It is currently 21 Jan 2018, 10:56

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A rectangular solid is changed such that the width and lengt

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

### Hide Tags

Senior Manager
Joined: 13 May 2013
Posts: 456

Kudos [?]: 211 [1], given: 134

A rectangular solid is changed such that the width and lengt [#permalink]

### Show Tags

26 May 2013, 11:21
1
This post received
KUDOS
11
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

75% (02:48) correct 25% (03:22) wrong based on 304 sessions

### HideShow timer Statistics

A rectangular solid is changed such that the width and length are increased by 1 inch apiece and the height is decreased by 9 inches. Despite these changes, the new rectangular solid has the same volume as the original rectangular solid. If the width and length of the original rectangular solid are equal and the height of the new rectangular solid is 4 times the width of the original rectangular solid, what is the volume of the rectangular solid?

(A) 18
(B) 50
(C) 100
(D) 200
(E) 400

[Reveal] Spoiler:
Ok, so here is what I know:

~Old Volume = New Volume

~(L+1)(W+1)(H-9) = (L*W*H)

~(H-9) = 4w

~width, length of original rectangular are equal

So, from that I get:

(L+1)(W+1)(4w)=(W*W*H)

But in the book, the equation differs from mine in two ways.

For starters, mine is L+1)(W+1)(4w)=(W*W*H) while theirs is (W+1)(W+1)(4w)=(W*W*H)

Also, because (H-9)=4w, they derive H=4w+9 then plug it in so (W+1)(W+1)(4w)=(W*W*4w+9)

But here is my (apparently incorrect) reasoning.

L=W in the old rectangle, so why plug "W" into the new rectangle volume?

if (H-9)=4w, then why do I plug 4w into the new rectangle volume and h=4w-9 into the old rectangle formula? It seems unnecessary to have to plug in 4w for (h-9) then derive h=4w-9 and plug in on the other side.

What's the reasoning!

Thanks!
[Reveal] Spoiler: OA

Last edited by Bunuel on 27 May 2013, 00:49, edited 1 time in total.
Edited the question and moved to PS forum.

Kudos [?]: 211 [1], given: 134

VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1121

Kudos [?]: 2442 [1], given: 219

Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Re: A rectangular solid is changed such that [#permalink]

### Show Tags

26 May 2013, 11:36
1
This post received
KUDOS
Ok, so here is what I know:
~Old Volume = New Volume
~(L+1)(W+1)(H-9) = (L*W*H)
~(H-9) = 4w
~width, length of original rectangular are equal
So, from that I get:
(L+1)(W+1)(4w)=(W*W*H)
But in the book, the equation differs from mine in two ways.
For starters, mine is L+1)(W+1)(4w)=(W*W*H) while theirs is (W+1)(W+1)(4w)=(W*W*H)

If L=W then substitute L with W in the equation and obtain
$$(W+1)(W+1)(4W)=(W*W*H)$$- the one in the book

But here is my (apparently incorrect) reasoning.
L=W in the old rectangle, so why plug "W" into the new rectangle volume?
if (H-9)=4w, then why do I plug 4w into the new rectangle volume and h=4w-9 into the old rectangle formula? It seems unnecessary to have to plug in 4w for (h-9) then derive h=4w-9 and plug in on the other side.

You have
$$(W+1)(W+1)(H-9)=(W*W*H)$$ and in order to solve it you need to express H in terms of W, so from $$H-9=4w$$ you get $$H=4W+9$$ and $$H-9=4W$$
$$(W+1)(W+1)(4W)=(W*W*(4W+9))$$

The above equation is in W and H, so have to express all the variables in one term (W) in order to solve it. You have to plug in those values at both sides in order to solve the equation.

Hope it's clear, let me know
_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

Kudos [?]: 2442 [1], given: 219

Manager
Joined: 07 May 2013
Posts: 104

Kudos [?]: 32 [0], given: 1

Re: A rectangular solid is changed such that the width and lengt [#permalink]

### Show Tags

21 Nov 2013, 16:59
Zarrolou, I followed your approach and I got the final quadratic equation as $$w^2-4w=0$$---->w=4. Then we get h=4w+9=25. Also l=w=4. Volume is 4*4*25=400. Your approach is correct and I don't think there is any other possibility.

