It is currently 20 Nov 2017, 09:12

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

What is the volume of a certain cube?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

1 KUDOS received
Intern
Intern
avatar
Joined: 25 Nov 2013
Posts: 17

Kudos [?]: 6 [1], given: 11

Concentration: Marketing, International Business
GMAT Date: 02-14-2014
GPA: 2.3
WE: Other (Internet and New Media)
What is the volume of a certain cube? [#permalink]

Show Tags

New post 10 Dec 2013, 14:12
1
This post received
KUDOS
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

86% (00:23) correct 14% (00:30) wrong based on 263 sessions

HideShow timer Statistics

What is the volume of a certain cube?

(1) The sum of the areas of the faces of the cube is 54.
(2) The greatest possible distance between two points on the cube is \(3\sqrt{3}\)
[Reveal] Spoiler: OA

Kudos [?]: 6 [1], given: 11

Senior Manager
Senior Manager
User avatar
Joined: 13 May 2013
Posts: 460

Kudos [?]: 202 [0], given: 134

Re: What is the volume of a certain cube? [#permalink]

Show Tags

New post 10 Dec 2013, 14:29
1
This post was
BOOKMARKED
What is the volume of a certain cube?

(1) The sum of the areas of the faces of the cube is 54.

Because this is a cube, all surface areas must a.) be equal to one another and b.) must have the same length and width.

I.) divide the sum of the surface areas into six equal parts (for the six faces of a cube)
54/6 = 9
area (of one face of cube) = l^2 --> 9 = L^2 --> L=3 Volume = l^3 --> v=27.

(2) The greatest possible distance between two points on the cube is 3\sqrt{3}

The greatest possible distance from one point to another in a cube is from one angle down to it's opposite angle (as shown in the diagram with a purple line) As you can see, the purple diagonal forms a right triangle inside the square. Therefore, the greatest possible distance can be found by finding the hypotenuse of the right triangle using the Pythagorean theorem:

a^2 + b^2 = c^2 --> x^2 + (x√2)^2 = (3/√3)^2
x^2 + x^2/2 = 3
2x^2/2 + x^2/2 = 3
3x^2/2 = 3
x = √2

So the side length of this cube is √2. Therefore, the volume of the cube = √2^3. Sufficient.

D
Attachments

EXAMPLE FOUR.png
EXAMPLE FOUR.png [ 18.16 KiB | Viewed 6462 times ]

Kudos [?]: 202 [0], given: 134

Intern
Intern
User avatar
Joined: 02 Sep 2011
Posts: 17

Kudos [?]: [0], given: 42

Schools: Goizueta '16
GPA: 3.94
Re: What is the volume of a certain cube? [#permalink]

Show Tags

New post 10 Dec 2013, 14:54
Dear WholeLottaLove,

In statement two, I calcilate X=1. Can you explain how you get X=√2.

Thanks in advance.

Papua

Kudos [?]: [0], given: 42

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42264

Kudos [?]: 132783 [0], given: 12372

Re: What is the volume of a certain cube? [#permalink]

Show Tags

New post 11 Dec 2013, 02:58
Expert's post
2
This post was
BOOKMARKED
papua wrote:
Dear WholeLottaLove,

In statement two, I calcilate X=1. Can you explain how you get X=√2.

Thanks in advance.

Papua


Actually x should be 3, there.

What is the volume of a certain cube?

(1) The sum of the areas of the faces of the cube is 54. A cube has 6 faces and the area of each is a^2, where a is the length of a side. Thus we have that \(6a^2=54\) --> \(a=3\) --> \(volume=a^3=27\). Sufficient.

(2) The greatest possible distance between two points on the cube is \(3\sqrt{3}\). The implies that the diagonal of the cube is \(3\sqrt{3}\) --> \(diagonal=a^2+a^2+a^2=(3\sqrt{3})^2\) --> \(a=3\) --> \(volume=a^3=27\). Sufficient.

