If the length of each edge of a certain rectangular solid is an integer and exactly four of its faces have the same dimensions, then what is the volume of the rectangular solid?(1) Two of the faces have areas of 32 square units and 16 square units.(2) One of the edges is twice the length of another edge.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer?

Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity

Open App

GMAT Exam > GMAT Questions > If the length of each edge of a certain recta...

Join the Discussion on the App

If the length of each edge of a certain rectangular solid is an integer and exactly four of its faces have the same dimensions, then what is the volume of the rectangular solid?

(1) Two of the faces have areas of 32 square units and 16 square units.

(2) One of the edges is twice the length of another edge.

a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
c)
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
d)
EACH statement ALONE is sufficient.
e)
Statements (1) and (2) TOGETHER are NOT sufficient.

Correct answer is option 'A'. Can you explain this answer?

FREE This question is part of

Test: Rectangular Solids- 1

Attempt Test

Attempt this Test

Verified Answer

If the length of each edge of a certain rectangular solid is an intege...

Steps 1 & 2: Understand Question and Draw Inferences

Some general points to be noted:

(a) In a rectangular solid, each pair of adjacent faces has one common edge.

(b) The opposite faces have the same dimensions.

Some inference that can be drawn from the question:

(d) Two of the faces which have different dimensions compared the four faces which have the same dimensions must have the following properties:

(i) They must be opposite to each other and their areas must be equal.

(ii) They must both be of the shape of a square.

(iii) Each of these two faces has a common edge with each one of the other four faces.

(e) The lengths of edges are positive integers.

Step 3: Analyze Statement 1

The possible values of the lengths and breadths for the face whose area is 32 sq. units are: 32 and 1, OR 16 and 2 OR 8 and 4.

The possible values of the lengths and breadths for the face whose area is 16 sq. units are: 16 and 1 OR 8 and 2 OR 4 and 4.

Since one of the surfaces must be a square and the lengths of edges are integers, between the two areas given only the face with area of 16 sq. units makes a square. There will be only two such surfaces in this solid with edge lengths 4 units each.

The only possible lengths of the faces whose areas are 32 square units are 8 units and 4 units.

We now know all the dimensions of the rectangular solid (8 units, 4 units, 4 units) and hence its volume can be found out.

SUFFICIENT.

Step 4: Analyze Statement 2

Let’s say that the square face has edges of lengths ‘a’ units each. This means that the length of the other side of the rectangular faces is ‘2a’ or ‘a/2’. (Depending on which length is the bigger one.)

Since we do not have the values of the edges or any other numeric information, we cannot ascertain the volume of this rectangular solid.

INSUFFICIENT.

Step 5: Analyze Both Statements Together (if needed)

Since the answer has been obtained in Step 3, there is no need to combine the statements.

Correct Answer: A

View all questions of this test

Most Upvoted Answer

If the length of each edge of a certain rectangular solid is an intege...

Given:
- The length of each edge of a certain rectangular solid is an integer.
- Exactly four of its faces have the same dimensions.

To find:
- The volume of the rectangular solid.

Statement 1: Two of the faces have areas of 32 square units and 16 square units.
- This means that the dimensions of the rectangular solid are in the ratio of 2:1.
- However, this information is not sufficient to determine the exact dimensions or volume of the rectangular solid.
- For example, the dimensions could be 4x2x1 or 8x4x2, resulting in different volumes.

Statement 2: One of the edges is twice the length of another edge.
- This statement alone does not provide any information about the dimensions or volume of the rectangular solid.
- We cannot determine the exact dimensions or volume with this information alone.

Combining both statements:
- The combination of both statements does not provide any additional information that can help determine the dimensions or volume of the rectangular solid.
- Statement 1 gives the ratio of the dimensions, but we still do not have enough information to determine the exact values.
- Therefore, both statements together are also not sufficient to answer the question.

Conclusion:
- Neither statement alone nor both statements together are sufficient to determine the volume of the rectangular solid.
- Hence, the correct answer is option A.

Answered by Talent Skill Learning · View profile

Attention GMAT Students!

To make sure you are not studying endlessly, EduRev has designed GMAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in GMAT.

GMAT Focus Edition Mock Test Series 2024

Quantitative for GMAT

Crash Course for GMAT

Data Insights for GMAT

View all answers Start learning for free

< Previous Question Next Question >

Explore Courses for GMAT exam

Similar GMAT Doubts

In the rectangular solid above, if each dimension of the solid is an integer, what is the volume of the solid?(1) The area of two sides of the rectangular solid is 4 and 20 respectively(2) The area of two sides of the rectangular solid is 4 and 5 respectively.

