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# A rectangle is defined to be "silver" if and only if the rat

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Director
Joined: 03 Aug 2012
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Concentration: General Management, General Management
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A rectangle is defined to be "silver" if and only if the rat  [#permalink]

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Updated on: 28 Nov 2018, 07:14
1
7
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Difficulty:

75% (hard)

Question Stats:

49% (01:43) correct 51% (01:39) wrong based on 290 sessions

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Project DS Butler: Day 23: Data Sufficiency (DS46)

A rectangle is defined to be "silver" if and only if the ratio of its length to its width is 2 to 1. If rectangle S is silver, is rectangle R silver?

(1) R has the same area as S
(2) The ratio of one side of R to one side of S is 2 to 1.

Originally posted by TGC on 17 Oct 2013, 21:31.
Last edited by gmatbusters on 28 Nov 2018, 07:14, edited 2 times in total.
Renamed the topic and edited the question.
Director
Joined: 03 Aug 2012
Posts: 712
Concentration: General Management, General Management
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)
Re: A rectangle is defined to be "silver" if and only if the rat  [#permalink]

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17 Oct 2013, 21:38
Since "S" is silver the ratio for its L/B=2/1

(1).

Sides of R can be in any ratio provided the area of R=S

Consider for S : 4:2
For R it can be : 4:2 or 8:1

Hence Insufficient

(2).

Consider this we don't have enough info

Hence Insufficient

Combining them

Consider length of R/S=2/1 and both the areas will have to be same

S: L=2 and B=1
R: L=4 and B=1/2 Hence R is not silver

Consider width of R/S = 2/1 and both the areas will have to be same

S: L=4 and B=2
R: L=2 and B=4 Hence R is not silver

Hence Both combined are sufficient. However , per the source the answer is (E).

Rgds,
TGC!
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Joined: 02 Sep 2009
Posts: 52921
Re: A rectangle is defined to be "silver" if and only if the rat  [#permalink]

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17 Oct 2013, 22:56
2
TGC wrote:
Since "S" is silver the ratio for its L/B=2/1

(1).

Sides of R can be in any ratio provided the area of R=S

Consider for S : 4:2
For R it can be : 4:2 or 8:1

Hence Insufficient

(2).

Consider this we don't have enough info

Hence Insufficient

Combining them

Consider length of R/S=2/1 and both the areas will have to be same

S: L=2 and B=1
R: L=4 and B=1/2 Hence R is not silver

Consider width of R/S = 2/1 and both the areas will have to be same

S: L=4 and B=2
R: L=2 and B=4 Hence R is not silver

Hence Both combined are sufficient. However , per the source the answer is (E).

Rgds,
TGC!

Consider two cases:
S is 4 by 2 and R is 4 by 2.
S is 4 by 2 and R is 8 by 1.

Hope it helps.
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Re: A rectangle is defined to be "silver" if and only if the rat  [#permalink]

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06 Dec 2013, 09:44
1
Because they are both rectangles, does it matter that we don't know the side which the ratio is applied to from (2)? In other words, is the test trying to trick us by specifying that "if and only if the ratio of its length to its width is 2 to 1" whereas (2) doesn't specify if the ratio is of length to width or width to length?
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Posts: 52921
Re: A rectangle is defined to be "silver" if and only if the rat  [#permalink]

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07 Dec 2013, 05:07
WholeLottaLove wrote:
Because they are both rectangles, does it matter that we don't know the side which the ratio is applied to from (2)? In other words, is the test trying to trick us by specifying that "if and only if the ratio of its length to its width is 2 to 1" whereas (2) doesn't specify if the ratio is of length to width or width to length?

(2) is not sufficient, because it talks about R and S, not only about R: The ratio of one side of R to one side of S is 2 to 1.
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Re: A rectangle is defined to be "silver" if and only if the rat  [#permalink]

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07 Dec 2013, 12:11
Bunuel wrote:
WholeLottaLove wrote:
Because they are both rectangles, does it matter that we don't know the side which the ratio is applied to from (2)? In other words, is the test trying to trick us by specifying that "if and only if the ratio of its length to its width is 2 to 1" whereas (2) doesn't specify if the ratio is of length to width or width to length?

(2) is not sufficient, because it talks about R and S, not only about R: The ratio of one side of R to one side of S is 2 to 1.

Does my attached diagram make sense?
Attachments

EXAMPLE.png [ 63.29 KiB | Viewed 3156 times ]

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Re: A rectangle is defined to be "silver" if and only if the rat  [#permalink]

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16 Sep 2018, 11:12
TGC wrote:
A rectangle is defined to be "silver" if and only if the ratio of its length to its width is 2 to 1. If rectangle S is silver, is rectangle R silver?

(1) R has the same area as S
(2) The ratio of one side of R to one side of S is 2 to 1.

The correct answer is (E) , as proved in the ALGEBRAIC-GEOMETRIC BIFURCATION shown in the image attached.

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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16Set18_4v.gif [ 20.06 KiB | Viewed 798 times ]

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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

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Re: A rectangle is defined to be "silver" if and only if the rat  [#permalink]

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16 Sep 2018, 16:14
S is 2x by x so that it's a "silver"

(1) Area of R is 2x^2
R can be 2x by x so that it's a "sliver"
or 2/3x by 3x so it's not a sliver
Insufficient

(2) R can be 4x by 100000x
Or 4x by 2x
ETC.
Insufficient

(1) and (2)
R is 4x by 1/2x which is not a sliver
Or 2x by x which is a sliver

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Re: A rectangle is defined to be "silver" if and only if the rat  [#permalink]

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28 Nov 2018, 07:16
Bumping for DS Butler Project:

Project DS Butler: Day 23: Data Sufficiency (DS46)

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Re: A rectangle is defined to be "silver" if and only if the rat   [#permalink] 28 Nov 2018, 07:16
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