Kudos [?]: 32 [0], given: 1

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7869

Kudos [?]: 18503 [3], given: 237

Location: Pune, India
Re: A rectangular solid is changed such that the width and lengt [#permalink]

### Show Tags

21 Nov 2013, 21:03
3
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
WholeLottaLove wrote:
A rectangular solid is changed such that the width and length are increased by 1 inch apiece and the height is decreased by 9 inches. Despite these changes, the new rectangular solid has the same volume as the original rectangular solid. If the width and length of the original rectangular solid are equal and the height of the new rectangular solid is 4 times the width of the original rectangular solid, what is the volume of the rectangular solid?

(A) 18
(B) 50
(C) 100
(D) 200
(E) 400

Let's try this question using only the change in volume. Since original volume = final volume, Decrease in volume = Increase in volume

You decrease volume by chopping off 9 inches of the height. Decrease = 9*w*l
You increase the volume now by adding an inch to the width and length. The height remains h-9.
Increase = 1*(l+1)*(h-9) + 1*w*(h-9) = (h-9)*(l+w+1) (make a rectangle and increase its width and length by 1 to see how area changes. This tells you how volume changes by just considering the height as well)

So 9*w*l = (h-9)*(l+w+1)
Given that (h-9) = 4w and l = w, substitute both in the equation to get
9*w*w = 4w*(2w+1)
Cancel w from both sides and get w = 4 = l
h-9 = 4w so h = 16+9 = 25

Volume = wlh = 4*4*25 = 400
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Kudos [?]: 18503 [3], given: 237 Manager Joined: 14 Nov 2011 Posts: 140 Kudos [?]: 22 [0], given: 103 Location: United States Concentration: General Management, Entrepreneurship GPA: 3.61 WE: Consulting (Manufacturing) Re: A rectangular solid is changed such that the width and lengt [#permalink] ### Show Tags 11 Dec 2013, 19:04 VeritasPrepKarishma wrote: WholeLottaLove wrote: A rectangular solid is changed such that the width and length are increased by 1 inch apiece and the height is decreased by 9 inches. Despite these changes, the new rectangular solid has the same volume as the original rectangular solid. If the width and length of the original rectangular solid are equal and the height of the new rectangular solid is 4 times the width of the original rectangular solid, what is the volume of the rectangular solid? (A) 18 (B) 50 (C) 100 (D) 200 (E) 400 Let's try this question using only the change in volume. Since original volume = final volume, Decrease in volume = Increase in volume You decrease volume by chopping off 9 inches of the height. Decrease = 9*w*l You increase the volume now by adding an inch to the width and length. The height remains h-9. Increase = 1*(l+1)*(h-9) + 1*w*(h-9) = (h-9)*(l+w+1) (make a rectangle and increase its width and length by 1 to see how area changes. This tells you how volume changes by just considering the height as well) So 9*w*l = (h-9)*(l+w+1) Given that (h-9) = 4w and l = w, substitute both in the equation to get 9*w*w = 4w*(2w+1) Cancel w from both sides and get w = 4 = l h-9 = 4w so h = 16+9 = 25 Volume = wlh = 4*4*25 = 400 Hi Karishma/Bunnel, Any more such questions? Kudos [?]: 22 [0], given: 103 Math Expert Joined: 02 Sep 2009 Posts: 43348 Kudos [?]: 139696 [0], given: 12794 Re: A rectangular solid is changed such that the width and lengt [#permalink] ### Show Tags 12 Dec 2013, 01:36 cumulonimbus wrote: VeritasPrepKarishma wrote: WholeLottaLove wrote: A rectangular solid is changed such that the width and length are increased by 1 inch apiece and the height is decreased by 9 inches. Despite these changes, the new rectangular solid has the same volume as the original rectangular solid. If the width and length of the original rectangular solid are equal and the height of the new rectangular solid is 4 times the width of the original rectangular solid, what is the volume of the rectangular solid? (A) 18 (B) 50 (C) 100 (D) 200 (E) 400 Let's try this question using only the change in volume. Since original volume = final volume, Decrease in volume = Increase in volume You decrease volume by chopping off 9 inches of the height. Decrease = 9*w*l You increase the volume now by adding an inch to the width and length. The height remains h-9. Increase = 1*(l+1)*(h-9) + 1*w*(h-9) = (h-9)*(l+w+1) (make a rectangle and increase its width and length by 1 to see how area changes. This tells you how volume changes by just considering the height as well) So 9*w*l = (h-9)*(l+w+1) Given that (h-9) = 4w and l = w, substitute both in the equation to get 9*w*w = 4w*(2w+1) Cancel w from both sides and get w = 4 = l h-9 = 4w so h = 16+9 = 25 Volume = wlh = 4*4*25 = 400 Hi Karishma/Bunnel, Any more such questions? Somewhat similar questions: a-closed-aluminum-rectangular-box-has-inner-dimensions-x-141049.html the-measurements-obtained-for-the-interior-dimensions-of-a-160295.html m01-70731.html a-cylindrical-tank-of-radius-r-and-height-h-must-be-redesign-122366.html Hope this helps. _________________ Kudos [?]: 139696 [0], given: 12794 Manager Joined: 07 Apr 2014 Posts: 135 Kudos [?]: 33 [0], given: 81 Re: A rectangular solid is changed such that the width and lengt [#permalink] ### Show Tags 21 Aug 2014, 22:13 Its hard to understand the increase & decrease thing in provided explanation. Please help me .. Kudos [?]: 33 [0], given: 81 Manager Joined: 13 Aug 2014 Posts: 86 Kudos [?]: 22 [0], given: 2 Location: India GRE 1: 322 Q163 V159 GPA: 3.67 WE: Marketing (Consulting) Re: A rectangular solid is changed such that the width and lengt [#permalink] ### Show Tags 21 Aug 2014, 23:54 Here's how i solved it Rectangle 1: length = l, width = w and height = h. Now l=w. so Volume V1 = l(squared)h Rectangle 2: length = l+1, width = w+1 or l+1 and height = h-9. So, volume V2 = (l+1)squared(h-9) Now new height = 4 times previous width => h-9 = 4w or (h-9) = 4l => h = 4l + 9 Substituting the value of h:- Volume V1 = l(squared)(4l+9) = 4l(cube) + 9 l(squared) and Volume V2 = (l+1)squared(4l) = 4lcube + 8lsquared = 4l Equating V1 and V2 we get: l = 0, 4. since length isnt 0, l=4 => w=4 and h = 16+9 = 25 therefore volume V = lwh = 4x4x25 = 400 Answer E _________________ All the Best __________________________________________________________________________________________________________ http://www.InterviewBay.com Application Reviews & Mock Interviews by Alumni of Your Target B-School Check out our free e-book How To Get Into A Top Business School here http://www.interviewbay.com/mba/how-to-get-into-a-top-business-school-ebook.php Check out our new free e-book Top Business Schools For Different Concentrations here http://www.interviewbay.com/ebooks.php Kudos [?]: 22 [0], given: 2 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7869 Kudos [?]: 18503 [1], given: 237 Location: Pune, India Re: A rectangular solid is changed such that the width and lengt [#permalink] ### Show Tags 24 Aug 2014, 21:30 1 This post received KUDOS Expert's post luckyme17187 wrote: Its hard to understand the increase & decrease thing in provided explanation. Please help me .. The increase/decrease method has fewer calculations and steps but its certainly a little trickier... Try to make diagrams at each step to understand what is going on. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Kudos [?]: 18503 [1], given: 237

