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

Question

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.

Bunuel · Accepted Answer

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.

TGC · Answer

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!

WholeLottaLove · Answer

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?

Bunuel · Answer

(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.

WholeLottaLove · Answer

Does my attached diagram make sense?

fskilnik · Answer

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.

gmatzpractice · Answer

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

Rickooreo · Answer

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?

gmatophobia · Answer

This logic is correct !

AVMachine · Answer

SL/SW = 2/1;

1. R has same area as S; hence RL * RW = SL * SW; not any other info, not sufficient.

2. The ratio of one side of R to one side of S is 2 to 1; this means RL/SL = 2/1 or RL/SW = 2/1 or RW/SL = 2/1 or RW/SW = 2/1; But this doesn't provide any other relationship, hence not Sufficient.

With both: 
1. RL = 2 * SL; from area equation: 2 SL * RW = SL * SW; RW = SW/2

RL/RW = 2 SL / SW / 2 = 4 * 2 /1 ; Not Silver.

2. RL = 2 * SW; from Area Equation: 2 SW * RW = SL * SW; RW = SL/2

RL/RW = 2 SW / SL / 2 = 4 / 2 = 2/1; Silver.

Hence, using both also can't provide a definitive answer. Both are also not sufficient.

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

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