It is currently 13 Dec 2017, 20:42

Decision(s) Day!:

CHAT Rooms | Ross R1 | Kellogg R1 | Darden R1 | Tepper R1


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 rectangular solid?

  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: 42597

Kudos [?]: 135562 [0], given: 12699

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

Show Tags

New post 08 Dec 2014, 06:32
kevin627 wrote:
deepbidwai wrote:
Information in (2) is redundant as from (1) we can know all required info.
(1) Two adjacent faces of the solid have areas 15 and 24, respectively.
So, one common side has to be 3. i.e. 5*3 and 8*3. From this info we can say area of the face is 8*5= 40.
Hence only (1) is sufficient.
Answer should be A and not C.


DeepakB


I also don't understand why A is not sufficient.

We need to determine the length of 3 sides.

If two adjacent faces share a side with respective areas 15 and 24, the only common prime they share is 3, which must be their shared side length.

If the area of one face is 15 and one side is 3, then the other side is 5.
If the area of one face is 24 and one side is 3, then the other side is 8.

Therefore, we have three side lengths: 5, 8, 3

Perhaps my mistake is assuming that the dimensions must be integers?


Have you read this: what-is-the-volume-of-a-certain-rectangular-solid-90748.html#p772095 ???
_________________

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 [?]: 135562 [0], given: 12699

Intern
Intern
avatar
Joined: 12 Nov 2014
Posts: 8

Kudos [?]: [0], given: 3

GMAT 1: 710 Q47 V40
Re: What is the volume of a certain rectangular solid? [#permalink]

Show Tags

New post 08 Dec 2014, 07:06
Bunuel wrote:
kevin627 wrote:
deepbidwai wrote:
Information in (2) is redundant as from (1) we can know all required info.
(1) Two adjacent faces of the solid have areas 15 and 24, respectively.
So, one common side has to be 3. i.e. 5*3 and 8*3. From this info we can say area of the face is 8*5= 40.
Hence only (1) is sufficient.
Answer should be A and not C.


DeepakB


I also don't understand why A is not sufficient.

We need to determine the length of 3 sides.

If two adjacent faces share a side with respective areas 15 and 24, the only common prime they share is 3, which must be their shared side length.

If the area of one face is 15 and one side is 3, then the other side is 5.
If the area of one face is 24 and one side is 3, then the other side is 8.

Therefore, we have three side lengths: 5, 8, 3

Perhaps my mistake is assuming that the dimensions must be integers?


Have you read this:


I did see your post before. After reading more carefully, I can clearly see why (1) is insufficient. Thanks :)

Kudos [?]: [0], given: 3

Current Student
avatar
Joined: 31 Jul 2014
Posts: 41

Kudos [?]: 20 [0], given: 0

Concentration: Finance, Technology
Schools: Owen '17 (M)
GMAT ToolKit User
What is the volume of a certain rectangular solid? [#permalink]

Show Tags

New post 06 Jan 2015, 15:55
Where am I going wrong on this?

If a side has area of 15 can't we factor to say that the side must be some combo of factors and since they are adjacent they must share a factor for the like side...so if 15 was 3x5 then 24 must be 8x3. Through this we get 8x3x5 for area?

I know I am wrong this was my initial reaction the question and trying to avoid it. Is it chance for fractional sides that makes this solution incorrect?

Kudos [?]: 20 [0], given: 0

Director
Director
User avatar
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 599

Kudos [?]: 649 [0], given: 298

Location: India
GMAT 1: 710 Q50 V36
GMAT 2: 750 Q51 V41
GMAT 3: 790 Q51 V49
GPA: 3.3
Re: What is the volume of a certain rectangular solid? [#permalink]

Show Tags

New post 06 Jul 2015, 00:50
Bunuel wrote:
This question is from Official Guide and Official Answer is C.

