer: (E)

Approach Solution 2:

The problem statement informs that

Given:

• A pyramid-shaped box is constructed with 4 lateral faces and an open bottom.

Asked:

• Find out the lateral area of the box.

1. The statement indicates that the base of the pyramid is a polygon with equal sides and the perimeter of the base is 1 meter.
   The statement does not offer sufficient facts or data to estimate the area of the faces of the pyramid.
   Though it is known to us that each side of the polygon at the base is .25 meters, we do not know anything about the height of the pyramid. Therefore, the height of each lateral face is unknown to us. Therefore, statement (1) alone is not sufficient.
2. The statement states that the lateral faces are isosceles triangles that hold the same size and shape. The statement does not offer any hard numbers to derive the lateral area of the pyramid. Hence the statement alone is insufficient.
   By combining both statements together:
   Though the two statements are taken together, it still does not offer any idea regarding the height of the pyramid. Therefore, it will not be possible to find the lateral area of the pyramid box.
   Hence, both statements together are insufficient to find the answer to the question.

Correct Answer: (E)

Suggested GMAT Data Sufficiency Questions:

• If x and y are positive integers and xy is divisible by prime number. Is p an even number? GMAT Data Sufficiency
• What is the Product of 6 Consecutive Numbers? GMAT Data Sufficiency
• If x is an integer is an x/12 integer? GMAT Data Sufficiency
• Is 7^7 / 7^x an integer? GMAT Data Sufficiency
• The length of the median BD in a triangle ABC is 12 centimeters, what is the length of the side AC? GMAT Data Sufficiency
• Is the area of the triangle ABC greater than the area of the triangle DEF? GMAT Data Sufficiency
• There is atleast one viper and atleast one cobra in Pandora’s Box GMAT data sufficiency
• If L not equals to 0, is 18K/L an Integer? GMAT Data Sufficiency
• If a, b, and c are positive and a^2 + c^2 = 202, what is the value of b – a – c? GMAT Data Sufficiency
• If x and y are positive integers, is x odd? GMAT Data Sufficiency
• If 0 < x < 53, what is the value of integer x? GMAT Data Sufficiency
• What is the value of 6x^2 + 9y^2 =? GMAT Data Sufficiency
• If x and y are integers and, is x=(y/5 +2) even? GMAT Data Sufficiency
• If m is a positive integer, is √m>25? GMAT Data Sufficiency
• If there are 78 people working at an office, how many of them are women older than 40? GMAT Data Sufficiency
• If ab = ac is b = 2? GMAT Data Sufficiency
• If x is a positive integer, what is the value of x? GMAT Data Sufficiency
• If 53 students are enrolled in both the CS103 (Algorithms and Data Structures) And M101 (Mathematics for Computer Science) classes, how many of the CS103 students are no enrolled in M101? GMAT Data Sufficiency
• Buster leaves the trailer at noon and walks towards the studio at a constant rate of B miles per hour. 20 minutes later, Charlie leaves the same studio and walks towards the same trailer at a constant rate of C miles per hour along the same route as Buster. Will Buster be closer to the trailer than to the studio when he passes Charlie? GMAT Data Sufficiency
• If sq rt{3+sq rt(x-1)} = 4, what is the value of x? GMAT Data Sufficiency