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Geometry

by vinay1983 » Wed Sep 18, 2013 7:19 am
A square wooden plaque has a square brass inlay in the center, leaving a wooden strip of uniform width around the brass square. lf 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) ll onlY
(C) I and ll only
(D) I and lll only
(E) l, ll, and lll

Original explanation is waaaaaayyyy to lengthy!Any simple method. Rather is there any conceptual approach to such problems?
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by Brent@GMATPrepNow » Wed Sep 18, 2013 7:29 am
vinay1983 wrote:A square wooden plaque has a square brass inlay in the center, leaving a wooden strip of uniform width around the brass square. lf 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) ll onlY
(C) I and ll only
(D) I and lll only
(E) l, ll, and lll
This is a bit of a trick question.
We have a brass square inside a wood frame. The ratio of the brass area to the wooden area is 25 to 39.
Once we find a width of the wooden strip that works, we can shrink or expand size of the plaque to get ANY width.
In other words, the wooden strip can have ANY length.
Answer: E

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by Brent@GMATPrepNow » Wed Sep 18, 2013 7:44 am
vinay1983 wrote:A square wooden plaque has a square brass inlay in the center, leaving a wooden strip of uniform width around the brass square. lf 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) ll onlY
(C) I and ll only
(D) I and lll only
(E) l, ll, and lll
Here are some diagrams to support the solution in my last post.

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.
Image


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
Image

At this point, if we shrink or expand the plaque . . .
Image
. . . 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
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by rupalie » Tue Dec 08, 2015 10:28 am
What's the answer to this question?
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by Brent@GMATPrepNow » Tue Dec 08, 2015 11:21 am
rupalie wrote:What's the answer to this question?
E
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by rupalie » Tue Dec 08, 2015 11:25 am
Thanks Brent, can you please explain...thanks!
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by DavidG@VeritasPrep » Wed Dec 09, 2015 1:45 pm
See here for a virtually identical question/discussion: https://www.beatthegmat.com/ds-geometry-t284497.html
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by sanju09 » Wed Dec 09, 2015 11:54 pm
vinay1983 wrote:A square wooden plaque has a square brass inlay in the center, leaving a wooden strip of uniform width around the brass square. lf 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) ll onlY
(C) I and ll only
(D) I and lll only
(E) l, ll, and lll

Original explanation is waaaaaayyyy to lengthy!Any simple method. Rather is there any conceptual approach to such problems?
E
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by Brent@GMATPrepNow » Thu Dec 10, 2015 6:55 am
rupalie wrote:Thanks Brent, can you please explain...thanks!
See my posts above
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