About rectangular solid:
Attachment:
800px-Cuboid.png

In a rectangular solid, all angles are right angles, and opposite faces are equal, so rectangular solid can have maximum 3 different areas of its faces, on the diagram: yellow, green and red faces can have different areas. I say at max, as for example rectangular solid can be a cube and in this case it'll have all faces equal, also it's possible to have only 2 different areas of the faces, for example when the base is square and the height does not equals to the side of this square.

Volume of rectangular solid is Volume=Length*Height*Depth.

BACK TO THE ORIGINAL QUESTION:

What is the volume of a certain rectangular solid?

(1) Two adjacent faces of the solid have areas 15 and 24, respectively --> let the two adjacent faces be blue and yellow faces on the diagram --> \(blue=d*h=15\) and \(yellow=l*h=24\) --> we have 2 equations with 3 unknowns, not sufficient to calculate the value of each or the product of the unknowns (\(V=l*h*d\)).

To elaborate more:
If \(blue=d*h=15*1=15\) and \(yellow=l*h=24*1=24\) then \(V=l*h*d=24*1*15=360\);
If \(blue=d*h=5*3=15\) and \(yellow=l*h=8*3=24\) then \(V=l*h*d=8*3*5=90\).

Two different answer, hence not sufficient.

(2) Each of two opposite faces of the solid has area 40 --> just gives the areas of two opposite faces, so clearly insufficient.

(1)+(2) From (1): \(blue=d*h=15\), \(yellow=l*h=24\) and from (2) each of two opposite faces of the solid has area 40, so it must be the red one: \(red=d*l=40\) --> here we have 3 distinct linear equations with 3 unknowns hence we can find the values of each and thus can calculate \(V=l*h*d\). Sufficient.

To show how it can be done: multiply these 3 equations --> \(l^2*h^2*d^2=(l*h*d)^2=15*24*40=24^2*5^2\) --> \(V=l*h*d=24*5=120\).

Answer: C.

Hope it helps.


Where am I wrong-

a x b = 15
b x c = 24

a x b = 5 x 3
b x c = 3 x 2 x 2 x 2

I have broken into prime numbers.

3 is common, so b must be 3.

a = 5
c = 8

we can find the area now? where I am going wrong? according to me statement A is sufficient.
_________________

Like my post Send me a Kudos :) It is a Good manner.
My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html

Kudos [?]: 649 [0], given: 298

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42597

Kudos [?]: 135562 [0], given: 12699

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

Show Tags

New post 06 Jul 2015, 06:45
honchos wrote:
Bunuel wrote:
This question is from Official Guide and Official Answer is C.

About rectangular solid:
Image

In a rectangular solid, all angles are right angles, and opposite faces are equal, so rectangular solid can have maximum 3 different areas of its faces, on the diagram: yellow, green and red faces can have different areas. I say at max, as for example rectangular solid can be a cube and in this case it'll have all faces equal, also it's possible to have only 2 different areas of the faces, for example when the base is square and the height does not equals to the side of this square.

Volume of rectangular solid is Volume=Length*Height*Depth.

BACK TO THE ORIGINAL QUESTION:

What is the volume of a certain rectangular solid?

(1) Two adjacent faces of the solid have areas 15 and 24, respectively --> let the two adjacent faces be blue and yellow faces on the diagram --> \(blue=d*h=15\) and \(yellow=l*h=24\) --> we have 2 equations with 3 unknowns, not sufficient to calculate the value of each or the product of the unknowns (\(V=l*h*d\)).

To elaborate more:
If \(blue=d*h=15*1=15\) and \(yellow=l*h=24*1=24\) then \(V=l*h*d=24*1*15=360\);
If \(blue=d*h=5*3=15\) and \(yellow=l*h=8*3=24\) then \(V=l*h*d=8*3*5=90\).

Two different answer, hence not sufficient.

(2) Each of two opposite faces of the solid has area 40 --> just gives the areas of two opposite faces, so clearly insufficient.

