Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 24 May 2017, 02:36

### 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

# Events & Promotions

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

# A square wooden plaque has a square brass inlay in the

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 38850
Followers: 7721

Kudos [?]: 105957 [0], given: 11602

A square wooden plaque has a square brass inlay in the [#permalink]

### Show Tags

15 Jan 2010, 04:00
Expert's post
68
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

43% (02:44) correct 57% (02:22) wrong based on 961 sessions

### HideShow timer Statistics

The Official Guide For GMAT® Quantitative Review, 2ND Edition

A square wooden plaque has a square brass inlay in the center, leaving a wooden strip of uniform width around the brass square. If the ratio of the brass area to the wooden area is 25 to 39, which of the following could be the width, in inches, of the wooden strip?

I. 1
II. 3
III. 4

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II , and III

Problem Solving
Question: 175
Category: Geometry Area
Page: 85
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!
[Reveal] Spoiler: OA

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 38850
Followers: 7721

Kudos [?]: 105957 [16] , given: 11602

Re: hard problem OG Quant 2nd edition [#permalink]

### Show Tags

15 Jan 2010, 04:26
16
KUDOS
Expert's post
3
This post was
BOOKMARKED
hrish88 wrote:
A square wooden plaque has a square brass inlay in the center ,leaving a wooden strip of uniform width around the brass square.if the ratio of the brass area to the wooden area is 25 to 39,which of the following could be the width ,in inches ,of the wooden strip.

I. 1
II. 3
III. 4

A.I only
B.II only
C.III only
D.I and III only
e.I,II and III

Why would ANY width of the strip be impossible?

_________________
Manager
Joined: 18 Jul 2009
Posts: 52
Followers: 3

Kudos [?]: 112 [0], given: 7

Re: hard problem OG Quant 2nd edition [#permalink]

### Show Tags

15 Jan 2010, 05:03
so doest it mean any width <= 39/4 is possible.

this is the 2nd last problem in OG.so i thought it would be difficult.
Math Expert
Joined: 02 Sep 2009
Posts: 38850
Followers: 7721

Kudos [?]: 105957 [13] , given: 11602

Re: hard problem OG Quant 2nd edition [#permalink]

### Show Tags

15 Jan 2010, 06:14
13
KUDOS
Expert's post
21
This post was
BOOKMARKED
hrish88 wrote:
so doest it mean any width <= 39/4 is possible.

this is the 2nd last problem in OG.so i thought it would be difficult.

No I mean ANY width is possible.

Let the the side of small square be $$x$$ and the big square $$y$$.

Given: $$\frac{x^2}{y^2-x^2}=\frac{25}{39}$$ --> $$\frac{x^2}{y^2}=\frac{25}{64}$$ --> $$\frac{x}{y}=\frac{5}{8}$$.

We are asked which value of $$\frac{y-x}{2}$$ is possible. $$\frac{y-\frac{5}{8}y}{2}=\frac{3}{16}y=?$$.

Well, expression $$\frac{3}{16}y$$ can take ANY value depending on $$y$$: 1, 3, 4, 444, 67556, 0,9, ... ANY. Basically we are given the ratios of the sides (5/8), half of their difference can be any value we choose, there won't be any "impossible" values at all.

Hope it's clear.
_________________
Manager
Joined: 25 Aug 2009
Posts: 169
Location: Streamwood IL
Schools: Kellogg(Evening),Booth (Evening)
WE 1: 5 Years
Followers: 12

Kudos [?]: 184 [0], given: 3

Re: hard problem OG Quant 2nd edition [#permalink]

### Show Tags

15 Jan 2010, 09:49
let the width of the wooden part = w
let the width of the brass part = b
given brass area/wooden area = 25/39
area of brass part = b^2
area of wooden part = (b+2w)^2 - b^2
Simplifying
64b^2=25(b+2w)^2
8b=5b+10w
b=10w/3

b has to be an integer or a terminating decimal. We can't have a width of 10/3 in real life (note the question doesn't ask for approximate width.) hence w has to be a multiple of 3.
_________________

Rock On

Math Expert
Joined: 02 Sep 2009
Posts: 38850
Followers: 7721

Kudos [?]: 105957 [4] , given: 11602

A square wooden plaque has a square brass inlay in the [#permalink]

### Show Tags

15 Jan 2010, 10:44
4
KUDOS
Expert's post
atish wrote:
let the width of the wooden part = w
let the width of the brass part = b
given brass area/wooden area = 25/39
area of brass part = b^2
area of wooden part = (b+2w)^2 - b^2
Simplifying
64b^2=25(b+2w)^2
8b=5b+10w
b=10w/3

b has to be an integer or a terminating decimal. We can't have a width of 10/3 in real life (note the question doesn't ask for approximate width.) hence w has to be a multiple of 3.

