GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Oct 2019, 04:27

### 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

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

# What is the ratio of the surface area of a cube to the surfa

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

### Hide Tags

Senior Manager
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 443
Location: United Kingdom
Concentration: International Business, Strategy
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
What is the ratio of the surface area of a cube to the surfa  [#permalink]

### Show Tags

12 Feb 2012, 21:33
2
11
00:00

Difficulty:

45% (medium)

Question Stats:

64% (01:37) correct 36% (01:18) wrong based on 245 sessions

### HideShow timer Statistics

What is the ratio of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?

A. 1/4
B. 3/8
C. 1/2
D. 3/5
E. 2

_________________
Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730
Math Expert
Joined: 02 Sep 2009
Posts: 58327
Re: What is the ratio of the surface area of a cube to the  [#permalink]

### Show Tags

13 Feb 2012, 06:25
4
4
enigma123 wrote:
What is the ratio of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?

A)¼
B)3/8
C)½
D)3/5
E)2

Any idea how to solve these guys?

30 second approach:
A cube has 6 faces, suppose each has an area of 1, so surface area of the cube will be 6;

A rectangular solid identical to the cube in all ways except that its length has been doubled is just complicated way of saying that the rectangular solid is built with two cubes, hence it has 4+4+2=10 faces of a little cube (just imagine to cubes put one on another) and thus the surface area of the rectangular solid will be 10;

Ratio: 6/10=3/5.

_________________
Manager
Joined: 31 Jan 2012
Posts: 69
Re: Surface area of a cube  [#permalink]

### Show Tags

12 Feb 2012, 21:41
4
1
Let X be the side of the cube. Therefore X^2*6= surface area.

the rectangle is the same other than length is 2X. The width and height are the same as the cube. 2*W*H+2*W*L+2*H*L= 2X^2+4X^2+4X^2= 10X^2.

6X^2/10X^2 = 3/5.

##### General Discussion
Intern
Joined: 16 Dec 2011
Posts: 38
GMAT Date: 04-23-2012
Re: What is the ratio of the surface area of a cube to the  [#permalink]

### Show Tags

23 Feb 2012, 06:57
surface area of Cube = 6sidesqr
surface area of rectangular soild = 2( lb + bh+ hl)
assume side of cube is X
its surface area is 6Xsqr
surface area of Recatngular solid is = 10Xsqr ( 2( 2Xsqr+Xsqr +2Xsqr))
take ratio of these two we will get 6/10 = 3/5
Intern
Joined: 09 May 2013
Posts: 43
Re: What is the ratio of the surface area of a cube to the  [#permalink]

### Show Tags

22 Jun 2013, 01:56
Bunuel wrote:
enigma123 wrote:
What is the ratio of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?

A)¼
B)3/8
C)½
D)3/5
E)2

Any idea how to solve these guys?

30 second approach:
A cube has 6 faces, suppose each has an area of 1, so surface area of the cube will be 6;

A rectangular solid identical to the cube in all ways except that its length has been doubled is just complicated way of saying that the rectangular solid is built with two cubes, hence it has 4+4+2=10 faces of a little cube (just imagine to cubes put one on another) and thus the surface area of the rectangular solid will be 10;

Ratio: 6/10=3/5.

why "4+4+2" if there are two cubes than it should be "4+4" = 8 faces
Math Expert
Joined: 02 Sep 2009
Posts: 58327
Re: What is the ratio of the surface area of a cube to the  [#permalink]

### Show Tags

22 Jun 2013, 03:31
WarriorGmat wrote:
Bunuel wrote:
enigma123 wrote:
What is the ratio of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?

A)¼
B)3/8
C)½
D)3/5
E)2

Any idea how to solve these guys?

30 second approach:
A cube has 6 faces, suppose each has an area of 1, so surface area of the cube will be 6;

A rectangular solid identical to the cube in all ways except that its length has been doubled is just complicated way of saying that the rectangular solid is built with two cubes, hence it has 4+4+2=10 faces of a little cube (just imagine to cubes put one on another) and thus the surface area of the rectangular solid will be 10;

Ratio: 6/10=3/5.

why "4+4+2" if there are two cubes than it should be "4+4" = 8 faces

Plus 2 faces on the top and bottom. Put two dice one on another and see how many faces will it have.
_________________
Manager
Joined: 07 May 2013
Posts: 87
Re: What is the ratio of the surface area of a cube to the surfa  [#permalink]

### Show Tags

14 Nov 2013, 20:12
$$\frac{6S^2}{2(lb+bh+hl)}$$=$$\frac{6x^2}{2(2x^2+x^2+2x^2)}$$=$$\frac{6x^2}{10x^2}$$=$$\frac{3}{5}$$
Manager
Joined: 07 May 2013
Posts: 87
Re: What is the ratio of the surface area of a cube to the surfa  [#permalink]