(1)+(2) From (1): \(blue=d*h=15\), \(yellow=l*h=24\) and from (2) each of two opposite faces of the solid has area 40, so it must be the red one: \(red=d*l=40\) --> here we have 3 distinct linear equations with 3 unknowns hence we can find the values of each and thus can calculate \(V=l*h*d\). Sufficient.

To show how it can be done: multiply these 3 equations --> \(l^2*h^2*d^2=(l*h*d)^2=15*24*40=24^2*5^2\) --> \(V=l*h*d=24*5=120\).

Answer: C.

Hope it helps.


Where am I wrong-

a x b = 15
b x c = 24

a x b = 5 x 3
b x c = 3 x 2 x 2 x 2

I have broken into prime numbers.

3 is common, so b must be 3.

a = 5
c = 8

we can find the area now? where I am going wrong? according to me statement A is sufficient.


Frankly, I don't know what to add after 3 pages of discussion...

In the very post you are quoting are TWO examples, which give TWO different answers.
_________________

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 [?]: 135562 [0], given: 12699

Director
Director
User avatar
Joined: 10 Mar 2013
Posts: 589

Kudos [?]: 492 [0], given: 200

Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
GMAT ToolKit User
What is the volume of a certain rectangular solid? [#permalink]

Show Tags

New post 09 Jul 2015, 12:17
Please correct me if I' wrong, it's just my observation:
I won't discuss why St1 and St2 alonne are not sufficient, as Bunuel have aleady shown some examples with yes/no outcome.
But St1+St2) I a solid rectangular all 3 different faces CAN NOT be adjacent on one side - so "1 feet" can not be can not be shae by all faces, hence --> let's find a common factors for all the areas --> 15=3*5 , 40=8*5, 24=3*8 as you see we have the numbe 3,5 and 8 just multiply them 3*5*8=120.

Here's is impotant to notice, if by St1) we haf some options 15*1 or 5*3 when both statements combined, we can eliminate 15*1, it can be only 5*3........... hope that was somehow clear...
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

Share some Kudos, if my posts help you. Thank you !

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660

Kudos [?]: 492 [0], given: 200

Manager
Manager
avatar
Joined: 29 Jul 2015
Posts: 159

Kudos [?]: 196 [0], given: 59

GMAT ToolKit User
What is the volume of a certain rectangular solid? [#permalink]

Show Tags

New post 28 Sep 2015, 16:48
Bunuel wrote:
This question is from Official Guide and Official Answer is C.

About rectangular solid:

Image

In a rectangular solid, all angles are right angles, and opposite faces are equal, so rectangular solid can have maximum 3 different areas of its faces, on the diagram: yellow, green and red faces can have different areas. I say at max, as for example rectangular solid can be a cube and in this case it'll have all faces equal, also it's possible to have only 2 different areas of the faces, for example when the base is square and the height does not equals to the side of this square.

Volume of rectangular solid is Volume=Length*Height*Depth.

BACK TO THE ORIGINAL QUESTION:

What is the volume of a certain rectangular solid?

(1) Two adjacent faces of the solid have areas 15 and 24, respectively --> let the two adjacent faces be blue and yellow faces on the diagram --> \(blue=d*h=15\) and \(yellow=l*h=24\) --> we have 2 equations with 3 unknowns, not sufficient to calculate the value of each or the product of the unknowns (\(V=l*h*d\)).

To elaborate more:
If \(blue=d*h=15*1=15\) and \(yellow=l*h=24*1=24\) then \(V=l*h*d=24*1*15=360\);
If \(blue=d*h=5*3=15\) and \(yellow=l*h=8*3=24\) then \(V=l*h*d=8*3*5=90\).

Two different answer, hence not sufficient.

(2) Each of two opposite faces of the solid has area 40 --> just gives the areas of two opposite faces, so clearly insufficient.

(1)+(2) From (1): \(blue=d*h=15\), \(yellow=l*h=24\) and from (2) each of two opposite faces of the solid has area 40, so it must be the red one: \(red=d*l=40\) --> here we have 3 distinct linear equations with 3 unknowns hence we can find the values of each and thus can calculate \(V=l*h*d\). Sufficient.

