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

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TGC
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A rectangle is defined to be "silver" if and only if the rat [#permalink] New post  Updated on: 13 Sep 2022, 02:57
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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.
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Originally posted by TGC on 17 Oct 2013, 22:31.
Last edited by Bunuel on 13 Sep 2022, 02:57, edited 3 times in total.
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TGC
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Re: A rectangle is defined to be "silver" if and only if the rat [#permalink] New post  17 Oct 2013, 22:38
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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).

Please advise what I am missing here.

Rgds,
TGC!
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Re: A rectangle is defined to be "silver" if and only if the rat [#permalink] New post  17 Oct 2013, 23:56
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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).

Please advise what I am missing here.

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.

Answer: E.

Hope it helps.
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Re: A rectangle is defined to be "silver" if and only if the rat [#permalink] New post  06 Dec 2013, 10:44
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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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Re: A rectangle is defined to be "silver" if and only if the rat [#permalink] New post  07 Dec 2013, 06:07
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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] New post  07 Dec 2013, 13:11
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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?
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EXAMPLE.png [ 63.29 KiB | Viewed 13181 times ]

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Re: A rectangle is defined to be "silver" if and only if the rat [#permalink] New post  16 Sep 2018, 12:12
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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
16Set18_4v.gif [ 20.06 KiB | Viewed 10713 times ]


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Re: A rectangle is defined to be "silver" if and only if the rat [#permalink] New post  16 Sep 2018, 17:14
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

Answer E
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Re: A rectangle is defined to be "silver" if and only if the rat [#permalink] New post  22 Nov 2022, 05:05
gmatophobia

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.



Let say side of S is 2cm, 4cm

Combining I and II, one of the side of R will be either 4cm or 8cm
Area of S is 8cm, now since area is same then, then sides of R will be 4cm*2cm or 8cm*1cm
Thus since we are getting two cases where one satisfies and other doesn't answer will be option E

Is this logic correct?
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Re: A rectangle is defined to be "silver" if and only if the rat [#permalink] New post  22 Nov 2022, 05:11
Rickooreo wrote:
gmatophobia

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.



Let say side of S is 2cm, 4cm

Combining I and II, one of the side of R will be either 4cm or 8cm
Area of S is 8cm, now since area is same then, then sides of R will be 4cm*2cm or 8cm*1cm
Thus since we are getting two cases where one satisfies and other doesn't answer will be option E

Is this logic correct?


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