It is currently 17 Oct 2017, 04:40

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

A rectangular solid has a surface area of 94 square inches. What is it

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41871

Kudos [?]: 128522 [0], given: 12180

A rectangular solid has a surface area of 94 square inches. What is it [#permalink]

Show Tags

New post 06 Jun 2017, 10:02
Expert's post
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

61% (01:11) correct 39% (01:05) wrong based on 157 sessions

HideShow timer Statistics

A rectangular solid has a surface area of 94 square inches. What is its volume?

(1) The surface area of one side of the rectangular solid is 12.

(2) The surface area of one side of the rectangular solid is 20.
[Reveal] Spoiler: OA

_________________

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 [?]: 128522 [0], given: 12180

Expert Post
SVP
SVP
User avatar
G
Joined: 08 Jul 2010
Posts: 1834

Kudos [?]: 2272 [0], given: 51

Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Re: A rectangular solid has a surface area of 94 square inches. What is it [#permalink]

Show Tags

New post 06 Jun 2017, 23:55
Expert's post
1
This post was
BOOKMARKED
Bunuel wrote:
A rectangular solid has a surface area of 94 square inches. What is its volume?

(1) The surface area of one side of the rectangular solid is 12.

(2) The surface area of one side of the rectangular solid is 20.


2(lb+BH+lh)=94
I.e. lb+BH+lh=47

Statement 1: lb=12
Not sufficient

Statement 2: bh=20
Not sufficient

Combining
lh= 47-12-20=15

Only possibility of l,b,h are 3,4,5
Hence volume = 60

Sufficient

Answer Option C
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Kudos [?]: 2272 [0], given: 51

Expert Post
Top Contributor
1 KUDOS received
SVP
SVP
User avatar
G
Joined: 12 Sep 2015
Posts: 1793

Kudos [?]: 2444 [1], given: 356

Location: Canada
Re: A rectangular solid has a surface area of 94 square inches. What is it [#permalink]

Show Tags

New post 07 Jun 2017, 12:28
1
This post received
KUDOS
Expert's post
Top Contributor
2
This post was
BOOKMARKED
Bunuel wrote:
A rectangular solid has a surface area of 94 square inches. What is its volume?

(1) The surface area of one side of the rectangular solid is 12.

(2) The surface area of one side of the rectangular solid is 20.


Great (and tricky) question!

Target question: What is the volume of the rectangular solid?

This is a good candidate for rephrasing the target question.

Let x, y, and z be the dimensions (length, width and height) of the rectangular solid.
So, xyz is its volume

REPHRASED target question: What is the value of xyz?

Given: The rectangular solid has a surface area of 94 square inches
Each side of the rectangular solid is a RECTANGLE.
So, 2 sides have the dimensions x by y, 2 sides have the dimensions x by z, and 2 sides have the dimensions y by z
So, the total surface area = 2(xy + xz + yz) = 94
Divide both sides by 2 to get: xy + xz + yz = 47

Statement 1: The surface area of one side of the rectangular solid is 12.
Let's say this is the side with dimensions x by y
So, xy = 12
Is this enough information to determine the value of xyz? No.
We know nothing about the value of z.
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The surface area of one side of the rectangular solid is 20
Let's say this is the side with dimensions x by z
So, xz = 20
For the same reason as above, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that xy = 12
Statement 2 tells us that xz = 20
We also know that xy + xz + yz = 47

NOTE: since this is system of 3 equations with 3 variables, many people will conclude that we can solve it for x, y, and z. However, that rule only applies to linear equations. In this case, the equations are quadratic equations. So, let's see if we can solve this system and find the value of xyz

Take xy + xz + yz = 47 and replace xy with 12 and xz with 20
We get: 12 + 20 + yz = 47
So, yz = 15

We now have:
xy = 12, xz = 20 and yz = 15
This means that (xy)(xz)(yz) = (12)(20)(15)
Simplify: x²y²z² = 3600
Rewrite as: (xyz)² = 3600
So, xyz = 60....DONE!!!
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer:
[Reveal] Spoiler:
C


ASIDE: Some people will say that, if (xyz)² = 3600, then EITHER xyz = 60 OR xyz = -60
However, we're dealing with a real world problem here, and in the real world, the volume cannot be negative. So, we can ignore the negative solution.


