Geometry : Area problem.

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AndyB: Senior | Next Rank: 100 Posts; Posts: 51; Joined: Sat Oct 16, 2010 9:31 pm

by AndyB » Fri Apr 01, 2011 1:10 am

Hi All,

I am not able to solve the below question.Could anyone please help me in understanding with the solution:

Q)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.

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manpsingh87: Master | Next Rank: 500 Posts; Posts: 436; Joined: Tue Feb 08, 2011 3:07 amFollowed by: 6 members; Thanked: 72 times

by manpsingh87 » Fri Apr 01, 2011 1:48 am

AndyB wrote:Hi All,

I am not able to solve the below question.Could anyone please help me in understanding with the solution:

Q)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.

let length of square wooden plaque be x, and length of square brass be y;
as per question, are of brass/area of wooden= 25/39;
hence y^2/x^2-y^2=25/39;
39y^2+25y^2=25x^2
x/y=8/5;
width of wooden strip would be x-y=x-5/8x=3/8x;
if x=8/3, then width=1,
if x=8, width=3;
if x=32/3, width =4;

as all values are possible, hence E

O Excellence... my search for you is on... you can be far.. but not beyond my reach!

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AndyB: Senior | Next Rank: 100 Posts; Posts: 51; Joined: Sat Oct 16, 2010 9:31 pm

by AndyB » Fri Apr 01, 2011 2:29 am

Hi Manpsingh,

I am unable to understand the following calculation, Why are we substituting x=8/3,x=8 and x=32/3 and how we could arrive at those values only.

Could you please elucidate on this:

if x=8/3, then width=1,
if x=8, width=3;
if x=32/3, width =4;

Regards,
AndyB.

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manpsingh87: Master | Next Rank: 500 Posts; Posts: 436; Joined: Tue Feb 08, 2011 3:07 amFollowed by: 6 members; Thanked: 72 times

by manpsingh87 » Fri Apr 01, 2011 2:33 am

AndyB wrote:Hi Manpsingh,

I am unable to understand the following calculation, Why are we substituting x=8/3,x=8 and x=32/3 and how we could arrive at those values only.

Could you please elucidate on this:

if x=8/3, then width=1,
if x=8, width=3;
if x=32/3, width =4;

Regards,
AndyB.

here important thing to understand is that x can take any value(both integral as well as non integral), that's why i'm plugging different values...!!!

i hope it helps..!!!!

O Excellence... my search for you is on... you can be far.. but not beyond my reach!

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AndyB: Senior | Next Rank: 100 Posts; Posts: 51; Joined: Sat Oct 16, 2010 9:31 pm

by AndyB » Fri Apr 01, 2011 2:51 am

Thanks Manpsingh,

For the explanation and patience.

Regards,
AndyB

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vineeshp: Legendary Member; Posts: 965; Joined: Thu Jan 28, 2010 12:52 amFollowed by: 34 members; Thanked: 156 times; GMAT Score:720

by vineeshp » Fri Apr 01, 2011 2:51 am

E: 1,2 and 3.
Let us assume the side of the brass square to be x and side of the total square to be y.
and difference to be z.

If you take the unit to be 1, Area of brass square is 25 and area of whole square is 25 + 39 = 64.

So side of total square is 8.

ad side of brass is 5.

If you take two sides of this ration, you can get the same ratio of areas.

Vineesh,
Just telling you what I know and think. I am not the expert.

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Fri Apr 01, 2011 3:29 am

AndyB wrote:Hi All,

I am not able to solve the below question.Could anyone please help me in understanding with the solution:

Q)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.

If x is the side of the square wooden plaque and w is the uniform width the wooden strip, then the brass area is (x - w) ^2 and the wooden area is x^2 - (x - w) ^2; such that

(x - w) ^2: x^2 - (x - w) ^2 = 25:39 or we've

[x^2 - (x - w) ^2]/ (x - w) ^2 = 39/25 {Use componendo law and add 1 to both sides}

{[x^2 - (x - w) ^2]/ (x - w) ^2} + 1 = (39/25) + 1 gives

x^2/ (x - w) ^2 = 64/25

or, x/(x - w) = 8/5,

or (x - w)/x = 5/8,

or w/x = 3/8,

and since w and x may or may not be integers, w = 1 is possible when when x = 8/3, w = 3 is possible when x = 8, and w = 4 is also possible when x = 32/3.

[spoiler]E

The new look of the BTG page is very abstemious, thanks Eric.[/spoiler]

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Apr 01, 2011 4:24 am

A square wooden plaque has a 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

There is no math to be done here; just use common sense. Why couldn't the width of the strip be any value? We could choose a width for the strip, then shrink or expand the inlay until the ratio of inlay area:strip area = 25:39.

The correct answer is E.

Last edited by GMATGuruNY on Fri Apr 01, 2011 4:33 am, edited 1 time in total.

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Fri Apr 01, 2011 4:31 am

GMATGuruNY wrote:
tonebeeze wrote:A square wooden plaque has a 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
There is no math to be done here; just use common sense. Why couldn't the width of the strip be any value? We could choose a width for the strip, then shrink or expand the inlay until the ratio of inlay area:strip area = 25:39.

The correct answer is E.

absolutely

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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Shadow88: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Sat Jun 09, 2012 5:25 am; Thanked: 2 times

by Shadow88 » Fri Nov 09, 2012 1:36 am

I seem to have trouble with this type of questions. Do you guys know where i can find similar problems?

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naseem_iqbal: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Fri Nov 29, 2013 5:46 am

by naseem_iqbal » Sat Jan 04, 2014 2:47 am

GMATGuruNY wrote:
A square wooden plaque has a 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
There is no math to be done here; just use common sense. Why couldn't the width of the strip be any value? We could choose a width for the strip, then shrink or expand the inlay until the ratio of inlay area:strip area = 25:39.

The correct answer is E.

Amazing!!

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Jan 04, 2014 7:00 am

AndyB 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)I and II only.
D)I and III only.
E)I, II and III.

Here's a visual solution:

Let's say we want to create a plaque with a square brass inlay in the center, and we want the brass to wood ratio to be 25:39

Let's begin a square wooden board with ANY dimensions.

Now place a square brass inlay in the middle of the wooden board, and keep adjusting the size of the brass inlay until we have a brass to wood ratio that is 25:39

At this point, if we shrink or expand the plaque . . .

. . . the brass to wood ratio will remain at 25:39

So, as you can see, this plaque can be ANY size, which means the width of the wooden strip can have ANY measurement.

Answer: E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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