To show how it can be done: multiply these 3 equations --> \(l^2*h^2*d^2=(l*h*d)^2=15*24*40=24^2*5^2\) --> \(V=l*h*d=24*5=120\).

Answer: C.

Hope it helps.

[Reveal] Spoiler:
Attachment:
800px-Cuboid.png


Sorry to bring this topic up again. I went through the discussion of this question but I'm still not satisfied with the explanation of statement 2.
Statement 2 seems a bit too ambiguous to me.
If we consider statement 1 to analyse statement 2, then the 2 opposite faces are the faces which were not included in statement 1.
If this is true, then solution above is perfect. Although it doesn't seem logical to me to consider statement 1 for analysing statement 2.
Let us not consider statement 1 at all and just focus on statement 2.
It says "each of the two opposite faces" has area 40.
There are three pairs of opposite faces. Red face and it's opposite face, blue face and it's opposite face and, yellow face and it's opposite face.
Question says each of the two opposite faces has area 40. So, each of the 6 faces must have area = 40.
Let l,b and h be the length, breadth and height respectively. Then, lb=40, bh = 40 and lh = 40.
Now,
\(lb*bh*lh = l^2b^2h^2 = 40*40*40\)
or \(l^2b^2h^2=64000\)
or \(lbh = 80\sqrt{10}\)
SUFFICIENT

Why is my solution wrong ?
Why do we have to consider constraints in statement 1 to analyse statement 2 individually ?

Kudos [?]: 196 [0], given: 59

Current Student
avatar
B
Joined: 20 Mar 2014
Posts: 2672

Kudos [?]: 1789 [0], given: 797

Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
Re: What is the volume of a certain rectangular solid? [#permalink]

Show Tags

New post 28 Sep 2015, 18:25
kunal555 wrote:
Bunuel wrote:
This question is from Official Guide and Official Answer is C.

About rectangular solid:

Image

In a rectangular solid, all angles are right angles, and opposite faces are equal, so rectangular solid can have maximum 3 different areas of its faces, on the diagram: yellow, green and red faces can have different areas. I say at max, as for example rectangular solid can be a cube and in this case it'll have all faces equal, also it's possible to have only 2 different areas of the faces, for example when the base is square and the height does not equals to the side of this square.

Volume of rectangular solid is Volume=Length*Height*Depth.

BACK TO THE ORIGINAL QUESTION:

What is the volume of a certain rectangular solid?

(1) Two adjacent faces of the solid have areas 15 and 24, respectively --> let the two adjacent faces be blue and yellow faces on the diagram --> \(blue=d*h=15\) and \(yellow=l*h=24\) --> we have 2 equations with 3 unknowns, not sufficient to calculate the value of each or the product of the unknowns (\(V=l*h*d\)).

To elaborate more:
If \(blue=d*h=15*1=15\) and \(yellow=l*h=24*1=24\) then \(V=l*h*d=24*1*15=360\);
If \(blue=d*h=5*3=15\) and \(yellow=l*h=8*3=24\) then \(V=l*h*d=8*3*5=90\).

Two different answer, hence not sufficient.

(2) Each of two opposite faces of the solid has area 40 --> just gives the areas of two opposite faces, so clearly insufficient.

(1)+(2) From (1): \(blue=d*h=15\), \(yellow=l*h=24\) and from (2) each of two opposite faces of the solid has area 40, so it must be the red one: \(red=d*l=40\) --> here we have 3 distinct linear equations with 3 unknowns hence we can find the values of each and thus can calculate \(V=l*h*d\). Sufficient.

To show how it can be done: multiply these 3 equations --> \(l^2*h^2*d^2=(l*h*d)^2=15*24*40=24^2*5^2\) --> \(V=l*h*d=24*5=120\).

Answer: C.

Hope it helps.