### Show Tags

14 Nov 2013, 20:17
Do not get confused as to why I took x. Let side of the cube be x. He says length is doubled. So, l=2x. However, b and h remain unchanged. So, b=h=x.
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1751
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: What is the ratio of the surface area of a cube to the surfa  [#permalink]

### Show Tags

27 Mar 2014, 02:09
2
Area of cube = $$a^2 + a^2 + a^2 + a^2 + a^2 + a^2 = 6 a^2$$

When one of the dimension is doubled, it has impact on 4 sides (rest 2 remains same)

Look at the diagram

Area of rectangular solid $$= a^2 + a^2 + 2 a^2 + 2 a^2 + 2 a^2 + 2 a^2 = 10 a^2$$

Ratio $$= \frac{6 a^2}{10 a^2} = \frac{3}{5}$$

Attachments

cub.jpg [ 22.23 KiB | Viewed 18246 times ]

_________________
Kindly press "+1 Kudos" to appreciate
SVP
Joined: 06 Sep 2013
Posts: 1572
Concentration: Finance
Re: What is the ratio of the surface area of a cube to the surfa  [#permalink]

### Show Tags

31 Mar 2014, 08:35
Hi All,

Let's assume leg of cube is 1 then surface area will be 6(1)^2=6. Now, rectangular solid will be (2)(1)(1), The area of the solid 2(ab+ac+bc) where a=2, b=1 and c=1. Thus its surface area totals 2(5)=10. So then D, 6/10=3/5 is the surface area.

D is the correct answer

Is this clear?

Cheers!
J

I'm back
Intern
Joined: 23 Dec 2014
Posts: 47
Re: What is the ratio of the surface area of a cube to the surfa  [#permalink]

### Show Tags

27 Jan 2015, 15:38
Assume the length is Y

Surface are of Cube= 6Y^2

As the length is doubled for rectangle , other remains same. That means, rectangle's width,and height is "Y" but it's length is "2Y" now.

Let's see the surface area of Rectangle

Length = 2Y
Width = Y
Height = Y

So,
Multiplying length with height, 2Y x Y = 2Y^2 . Since there are two sides then it will be multiplied by two. So it will be 4Y^2

Multiplying length with width, 2Yx Y = 2Y^2 .Now multiply with two and we get 4Y^2

Multiplying Width with height, Y x Y = Y^2 Now multiply with two and we get 2Y^2

After Adding them , 4Y^2+4Y^2+2Y^2 = 10Y^2

Now,
6y^2/10Y^2 = 3/5
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9701
Location: Pune, India
Re: What is the ratio of the surface area of a cube to the surfa  [#permalink]

### Show Tags

27 Jan 2015, 22:15
enigma123 wrote:
What is the ratio of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?

A. 1/4
B. 3/8
C. 1/2
D. 3/5
E. 2

Another way to think about it:

Imagine the cube with 6 equal faces. The surface area will be 6s^2 (s is the length of the edge of the cube).
Now imagine pulling on one face of the cube to elongate it. Now you have 4 extra equal faces on the four sides. The extra surface area is 4s^2.

Ratio of surface area of cube:surface area of rectangular solid = 6:10 = 3:5

_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Board of Directors
Joined: 17 Jul 2014
Posts: 2514
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: What is the ratio of the surface area of a cube to the surfa  [#permalink]

### Show Tags

22 Nov 2015, 10:57
did it by knowing that surface area of a cube is always 6*side^2
since the rectangular has 2x as it's length and the rest is the same, we have:
2*(2x*x)+2(2x*x)+2x^2 = 10x^2

6x^2/10x^10 = 3/5
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15250
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: What is the ratio of the surface area of a cube to the surfa  [#permalink]

### Show Tags

25 Nov 2015, 15:38
Hi All,

This question can be solved by TESTing VALUES. You would likely find it helpful to physically draw the cube and solid.

Since the answer choices do not include variables, we can use whatever values we'd like for the dimensions of the cube and for the rectangular solid (as long as we follow the Facts described in the prompt). Given the one specific rule (the length of the rectangular solid is double the length of the cube), I'll TEST the easiest VALUES that I can think of...

Cube = (1)(1)(1)
Solid = (1)(1)(2)

Surface Area of Cube = 6(1) = 6
Surface Area of Solid = 2(1) + 4(2) = 10

Thus, the ratio of the two Surface Areas is 6:10 = 3:5

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Non-Human User
Joined: 09 Sep 2013
Posts: 13154
Re: What is the ratio of the surface area of a cube to the surfa  [#permalink]

### Show Tags

01 Apr 2019, 00:26
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.
_________________
Re: What is the ratio of the surface area of a cube to the surfa   [#permalink] 01 Apr 2019, 00:26
Display posts from previous: Sort by

# What is the ratio of the surface area of a cube to the surfa

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

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