Answer: D.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132783 [0], given: 12372

Expert Post
3 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42264

Kudos [?]: 132783 [3], given: 12372

Re: What is the volume of a certain cube? [#permalink]

Show Tags

New post 11 Dec 2013, 03:03
3
This post received
KUDOS
Expert's post
Bunuel wrote:
papua wrote:
Dear WholeLottaLove,

In statement two, I calcilate X=1. Can you explain how you get X=√2.

Thanks in advance.

Papua


Actually x should be 3, there.

What is the volume of a certain cube?

(1) The sum of the areas of the faces of the cube is 54. A cube has 6 faces and the area of each is a^2, where a is the length of a side. Thus we have that \(6a^2=54\) --> \(a=3\) --> \(volume=a^3=27\). Sufficient.

(2) The greatest possible distance between two points on the cube is \(3\sqrt{3}\). The implies that the diagonal of the cube is \(3\sqrt{3}\) --> \(diagonal=a^2+a^2+a^2=(3\sqrt{3})^2\) --> \(a=3\) --> \(volume=a^3=27\). Sufficient.

Answer: D.


Similar questions to practice:
a-sphere-is-inscribed-in-a-cube-with-an-edge-of-10-what-is-100798.html
if-the-box-shown-is-a-cube-then-the-difference-in-length-127463.html
a-sphere-is-inscribed-in-a-cube-with-an-edge-of-x-centimeter-156346.html
a-sphere-is-inscribed-in-a-cube-with-an-edge-of-10-what-is-127461.html
what-is-the-volume-of-the-cube-above-103680.html
a-rectangular-box-has-dimensions-of-8-feet-8-feet-and-z-128483.html
for-the-cube-shown-above-what-is-the-degree-measure-of-pqr-13841.html
a-rectangular-box-is-10-inches-wide-10-inches-long-and-144733.html

Hope this helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132783 [3], given: 12372

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42264

Kudos [?]: 132783 [1], given: 12372

Re: What is the volume of a certain cube? [#permalink]

Show Tags

New post 11 Dec 2013, 03:05
1
This post received
KUDOS
Expert's post
WholeLottaLove wrote:
What is the volume of a certain cube?

(1) The sum of the areas of the faces of the cube is 54.

Because this is a cube, all surface areas must a.) be equal to one another and b.) must have the same length and width.

I.) divide the sum of the surface areas into six equal parts (for the six faces of a cube)
54/6 = 9
area (of one face of cube) = l^2 --> 9 = L^2 --> L=3 Volume = l^3 --> v=27.

(2) The greatest possible distance between two points on the cube is 3\sqrt{3}

The greatest possible distance from one point to another in a cube is from one angle down to it's opposite angle (as shown in the diagram with a purple line) As you can see, the purple diagonal forms a right triangle inside the square. Therefore, the greatest possible distance can be found by finding the hypotenuse of the right triangle using the Pythagorean theorem:

a^2 + b^2 = c^2 --> x^2 + (x√2)^2 = (3/√3)^2
x^2 + x^2/2 = 3
2x^2/2 + x^2/2 = 3
3x^2/2 = 3
x = √2

So the side length of this cube is √2. Therefore, the volume of the cube = √2^3. Sufficient.

D


You should have spotted that there was something wrong with your solution since you got two different values for the volume from (1) and (2). On the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other or the stem.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132783 [1], given: 12372

Intern
Intern
User avatar
Joined: 02 Sep 2011
Posts: 17

Kudos [?]: [0], given: 42

Schools: Goizueta '16
GPA: 3.94
Re: What is the volume of a certain cube? [#permalink]

Show Tags

New post 11 Dec 2013, 14:04
Thanks Bunuel for your explanation.

Kudos [?]: [0], given: 42

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15638

Kudos [?]: 283 [0], given: 0

Premium Member
Re: What is the volume of a certain cube? [#permalink]

Show Tags

New post 26 May 2017, 18:20
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 283 [0], given: 0

Re: What is the volume of a certain cube?   [#permalink] 26 May 2017, 18:20
Display posts from previous: Sort by

What is the volume of a certain cube?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.