[Reveal] Spoiler:
Attachment:
800px-Cuboid.png


Sorry to bring this topic up again. I went through the discussion of this question but I'm still not satisfied with the explanation of statement 2.
Statement 2 seems a bit too ambiguous to me.
If we consider statement 1 to analyse statement 2, then the 2 opposite faces are the faces which were not included in statement 1.
If this is true, then solution above is perfect. Although it doesn't seem logical to me to consider statement 1 for analysing statement 2.
Let us not consider statement 1 at all and just focus on statement 2.
It says "each of the two opposite faces" has area 40.
There are three pairs of opposite faces. Red face and it's opposite face, blue face and it's opposite face and, yellow face and it's opposite face.
Question says each of the two opposite faces has area 40. So, each of the 6 faces must have area = 40.
Let l,b and h be the length, breadth and height respectively. Then, lb=40, bh = 40 and lh = 40.
Now,
\(lb*bh*lh = l^2b^2h^2 = 40*40*40\)
or \(l^2b^2h^2=64000\)
or \(lbh = 80\sqrt{10}\)
SUFFICIENT

Why is my solution wrong ?
Why do we have to consider constraints in statement 1 to analyse statement 2 individually ?



Good question but what you are assuming is that every pair of opposite sides have area 40. Statement 2 talks about just 1 pair of opposite sides. Bunuel covers this at what-is-the-volume-of-a-certain-rectangular-solid-90748.html#p772623

The statement couldve done better to remove this ambiguity but as it is an official question, it is not my place to doubt the wording of the question.

Hope this helps.

Kudos [?]: 1789 [0], given: 797

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42597

Kudos [?]: 135562 [0], given: 12699

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

Show Tags

New post 22 Jan 2016, 08:59

Kudos [?]: 135562 [0], given: 12699

Expert Post
Top Contributor
1 KUDOS received
SVP
SVP
User avatar
G
Joined: 11 Sep 2015
Posts: 1908

Kudos [?]: 2747 [1], given: 364

Location: Canada
Re: What is the volume of a certain rectangular solid? [#permalink]

Show Tags

New post 30 Jul 2016, 06:46
1
This post received
KUDOS
Expert's post
Top Contributor
amod243 wrote:
What is the volume of a certain rectangular solid?

(1) Two adjacent faces of the solid have areas 15 and 24, respectively.
(2) Each of two opposite faces of the solid has area 40.


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

Aside: A rectangular solid is a box

Statement 1: Two adjacent faces of the solid have areas 15 and 24, respectively.
There are several different rectangular solids that meet this condition. Here are two:
Case a: the dimensions are 1x15x24, in which case the volume is 360
Case b: the dimensions are 3x5x8, in which case the volume is 120
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Each of two opposite faces of the solid has area 40.
So, there are two opposite faces that each have area 40.
Definitely NOT SUFFICIENT

Statements 1 and 2 combined:
So, we know the area of each face (noted in blue on the diagram below).
Let's let x equal the length of one side.
Image


Since the area of each face = (length)(width), we can express the other two dimensions in terms of x.
Image

From here, we'll focus on the face that has area 40.
This face has dimensions (15/x) by (24/x)
Since the area is 40, we know that (15/x)(24/x) = 40
Expand: 360/(x^2) = 40
Simplify: 360 = 40x^2
Simplify: 9 = x^2
Solve: x = 3 or -3
Since the side lengths must be positive, we can be certain that x = 3

When we plug x=3 into the other two dimensions, we get 15/3 and 24/3
So, the 3 dimensions are 3, 5, and 8, which means the volume of the rectangular solid must be 120.
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer =
[Reveal] Spoiler:
C


RELATED VIDEOS



_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Kudos [?]: 2747 [1], given: 364

Intern
Intern
avatar
Joined: 23 Nov 2016
Posts: 4

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

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

Show Tags

New post 23 Dec 2016, 10:31
tingle15 wrote:
Yes, the second statement is confusing but the catch is in the question itself. The question states a rectangular solid. All the faces cannot have an area of 40 if the solid is rectangular.

