Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 64101

A square wooden plaque has a square brass inlay in the
[#permalink]
Show Tags
15 Jan 2010, 03:00
Question Stats:
38% (02:30) correct 62% (02:49) wrong based on 1958 sessions
HideShow timer Statistics
The Official Guide For GMAT® Quantitative Review, 2ND EditionA 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 ProjectEach 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: 1. Please provide your solutions to the questions; 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!
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Math Expert
Joined: 02 Sep 2009
Posts: 64101

Re: hard problem OG Quant 2nd edition
[#permalink]
Show Tags
15 Jan 2010, 05:14
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: \(\frac{x^2}{y^2x^2}=\frac{25}{39}\) > \(\frac{x^2}{y^2}=\frac{25}{64}\) > \(\frac{x}{y}=\frac{5}{8}\). We are asked which value of \(\frac{yx}{2}\) 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.
_________________



Math Expert
Joined: 02 Sep 2009
Posts: 64101

Re: hard problem OG Quant 2nd edition
[#permalink]
Show Tags
15 Jan 2010, 03:26
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? Answer: E.
_________________




Manager
Joined: 13 Dec 2009
Posts: 167

Re: hard problem OG Quant 2nd edition
[#permalink]
Show Tags
24 Mar 2010, 05:10
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 lx =>x = 5l/8 so l x = l = 5l/8 = 3l/8 Now 3l/8 could be any value depending on the value of l so answer is E.




Intern
Joined: 18 Jul 2009
Posts: 24

Re: hard problem OG Quant 2nd edition
[#permalink]
Show Tags
15 Jan 2010, 04:03
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.



Manager
Joined: 25 Aug 2009
Posts: 97
Location: Streamwood IL
Schools: Kellogg(Evening),Booth (Evening)
WE 1: 5 Years

Re: hard problem OG Quant 2nd edition
[#permalink]
Show Tags
15 Jan 2010, 08:49
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. Answer is B.



Math Expert
Joined: 02 Sep 2009
Posts: 64101

A square wooden plaque has a square brass inlay in the
[#permalink]
Show Tags
15 Jan 2010, 09:44
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. Answer is B. Are you saying that in real life everything has 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: 97
Location: Streamwood IL
Schools: Kellogg(Evening),Booth (Evening)
WE 1: 5 Years

Re: hard problem OG Quant 2nd edition
[#permalink]
Show Tags
15 Jan 2010, 10:25
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.



Intern
Joined: 18 Jul 2009
Posts: 24

Re: hard problem OG Quant 2nd edition
[#permalink]
Show Tags
15 Jan 2010, 12:09
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.



Director
Status: Apply  Last Chance
Affiliations: IIT, Purdue, PhD, TauBetaPi
Joined: 17 Jul 2010
Posts: 571
Schools: Wharton, Sloan, Chicago, Haas
WE 1: 8 years in Oil&Gas

Re: hard problem OG Quant 2nd edition
[#permalink]
Show Tags
07 Aug 2010, 16:32
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: \(\frac{x^2}{y^2x^2}=\frac{25}{39}\) > \(\frac{x^2}{y^2}=\frac{25}{64}\) > \(\frac{x}{y}=\frac{5}{8}\). We are asked which value of \(\frac{yx}{2}\) 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?



Math Expert
Joined: 02 Sep 2009
Posts: 64101

Re: hard problem OG Quant 2nd edition
[#permalink]
Show Tags
08 Aug 2010, 00:32
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: \(\frac{x^2}{y^2x^2}=\frac{25}{39}\) > \(\frac{x^2}{y^2}=\frac{25}{64}\) > \(\frac{x}{y}=\frac{5}{8}\). We are asked which value of \(\frac{yx}{2}\) 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: 18
Location: United Kingdom
Concentration: International Business, Entrepreneurship
GMAT Date: 01302012
GPA: 3
WE: Consulting (Computer Software)

Re: hard problem OG Quant 2nd edition
[#permalink]
Show Tags
19 Sep 2010, 10:29
Hi Bunuel,
Thanx for the explanation. I didn't understand one part:
We are asked which value of \frac{yx}{2} is possible. \frac{y\frac{5}{8}y}{2}=\frac{3}{16}y=?
Please enlighten me.



Math Expert
Joined: 02 Sep 2009
Posts: 64101

Re: hard problem OG Quant 2nd edition
[#permalink]
Show Tags
19 Sep 2010, 10:49
appy001 wrote: Hi Bunuel,
Thanx for the explanation. I didn't understand one part:
We are asked which value of \frac{yx}{2} is possible. \frac{y\frac{5}{8}y}{2}=\frac{3}{16}y=?
Please enlighten me. We have that \(\frac{x}{y}=\frac{5}{8}\) > \(x=\frac{5}{8}y\) The width of the wooden strip would be \(\frac{yx}{2}\), 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.
_________________



Manager
Joined: 20 Jul 2010
Posts: 166

Re: hard problem OG Quant 2nd edition
[#permalink]
Show Tags
19 Sep 2010, 14:41
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.



Manager
Status: Current MBA Student
Joined: 19 Nov 2009
Posts: 89
Concentration: Finance, General Management

Re: hard problem OG Quant 2nd edition
[#permalink]
Show Tags
17 Jan 2011, 11:50
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? Answer: E. 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: 58

Re: A square wooden plaque has a square brass inlay in the
[#permalink]
Show Tags
01 Apr 2012, 06:48
I didn't understand the statement "We are asked which value of (yx)/2 is possible" . Can someone explain?
_________________
http://mymbadreamz.blogspot.com



Math Expert
Joined: 02 Sep 2009
Posts: 64101

Re: A square wooden plaque has a square brass inlay in the
[#permalink]
Show Tags
01 Apr 2012, 07:43
mymbadreamz wrote: I didn't understand the statement "We are asked which value of (yx)/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 \(\frac{yx}{2}\), 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: 64101

Re: A square wooden plaque has a square brass inlay in the
[#permalink]
Show Tags
01 Apr 2012, 08:16
mymbadreamz wrote: Why is it not yx? Why do we calculate (yx)/2? Consider the diagram below: Attachment:
Wooden strip.png [ 2.75 KiB  Viewed 71648 times ]
As you can see the width of the wooden strip (the width of grey strip) is \(\frac{yx}{2}\).
_________________



Manager
Joined: 23 Aug 2011
Posts: 61

Re: hard problem OG Quant 2nd edition
[#permalink]
Show Tags
01 Sep 2012, 06:48
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? Answer: E. 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?



Manager
Joined: 15 Apr 2012
Posts: 81
Location: Bangladesh
Concentration: Technology, Entrepreneurship
GPA: 3.56

Re: A square wooden plaque has a square brass inlay in the
[#permalink]
Show Tags
18 Sep 2012, 10:50
Bunuel wrote: mymbadreamz wrote: Why is it not yx? Why do we calculate (yx)/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 \(\frac{yx}{2}\). total length is 8x and the length of the countertop is 5x.so the one side length of the untiled area is w = 8x5x/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, 10:50



Go to page
1 2 3
Next
[ 54 posts ]