Manager
Status: How easy it is?
Joined: 09 Nov 2012
Posts: 119

Kudos [?]: 110 [0], given: 174

Location: India
Concentration: Operations, General Management
GMAT 1: 650 Q50 V27
GMAT 2: 710 Q49 V37
GPA: 3.5
WE: Operations (Other)
Re: A rectangular solid is changed such that the width and lengt [#permalink]

### Show Tags

01 Oct 2014, 05:35
Hi VeritasPrepKarishma,
I tried to solve the question by increase=decrease method. I took increase first and equated the same to decrease keeping the length and breadth same. Equation was:
1*b*h + l*1*h = (l+1)(b+1)*9 -> Keeping the length and breadth same. As l=b,
-> 2lh = (l+1)² *9 ; h-9= 4l -> h = 9+4l
-> 2l*(4l+9) = (l²+2l+1)9
-> 8l²+18l = 9l²+18l+9
As you can see , there is not definite solution with this equation. Can you please point out the flaw in the method?

Kudos [?]: 110 [0], given: 174

Intern
Joined: 03 Oct 2011
Posts: 17

Kudos [?]: 10 [0], given: 4

Re: A rectangular solid is changed such that the width and lengt [#permalink]

### Show Tags

01 Oct 2014, 23:33
VeritasPrepKarishma wrote:
WholeLottaLove wrote:
A rectangular solid is changed such that the width and length are increased by 1 inch apiece and the height is decreased by 9 inches. Despite these changes, the new rectangular solid has the same volume as the original rectangular solid. If the width and length of the original rectangular solid are equal and the height of the new rectangular solid is 4 times the width of the original rectangular solid, what is the volume of the rectangular solid?