Are you saying that in real life everything has the integer or terminating decimal length? Why cannot we have repeated decimal or even irrational number as width of something?

Take the square with side 1, diagonal would be $$\sqrt{2}$$, it's not an integer or terminating decimal.

Also it's possible to divide the line segment into three equal parts, Google it and you find that it's quite easy.
_________________
Manager
Joined: 25 Aug 2009
Posts: 169
Location: Streamwood IL
Schools: Kellogg(Evening),Booth (Evening)
WE 1: 5 Years
Followers: 12

Kudos [?]: 184 [2] , given: 3

Re: hard problem OG Quant 2nd edition [#permalink]

### Show Tags

15 Jan 2010, 11:25
2
KUDOS
Quote:
Are you saying that in real life everything has the integer or terminating decimal length? Why can not we have repeated decimal or even irrational number as width of something?

Take the square with side 1, diagonal would be $$\sqrt{2}$$, it's not an integer or terminating decimal.

Also it's possible to divide the line segment into three equal parts, google it and you find that it's quite easy.

That takes the question to a whole new dimension, I do understand what you are saying though. If the width of something is 10/3 that means you can never (accurately) measure it. The width of the brass square can never be measured practically, it can be only measured mathematically. If such a square was to be made, the creator would have to take a square of 10/10 dimension, divide it into 9 exactly equal parts and use one of them, he/she could never make just the square as it would be impossible to measure 10/3 inches. I do get the concept, but don't like the fact that a question can be based on it.
_________________

Rock On

Manager
Joined: 18 Jul 2009
Posts: 52
Followers: 3

Kudos [?]: 112 [0], given: 7

Re: hard problem OG Quant 2nd edition [#permalink]

### Show Tags

15 Jan 2010, 13:09
Bunuel wrote:

Basically we are given the ratios of the sides (5/8), half of their difference can be any value we choose, there won't be any "impossible" values at all.

Hope it's clear.

Wow such a simple concept i must have left my brain someplace else.

Nice explanation.You rock man as always.
Senior Manager
Joined: 13 Dec 2009
Posts: 263
Followers: 10

Kudos [?]: 193 [5] , given: 13

Re: hard problem OG Quant 2nd edition [#permalink]

### Show Tags

24 Mar 2010, 06:10
5
KUDOS
hrish88 wrote:
A square wooden plaque has a square brass inlay in the center ,leaving a wooden strip of uniform width around the brass square.if the ratio of the brass area to the wooden area is 25 to 39,which of the following could be the width ,in inches ,of the wooden strip.

I. 1
II. 3
III. 4

A.I only
B.II only
C.III only
D.I and III only
e.I,II and III

Area of brass square/ area of wooden strip = 25 /39
lets say length of the wooden plaque= l and length of the square brass = x
then
x^2 / (l^2 - x^2) = 25/39
=>39x^2 = 25l^2 - 25x^2
=>64x^2 = 25l^2
=>8x = 5l
Width of wooden strip should be l-x
=>x = 5l/8
so l -x = l = 5l/8 = 3l/8

Now 3l/8 could be any value depending on the value of l
_________________

My debrief: done-and-dusted-730-q49-v40

Director
Status: Apply - Last Chance
Affiliations: IIT, Purdue, PhD, TauBetaPi
Joined: 18 Jul 2010
Posts: 689
Schools: Wharton, Sloan, Chicago, Haas
WE 1: 8 years in Oil&Gas
Followers: 15

Kudos [?]: 158 [1] , given: 15

Re: hard problem OG Quant 2nd edition [#permalink]

### Show Tags

07 Aug 2010, 17:32
1
KUDOS
Bunuel wrote:
hrish88 wrote:
so doest it mean any width <= 39/4 is possible.

this is the 2nd last problem in OG.so i thought it would be difficult.

No I mean ANY width is possible.

Let the the side of small square be $$x$$ and the big square $$y$$.

Given: $$\frac{x^2}{y^2-x^2}=\frac{25}{39}$$ --> $$\frac{x^2}{y^2}=\frac{25}{64}$$ --> $$\frac{x}{y}=\frac{5}{8}$$.

We are asked which value of $$\frac{y-x}{2}$$ is possible. $$\frac{y-\frac{5}{8}y}{2}=\frac{3}{16}y=?$$.