RELATED VIDEO

_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Kudos [?]: 2444 [1], given: 356

Intern
Intern
avatar
B
Joined: 15 Mar 2017
Posts: 2

Kudos [?]: 0 [0], given: 8

CAT Tests
Re: A rectangular solid has a surface area of 94 square inches. What is it [#permalink]

Show Tags

New post 24 Aug 2017, 06:24
I have a different answer to this. I find each of the information suffecient. Please hear me out

Let the sides be a, b and c.

2(ab+bc+ac) = 94
Therefore, ab+bc+ac = 47.

Now, statement 1 = lets assume ab, side is 12

therefore, bc+ac = 35
(b+a).c =35
Now either b+a = 7 and c = 5 or
b+a = 5, c = 7
If b+a= 7, possible values of abc are (5,2,5) (4,3,5) or (6,1,5). However, only 1 combination gives 1 side area as 12 which is the (4,3,5)

If b+a=5 possible values of abc are (3,2,7) ,(4,1,7) . Ans none of them give 12 as the area. b+a will not be 5.

Therefore, the only possible value is (3,4,5)

Similarly, I found the same value by Statement 2 and I think both are sufficient on their own.

Please help me understand where I am wrong.

Kudos [?]: 0 [0], given: 8

Intern
Intern
avatar
B
Joined: 29 Jul 2012
Posts: 17

Kudos [?]: 1 [0], given: 21

Re: A rectangular solid has a surface area of 94 square inches. What is it [#permalink]

Show Tags

New post 05 Sep 2017, 11:27
Bunuel VeritasPrepKarishma
Could you please clarify, as even I feel that answer should be D.

l*b+b*w+w*l=47

From B: Assuming l*b=20, we have w(l+b)=27, only combination that satisfies is l & b equals 5 & 4, hence w=3.
Similarly answer can be derived from A as well.

Kudos [?]: 1 [0], given: 21

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41871

Kudos [?]: 128522 [0], given: 12180

Re: A rectangular solid has a surface area of 94 square inches. What is it [#permalink]

Show Tags

New post 05 Sep 2017, 11:31
ravjai81 wrote:
Bunuel VeritasPrepKarishma
Could you please clarify, as even I feel that answer should be D.

l*b+b*w+w*l=47

From B: Assuming l*b=20, we have w(l+b)=27, only combination that satisfies is l & b equals 5 & 4, hence w=3.
Similarly answer can be derived from A as well.


We are not told that the dimensions of the solid are necessarily integers.
_________________

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 [?]: 128522 [0], given: 12180

Senior Manager
Senior Manager
User avatar
G
Joined: 29 Jun 2017
Posts: 345

Kudos [?]: 65 [0], given: 64

WE: Engineering (Transportation)
GMAT ToolKit User Reviews Badge
Re: A rectangular solid has a surface area of 94 square inches. What is it [#permalink]

Show Tags

New post 05 Sep 2017, 11:49
1) insufficient LB =12 H=?
2) insufficient BH = 20 L=?
combine 1&2
LB=12, BH=20
total area =94
2(LB+LB+LH) =94
LB+BH+LH=47
LB=12 BH=20 so LH=15
we dont require to calculate l,b,h
JUST MULTIPLY ALL
LBxBHxLH= (LBH)^2 = V^2
12x20x15 = V
Definite Ans C
_________________

Give Kudos for correct answer and/or if you like the solution.

Kudos [?]: 65 [0], given: 64

Intern
Intern
avatar
B
Joined: 29 Jul 2012
Posts: 17

Kudos [?]: 1 [0], given: 21

Re: A rectangular solid has a surface area of 94 square inches. What is it [#permalink]

Show Tags

New post 05 Sep 2017, 22:11
Thanks Bunuel and Sahilvijay

Kudos [?]: 1 [0], given: 21

Re: A rectangular solid has a surface area of 94 square inches. What is it   [#permalink] 05 Sep 2017, 22:11
Display posts from previous: Sort by

A rectangular solid has a surface area of 94 square inches. What is it

  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®.