Why not? A cube falls under the definition of ''rectangular''.

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

Manager
Manager
User avatar
S
Joined: 24 Dec 2016
Posts: 74

Kudos [?]: 13 [0], given: 83

Location: India
Concentration: Finance, General Management
WE: Information Technology (Computer Software)
Re: What is the volume of a certain rectangular solid? [#permalink]

Show Tags

New post 17 May 2017, 22:55
Bunuel wrote:
This question is from Official Guide and Official Answer is C.

About rectangular solid:

Image

In a rectangular solid, all angles are right angles, and opposite faces are equal, so rectangular solid can have maximum 3 different areas of its faces, on the diagram: yellow, green and red faces can have different areas. I say at max, as for example rectangular solid can be a cube and in this case it'll have all faces equal, also it's possible to have only 2 different areas of the faces, for example when the base is square and the height does not equals to the side of this square.

Volume of rectangular solid is Volume=Length*Height*Depth.

BACK TO THE ORIGINAL QUESTION:

What is the volume of a certain rectangular solid?

(1) Two adjacent faces of the solid have areas 15 and 24, respectively --> let the two adjacent faces be blue and yellow faces on the diagram --> \(blue=d*h=15\) and \(yellow=l*h=24\) --> we have 2 equations with 3 unknowns, not sufficient to calculate the value of each or the product of the unknowns (\(V=l*h*d\)).

To elaborate more:
If \(blue=d*h=15*1=15\) and \(yellow=l*h=24*1=24\) then \(V=l*h*d=24*1*15=360\);
If \(blue=d*h=5*3=15\) and \(yellow=l*h=8*3=24\) then \(V=l*h*d=8*3*5=90\).

Two different answer, hence not sufficient.

(2) Each of two opposite faces of the solid has area 40 --> just gives the areas of two opposite faces, so clearly insufficient.

(1)+(2) From (1): \(blue=d*h=15\), \(yellow=l*h=24\) and from (2) each of two opposite faces of the solid has area 40, so it must be the red one: \(red=d*l=40\) --> here we have 3 distinct linear equations with 3 unknowns hence we can find the values of each and thus can calculate \(V=l*h*d\). Sufficient.

To show how it can be done: multiply these 3 equations --> \(l^2*h^2*d^2=(l*h*d)^2=15*24*40=24^2*5^2\) --> \(V=l*h*d=24*5=120\).

Answer: C.

Hope it helps.

[Reveal] Spoiler:
Attachment:
800px-Cuboid.png



Hi Bunuel,

Although I understand your solution, I'm still a little confused with the 2nd statement. On the GMAT, doesn't each mean All ? I mean, if a random statement is worded as : Each of the students got 5 dollars, doesn't it mean all the students got 5 dollars ? Also, isn't square just a special kind of a rectangle ?

Please help. Thanks in advance!

Kudos [?]: 13 [0], given: 83

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42597

Kudos [?]: 135562 [0], given: 12699

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

Show Tags

New post 17 May 2017, 23:09
Shruti0805 wrote:
Bunuel wrote:
This question is from Official Guide and Official Answer is C.

About rectangular solid:

Image

In a rectangular solid, all angles are right angles, and opposite faces are equal, so rectangular solid can have maximum 3 different areas of its faces, on the diagram: yellow, green and red faces can have different areas. I say at max, as for example rectangular solid can be a cube and in this case it'll have all faces equal, also it's possible to have only 2 different areas of the faces, for example when the base is square and the height does not equals to the side of this square.

Volume of rectangular solid is Volume=Length*Height*Depth.

BACK TO THE ORIGINAL QUESTION:

What is the volume of a certain rectangular solid?

(1) Two adjacent faces of the solid have areas 15 and 24, respectively --> let the two adjacent faces be blue and yellow faces on the diagram --> \(blue=d*h=15\) and \(yellow=l*h=24\) --> we have 2 equations with 3 unknowns, not sufficient to calculate the value of each or the product of the unknowns (\(V=l*h*d\)).