Well, expression $$\frac{3}{16}y$$ can take ANY value depending on $$y$$: 1, 3, 4, 444, 67556, 0,9, ... ANY. Basically we are given the ratios of the sides (5/8), half of their difference can be any value we choose, there won't be any "impossible" values at all.

Hope it's clear.

To generalize then, since the answer does not seem to depend on the fact that the ration is 25/39, can it be said that regardless of what the ratio is, the width of strip can be ANYTHING?
_________________

Consider kudos, they are good for health

Math Expert
Joined: 02 Sep 2009
Posts: 38850
Followers: 7721

Kudos [?]: 105957 [2] , given: 11602

Re: hard problem OG Quant 2nd edition [#permalink]

### Show Tags

08 Aug 2010, 01:32
2
KUDOS
Expert's post
1
This post was
BOOKMARKED
mainhoon wrote:
Bunuel wrote:
hrish88 wrote:
so doest it mean any width <= 39/4 is possible.

this is the 2nd last problem in OG.so i thought it would be difficult.

No I mean ANY width is possible.

Let the the side of small square be $$x$$ and the big square $$y$$.

Given: $$\frac{x^2}{y^2-x^2}=\frac{25}{39}$$ --> $$\frac{x^2}{y^2}=\frac{25}{64}$$ --> $$\frac{x}{y}=\frac{5}{8}$$.

We are asked which value of $$\frac{y-x}{2}$$ is possible. $$\frac{y-\frac{5}{8}y}{2}=\frac{3}{16}y=?$$.

Well, expression $$\frac{3}{16}y$$ can take ANY value depending on $$y$$: 1, 3, 4, 444, 67556, 0,9, ... ANY. Basically we are given the ratios of the sides (5/8), half of their difference can be any value we choose, there won't be any "impossible" values at all.

Hope it's clear.

To generalize then, since the answer does not seem to depend on the fact that the ration is 25/39, can it be said that regardless of what the ratio is, the width of strip can be ANYTHING?

Yes, width can have any positive value: the larger the width is the larger the whole square would be.
_________________
Intern
Status: Simply - Chasing GMAT
Joined: 04 May 2010
Posts: 27
Location: United Kingdom
GMAT Date: 01-30-2012
GPA: 3
WE: Consulting (Computer Software)
Followers: 1

Kudos [?]: 34 [0], given: 5

Re: hard problem OG Quant 2nd edition [#permalink]

### Show Tags

19 Sep 2010, 11:29
Hi Bunuel,

Thanx for the explanation.
I didn't understand one part:

We are asked which value of \frac{y-x}{2} is possible. \frac{y-\frac{5}{8}y}{2}=\frac{3}{16}y=?

Math Expert
Joined: 02 Sep 2009
Posts: 38850
Followers: 7721

Kudos [?]: 105957 [0], given: 11602

Re: hard problem OG Quant 2nd edition [#permalink]

### Show Tags

19 Sep 2010, 11:49
appy001 wrote:
Hi Bunuel,

Thanx for the explanation.
I didn't understand one part:

We are asked which value of \frac{y-x}{2} is possible. \frac{y-\frac{5}{8}y}{2}=\frac{3}{16}y=?

We have that $$\frac{x}{y}=\frac{5}{8}$$ --> $$x=\frac{5}{8}y$$

The width of the wooden strip would be $$\frac{y-x}{2}$$, substitute $$x$$: $$\frac{y-\frac{5}{8}y}{2}=\frac{3}{16}y$$.

So the question is: which of the following could be the value of $$\frac{3}{16}y$$?
Answer: expression $$\frac{3}{16}y$$ can take ANY value depending on $$y$$.

Hope it's clear.
_________________
Senior Manager
Joined: 20 Jul 2010
Posts: 264
Followers: 2

Kudos [?]: 87 [0], given: 9

Re: hard problem OG Quant 2nd edition [#permalink]

### Show Tags

19 Sep 2010, 15:41
I actually created equation and substituted width value to conclude E. I should have simply thought straight like Bunuel and marked E in 15 sec.
_________________

If you like my post, consider giving me some KUDOS !!!!! Like you I need them

Manager
Status: Current MBA Student
Joined: 19 Nov 2009
Posts: 128
Concentration: Finance, General Management
GMAT 1: 720 Q49 V40
Followers: 13

Kudos [?]: 386 [0], given: 210

Re: hard problem OG Quant 2nd edition [#permalink]

### Show Tags

17 Jan 2011, 12:50
Bunuel wrote:
hrish88 wrote:
A square wooden plaque has a square brass inlay in the center ,leaving a wooden strip of uniform width around the brass square.if the ratio of the brass area to the wooden area is 25 to 39,which of the following could be the width ,in inches ,of the wooden strip.