View answer

Directions: Each Data Sufficiency problem consists of a question and two statements labeled (1) and (2), that provide data. Based on the data given plus your knowledge of mathematics and everyday facts, you must decide whether the data are sufficient for answering the question. The five answer choices are the same for every data sufficiency question.A codebreaking device is made up of a rectangular box filled with x cylinders of ball bearings placed together such that the diameter of the bearings and the cylinders are equal, and the cylinders line up evenly, touching, with no extra room inside the device. If the cylinders are the same height as the box, and the box is 18 inches long and 10 inches wide, what’s the value of x?(1) 9 cylinders can line up along the length of the box.(2) Each ball bearing has a radius of 1.

View answer

Is ABCD rectangular?(1) Angle ABC and BCD are right angle(2) Two diagonal have the same length.

View answer

What is the greatest possible (straight-lin e) distance between any two points on a certain rectangular solid of length L, width W, and height H, where H W L ?(1) The length, width, and height of the rectangular solid are the squares of prime integers.(2) The roots of the equation x2 13x = -36 are the width and the height of the rectangular solid.

View answer

A rectangular photograph shown by the white region in the figure is enclosed by a frame of uniform width. The shaded region in the figure represents the frame. What is the ratio of AB to BC?(1) The ratio of the longer dimension to the smaller dimension of the photograph is 3:2.(2) If a frame of twice the width was used then the ratio of AB to BC would have been 5:4.

View answer

Top Courses for GMATView all

GMAT Focus Edition Mock Test Series 2024

Quantitative for GMAT

Crash Course for GMAT

Data Insights for GMAT

100 RCs for GMAT

Top Courses for GMAT

View all

If the length of each edge of a certain rectangular solid is an integer and exactly four of its faces have the same dimensions, then what is the volume of the rectangular solid?(1) Two of the faces have areas of 32 square units and 16 square units.(2) One of the edges is twice the length of another edge.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer?

Share with a Friend

Answer this doubt

Question Description
If the length of each edge of a certain rectangular solid is an integer and exactly four of its faces have the same dimensions, then what is the volume of the rectangular solid?(1) Two of the faces have areas of 32 square units and 16 square units.(2) One of the edges is twice the length of another edge.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If the length of each edge of a certain rectangular solid is an integer and exactly four of its faces have the same dimensions, then what is the volume of the rectangular solid?(1) Two of the faces have areas of 32 square units and 16 square units.(2) One of the edges is twice the length of another edge.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the length of each edge of a certain rectangular solid is an integer and exactly four of its faces have the same dimensions, then what is the volume of the rectangular solid?(1) Two of the faces have areas of 32 square units and 16 square units.(2) One of the edges is twice the length of another edge.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer?.

Solutions for If the length of each edge of a certain rectangular solid is an integer and exactly four of its faces have the same dimensions, then what is the volume of the rectangular solid?(1) Two of the faces have areas of 32 square units and 16 square units.(2) One of the edges is twice the length of another edge.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT. Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.

Here you can find the meaning of If the length of each edge of a certain rectangular solid is an integer and exactly four of its faces have the same dimensions, then what is the volume of the rectangular solid?(1) Two of the faces have areas of 32 square units and 16 square units.(2) One of the edges is twice the length of another edge.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of If the length of each edge of a certain rectangular solid is an integer and exactly four of its faces have the same dimensions, then what is the volume of the rectangular solid?(1) Two of the faces have areas of 32 square units and 16 square units.(2) One of the edges is twice the length of another edge.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer?, a detailed solution for If the length of each edge of a certain rectangular solid is an integer and exactly four of its faces have the same dimensions, then what is the volume of the rectangular solid?(1) Two of the faces have areas of 32 square units and 16 square units.(2) One of the edges is twice the length of another edge.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of If the length of each edge of a certain rectangular solid is an integer and exactly four of its faces have the same dimensions, then what is the volume of the rectangular solid?(1) Two of the faces have areas of 32 square units and 16 square units.(2) One of the edges is twice the length of another edge.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice If the length of each edge of a certain rectangular solid is an integer and exactly four of its faces have the same dimensions, then what is the volume of the rectangular solid?(1) Two of the faces have areas of 32 square units and 16 square units.(2) One of the edges is twice the length of another edge.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice GMAT tests.

Explore Courses for GMAT exam