To elaborate more:
If \(blue=d*h=15*1=15\) and \(yellow=l*h=24*1=24\) then \(V=l*h*d=24*1*15=360\);
If \(blue=d*h=5*3=15\) and \(yellow=l*h=8*3=24\) then \(V=l*h*d=8*3*5=90\).

Two different answer, hence not sufficient.

(2) Each of two opposite faces of the solid has area 40 --> just gives the areas of two opposite faces, so clearly insufficient.

(1)+(2) From (1): \(blue=d*h=15\), \(yellow=l*h=24\) and from (2) each of two opposite faces of the solid has area 40, so it must be the red one: \(red=d*l=40\) --> here we have 3 distinct linear equations with 3 unknowns hence we can find the values of each and thus can calculate \(V=l*h*d\). Sufficient.

To show how it can be done: multiply these 3 equations --> \(l^2*h^2*d^2=(l*h*d)^2=15*24*40=24^2*5^2\) --> \(V=l*h*d=24*5=120\).

Answer: C.

Hope it helps.

[Reveal] Spoiler:
Attachment:
800px-Cuboid.png



Hi Bunuel,

Although I understand your solution, I'm still a little confused with the 2nd statement. On the GMAT, doesn't each mean All ? I mean, if a random statement is worded as : Each of the students got 5 dollars, doesn't it mean all the students got 5 dollars ? Also, isn't square just a special kind of a rectangle ?

Please help. Thanks in advance!


Pay attention to the highlighted part:
"(2) Each of TWO opposite faces of the solid has area 40" means that one pair of opposite faces (two opposite faces) has an area 40.

As for your other question: yes, a square is a special type of a rectangle.

I suggest you to go through the previous pages of discussion where you can find several different ways of solving the question as well as answers to many questions and doubts.

Hope it 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 [?]: 135562 [0], given: 12699

Intern
Intern
avatar
B
Joined: 09 Jan 2017
Posts: 6

Kudos [?]: [0], given: 3

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

Show Tags

New post 28 Jul 2017, 07:04
Total different faces of cubes is 3

Statmnt 1 area of 2 faces given

Statmnt 2 area of 1 face given

So answer is C

Kudos [?]: [0], given: 3

Intern
Intern
avatar
B
Affiliations: Xado Technology Inc., Shomal University
Joined: 22 May 2014
Posts: 31

Kudos [?]: 6 [0], given: 13

Location: Iran (Islamic Republic of)
Concentration: Marketing, Strategy
Schools: HEC Montreal '20
GPA: 3
WE: Marketing (Consumer Products)
Premium Member
Re: What is the volume of a certain rectangular solid? [#permalink]

Show Tags

New post 30 Aug 2017, 05:56
Bunuel
please read this carefully
The second statement is ambiguous as each of the two opposite faces means any two opposite faces and note that rectangular solid is also a cube solid.
this question is ambiguous and hence is not correct basically.

Kudos [?]: 6 [0], given: 13

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42597

Kudos [?]: 135562 [0], given: 12699

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

Show Tags

New post 30 Aug 2017, 06:02
parham wrote:
Bunuel
please read this carefully
The second statement is ambiguous as each of the two opposite faces means any two opposite faces and note that rectangular solid is also a cube solid.
this question is ambiguous and hence is not correct basically.


I understand what you mean but don't agree. I tried to explain this question several times on previous 3 pages, so I've already said what I had to say. This is an Official Guide question though, so you are not agreeing with them...
_________________

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 [?]: 135562 [0], given: 12699

Re: What is the volume of a certain rectangular solid?   [#permalink] 30 Aug 2017, 06:02

Go to page   Previous    1   2   3   [ 56 posts ] 

Display posts from previous: Sort by

What is the volume of a certain rectangular solid?

  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®.