Last visit was: 23 Apr 2026, 00:16 It is currently 23 Apr 2026, 00:16
Home
Messages
Tests
Schools
Events
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
655-705 (Hard)|   Geometry|         
User avatar
TGC
User avatar
Joined: 03 Aug 2012
Last visit: 19 Jul 2017
Posts: 572
Own Kudos:
3,621
 [68]
Given Kudos: 322
Concentration: General Management, General Management
Schools: ISB '16 NUS '17 NTU '17 XLRI SMU '17 IIM Lucknow IPMX'16 (A)
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
WE:Information Technology (Finance: Investment Banking)
Schools: ISB '16 NUS '17 NTU '17 XLRI SMU '17 IIM Lucknow IPMX'16 (A)
GMAT 2: 680 Q50 V32
Posts: 572
Kudos: 3,621
 [68]
A rectangle is defined to be "silver" if and only if the rat Updated on: 13 Sep 2022, 02:57
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.
1
Kudos
Add Kudos
67
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

65% (hard)

Question Stats:

55% (01:48) correct 45% (01:46) wrong based on 1414 sessions

History

Date
Time
Result
Not Attempted Yet
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.
ShowHide Answer
Official Answer
E
If this question felt shaky, try an adaptive mini quiz of similar problems in GMAT Club Forum Quiz →. Free plan gives 5 questions per day.
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 22 Apr 2026
Posts: 109,763
Own Kudos:
810,709
 [5]
Given Kudos: 105,850
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,763
Kudos: 810,709
 [5]
A rectangle is defined to be "silver" if and only if the rat 17 Oct 2013, 23:56
5
Kudos
Add Kudos
Bookmarks
Bookmark this Post
TGC
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!
Show more

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.
General Discussion
User avatar
TGC
User avatar
Joined: 03 Aug 2012
Last visit: 19 Jul 2017
Posts: 572
Own Kudos:
3,621
 [3]
Given Kudos: 322
Concentration: General Management, General Management
Schools: ISB '16 NUS '17 NTU '17 XLRI SMU '17 IIM Lucknow IPMX'16 (A)
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
WE:Information Technology (Finance: Investment Banking)
Schools: ISB '16 NUS '17 NTU '17 XLRI SMU '17 IIM Lucknow IPMX'16 (A)
GMAT 2: 680 Q50 V32
Posts: 572
Kudos: 3,621
 [3]
A rectangle is defined to be "silver" if and only if the rat 17 Oct 2013, 22:38
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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!
User avatar
WholeLottaLove
User avatar
Joined: 13 May 2013
Last visit: 13 Jan 2014
Posts: 301
Own Kudos:
640
 [1]
Given Kudos: 134
Posts: 301
Kudos: 640
 [1]
A rectangle is defined to be "silver" if and only if the rat 06 Dec 2013, 10:44
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 22 Apr 2026
Posts: 109,763
Own Kudos:
810,709
 [1]
Given Kudos: 105,850
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,763
Kudos: 810,709
 [1]
A rectangle is defined to be "silver" if and only if the rat 07 Dec 2013, 06:07
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
WholeLottaLove
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?
Show more

(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.
User avatar
WholeLottaLove
User avatar
Joined: 13 May 2013
Last visit: 13 Jan 2014
Posts: 301
Own Kudos:
640
 [1]
Given Kudos: 134
Posts: 301
Kudos: 640
 [1]
A rectangle is defined to be "silver" if and only if the rat 07 Dec 2013, 13:11
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
WholeLottaLove
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.
Show more

Does my attached diagram make sense?
Attachments

EXAMPLE.png
EXAMPLE.png [ 63.29 KiB | Viewed 15997 times ]

User avatar
fskilnik
User avatar
Joined: 12 Oct 2010
Last visit: 03 Jan 2025
Posts: 883
Own Kudos:
1,880
 [2]
Given Kudos: 57
Status:GMATH founder
Expert
Expert reply
Posts: 883
Kudos: 1,880
 [2]
A rectangle is defined to be "silver" if and only if the rat 16 Sep 2018, 12:12
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
TGC
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.
Show more

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.
Attachments

16Set18_4v.gif
16Set18_4v.gif [ 20.06 KiB | Viewed 13506 times ]

User avatar
gmatzpractice
User avatar
Joined: 07 Feb 2017
Last visit: 25 Nov 2024
Posts: 122
Own Kudos:
82
Given Kudos: 11
GMAT 1: 710 Q48 V40
GMAT 1: 710 Q48 V40
Posts: 122
Kudos: 82
A rectangle is defined to be "silver" if and only if the rat 16 Sep 2018, 17:14
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
User avatar
Rickooreo
User avatar
Joined: 24 Dec 2021
Last visit: 15 Mar 2026
Posts: 291
Own Kudos:
32
Given Kudos: 239
Location: India
Concentration: Finance, General Management
Schools: ISB '24 Moore '25
GMAT 1: 690 Q48 V35
GPA: 3.95
WE:Real Estate (Consulting)
Schools: ISB '24 Moore '25
GMAT 1: 690 Q48 V35
Posts: 291
Kudos: 32
A rectangle is defined to be "silver" if and only if the rat 22 Nov 2022, 05:05
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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?
User avatar
gmatophobia
User avatar
Quant Chat Moderator
Joined: 22 Dec 2016
Last visit: 19 Apr 2026
Posts: 3,173
Own Kudos:
11,450
Given Kudos: 1,862
Location: India
Concentration: Strategy, Leadership
Posts: 3,173
Kudos: 11,450
A rectangle is defined to be "silver" if and only if the rat 22 Nov 2022, 05:11
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Rickooreo
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?
Show more

This logic is correct !
User avatar
AVMachine
User avatar
Joined: 03 May 2024
Last visit: 26 Mar 2026
Posts: 190
Own Kudos:
154
Given Kudos: 40
Posts: 190
Kudos: 154
A rectangle is defined to be "silver" if and only if the rat 18 Mar 2025, 06:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
TGC
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.
Show more
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.
Moderators:
Bunuel
Math Expert
109763 posts
kingbucky
498 posts
Gmat860sanskar
212 posts