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

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## Global Stats

Difficult

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.

OA E

Source: Veritas Prep

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BTGmoderatorDC 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 a 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.

OA E

Source: Veritas Prep
Given: Rectangle S is silver, i.e., the ratio of its length to its width is 2 to 1

Question: Is a rectangle R silver?

Question rephrased: Does rectangle R has the ratio of its length to its width is 2 to 1?

Let's take each statement one by one.

(1) R has the same area as S.

Case 1: Say the length and the width of the rectangle S and R are 2 and 1, respective. The answer is yes.
Case 2: Say the length and the width of the rectangle S are 2 and 1, respective. However, the length and the width of the rectangle R are 1 and 2, respective. The answer is no.

Insufficient.

(2) The ratio of one side of R to one side of S is 2 to 1.

Cases discussed above are applicable here too. Insufficient.

(1) and (2) together

Cases discussed above are applicable here too. Insufficient.

Hope this helps!

-Jay
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### GMAT/MBA Expert

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BTGmoderatorDC 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.

Source: Veritas Prep

The correct answer is therefore __(E)______ .

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

Regards,
Fabio.

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Fabio Skilnik :: www.GMATH.net (Math for the GMAT)
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