(A) 18
(B) 50
(C) 100
(D) 200
(E) 400

Let's try this question using only the change in volume. Since original volume = final volume, Decrease in volume = Increase in volume

You decrease volume by chopping off 9 inches of the height. Decrease = 9*w*l
You increase the volume now by adding an inch to the width and length. The height remains h-9.
Increase = 1*(l+1)*(h-9) + 1*w*(h-9) = (h-9)*(l+w+1) (make a rectangle and increase its width and length by 1 to see how area changes. This tells you how volume changes by just considering the height as well)

So 9*w*l = (h-9)*(l+w+1)
Given that (h-9) = 4w and l = w, substitute both in the equation to get
9*w*w = 4w*(2w+1)
Cancel w from both sides and get w = 4 = l
h-9 = 4w so h = 16+9 = 25

Volume = wlh = 4*4*25 = 400

Shouldn't Increase = 1*(l+1)*(h-9) + 1*w*(h-9) = (h-9)*(l+w+1) be Increase = 1*(l+1)*(h-9) + 1*(w+1)*(h-9) = (h-9)*(l+w+2) since the width increased by 1 too?

Kudos [?]: 10 [0], given: 4

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1844

Kudos [?]: 2866 [2], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: A rectangular solid is changed such that the width and lengt [#permalink]

### Show Tags

02 Oct 2014, 00:34
2
This post received
KUDOS
1
This post was
BOOKMARKED
Width .............. Length .................. Height

a ........................ a .......................... b (Original dimensions; Length = Width)

a+1 ................... a+1 ....................... b-9 (Post changes)

Given that (b-9) = 4a

b = 4a+9 .............. (1)

Original Volume = Post change Volume

$$a^2* b = (a+1)^2 * (b-9)$$

Placing value of b from (1) in the above equation

$$a^2* (4a+9) = (a+1)^2 * (4a+9-9)$$

a = 4

Volume = 4 * 4 * 25 = 400

Answer = E
_________________

Kindly press "+1 Kudos" to appreciate

Kudos [?]: 2866 [2], given: 193

Verbal Forum Moderator
Joined: 15 Apr 2013
Posts: 195

Kudos [?]: 926 [0], given: 30

Location: India
Concentration: General Management, Marketing
GMAT Date: 11-23-2015
GPA: 3.6
WE: Science (Other)
Re: A rectangular solid is changed such that the width and lengt [#permalink]

### Show Tags

07 Jun 2015, 04:33
Hello,

I really liked the increase/decrease method.

Could you please suggest how you derived this equation:

Increase = 1*(l+1)*(h-9) + 1*w*(h-9) = (h-9)*(l+w+1)

thank you.

Kudos [?]: 926 [0], given: 30

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7869

Kudos [?]: 18503 [3], given: 237

Location: Pune, India
Re: A rectangular solid is changed such that the width and lengt [#permalink]

### Show Tags

08 Jun 2015, 06:43
3
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
vikasbansal227 wrote:
Hello,

I really liked the increase/decrease method.

Could you please suggest how you derived this equation:

Increase = 1*(l+1)*(h-9) + 1*w*(h-9) = (h-9)*(l+w+1)

thank you.

Attachment:

InceaseDecrease.jpg [ 470.15 KiB | Viewed 4813 times ]

So in step 1, you chop off a block to decrease the area. The area of that block is l*w*9

Then in step 2, you add a block to increase the length. The area of this block is 1*w*(h-9)

Then you add another block to increase the width. The area of this block is 1*(l + 1)*(h - 9)

The decrease = Both increases
l*w*9 = 1*w*(h-9) + 1*(l+1)*(h - 9)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 18503 [3], given: 237

Non-Human User
Joined: 09 Sep 2013
Posts: 14201

Kudos [?]: 291 [0], given: 0

Re: A rectangular solid is changed such that the width and lengt [#permalink]

### Show Tags

30 Aug 2016, 05:41
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.
_________________

Kudos [?]: 291 [0], given: 0

Non-Human User
Joined: 09 Sep 2013
Posts: 14201

Kudos [?]: 291 [0], given: 0

Re: A rectangular solid is changed such that the width and lengt [#permalink]

### Show Tags

15 Sep 2017, 21:46
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.
_________________

Kudos [?]: 291 [0], given: 0

Re: A rectangular solid is changed such that the width and lengt   [#permalink] 15 Sep 2017, 21:46
Display posts from previous: Sort by

# A rectangular solid is changed such that the width and lengt

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

 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®.