I. 1
II. 3
III. 4

A.I only
B.II only
C.III only
D.I and III only
e.I,II and III

Why would ANY width of the strip be impossible?

That was my rationale exactly. I got the answer correct, but the explanation in the book made me feel like I did not grasp the underlying math. Thanks Bunuel.
Manager
Joined: 15 Apr 2011
Posts: 70
Followers: 0

Kudos [?]: 17 [0], given: 45

Re: A square wooden plaque has a square brass inlay in the [#permalink]

### Show Tags

01 Apr 2012, 07:48
I didn't understand the statement "We are asked which value of (y-x)/2 is possible" . Can someone explain?
_________________

Math Expert
Joined: 02 Sep 2009
Posts: 38850
Followers: 7721

Kudos [?]: 105957 [1] , given: 11602

Re: A square wooden plaque has a square brass inlay in the [#permalink]

### Show Tags

01 Apr 2012, 08:43
1
KUDOS
Expert's post
I didn't understand the statement "We are asked which value of (y-x)/2 is possible" . Can someone explain?

Question asks about the possible width, in inches, of the wooden strip.

Let the the side of small square be $$x$$ and the big square $$y$$, then the width of the wooden strip would be $$\frac{y-x}{2}$$, which means that we are asked to determine the possible values of this exact expression.

Hope it's clear.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 38850
Followers: 7721

Kudos [?]: 105957 [2] , given: 11602

Re: A square wooden plaque has a square brass inlay in the [#permalink]

### Show Tags

01 Apr 2012, 09:16
2
KUDOS
Expert's post
Why is it not y-x? Why do we calculate (y-x)/2?

Consider the diagram below:
Attachment:

Wooden strip.png [ 2.75 KiB | Viewed 29847 times ]
As you can see the width of the wooden strip (the width of grey strip) is $$\frac{y-x}{2}$$.
_________________
Manager
Joined: 23 Aug 2011
Posts: 81
Followers: 3

Kudos [?]: 222 [0], given: 13

Re: hard problem OG Quant 2nd edition [#permalink]

### Show Tags

01 Sep 2012, 07:48
Bunuel wrote:
hrish88 wrote:
A square wooden plaque has a square brass inlay in the center ,leaving a wooden strip of uniform width around the brass square.if the ratio of the brass area to the wooden area is 25 to 39,which of the following could be the width ,in inches ,of the wooden strip.

I. 1
II. 3
III. 4

A.I only
B.II only
C.III only
D.I and III only
e.I,II and III

Why would ANY width of the strip be impossible?

Hi Bunuel, this was the most appropriate reason for the answer; however, can there be a case where such a condition("any possible width of the strip") might fail, provided there is no restriction on dimensions to be integral or non integral?
_________________

Whatever one does in life is a repetition of what one has done several times in one's life!
If my post was worth it, then i deserve kudos

Manager
Joined: 15 Apr 2012
Posts: 93
Concentration: Technology, Entrepreneurship
GMAT 1: 460 Q38 V17
GPA: 3.56
Followers: 0

Kudos [?]: 46 [0], given: 134

Re: A square wooden plaque has a square brass inlay in the [#permalink]

### Show Tags

18 Sep 2012, 11:50
Bunuel wrote:
Why is it not y-x? Why do we calculate (y-x)/2?

Consider the diagram below:
Attachment:
Wooden strip.png
As you can see the width of the wooden strip (the width of grey strip) is $$\frac{y-x}{2}$$.

total length is 8x and the length of the countertop is 5x.so the one side length of the untiled area is w = 8x-5x/2 =3x/2 .Since x could be any value so the answer is E..Am I right Bunuel ?
Re: A square wooden plaque has a square brass inlay in the   [#permalink] 18 Sep 2012, 11:50

Go to page    1   2    Next  [ 40 posts ]

Similar topics Replies Last post
Similar
Topics:
1 In the figure above every square is contained within a square that has 3 09 Jan 2015, 06:57
11 A square board that has an area of 25 square inches is to be 12 17 Apr 2016, 03:37
4 A square wooden plaque has a square brass inlay in the center, leaving 6 14 Jan 2015, 01:39
A square counter top has a square tile inlay in the center, 4 21 Jan 2011, 17:25
10 A square counter top has a square tile inlay in the center 7 30 Jun 2012, 09:37
Display posts from previous: Sort by