Does rectangle A have a greater perimeter than rectangle B? : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 23 Feb 2017, 08:22

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Does rectangle A have a greater perimeter than rectangle B?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 21 Feb 2010
Posts: 212
Followers: 2

Kudos [?]: 31 [1] , given: 1

Does rectangle A have a greater perimeter than rectangle B? [#permalink]

### Show Tags

28 Jul 2010, 04:45
1
KUDOS
4
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

49% (02:39) correct 51% (01:13) wrong based on 122 sessions

### HideShow timer Statistics

Does rectangle A have a greater perimeter than rectangle B?

(1) The length of a side of rectangle A is twice the length of a side of rectangle B
(2) The area of rectangle A is twice the area of rectangle B
[Reveal] Spoiler: OA
Manager
Joined: 16 Apr 2010
Posts: 221
Followers: 4

Kudos [?]: 121 [0], given: 12

### Show Tags

28 Jul 2010, 05:04
Hi,

Statement one provides information about one side only. This is not enough since one side of rect A can be greater than one side of rect B while the second side of rectangle A can be either less or greater than the second side of rectangle B. Remember Perimeter = 2(L+W).
Consider:
Rect A: 20*20
Rect B: 1*2
or
Rect A: 20*1
Rect B: 1*40

Statement 2 is not sufficient as well. Consider:
Rect A: 20*1, P=42
Rect B: 1*10, P=22
or
Rect A: 2*2, P=8
Rect B: 20:0.1, P=40.2

Taking both conditions, the answer will be sufficient.
You can also solve this problem by equations.

regards,
Jack
Math Expert
Joined: 02 Sep 2009
Posts: 37098
Followers: 7249

Kudos [?]: 96415 [2] , given: 10738

### Show Tags

28 Jul 2010, 05:09
2
KUDOS
Expert's post
2
This post was
BOOKMARKED
tt11234 wrote:
hello all,
here's the question...
does rectangle A have a greater perimeter than rectangle B?
1) the length of a side of rectangle A is twice the length of a side of rectangle B
2) the area of rectangle A is twice the area of rectangle B

Let the sides of rectangle A be $$s$$ and $$t$$ and the side of rectangle B $$m$$ and $$n$$.

Question: is $$2(s+t)>2(m+n)$$? --> or is $$s+t>m+n$$?

(1) $$s=2m$$, clearly insufficient as no info about the other side of rectangles.

(2) $$st=2mn$$, also insufficient as if $$s=t=2$$, $$m=1$$ and $$n=2$$ then the answer would be YES, but if $$s=t=2$$, $$m=\frac{1}{2}$$ and $$n=4$$ then the answer would be NO.

(1)+(2) $$s=2m$$ and $$st=2mn$$ --> substitute $$s$$: $$2m*t=2mn$$, so $$t=n$$. Thus as $$s=2m$$ and $$t=n$$: $$s+t=2m+n$$ which is obviously more than $$m+n$$. Sufficient.

_________________
Intern
Joined: 16 Jul 2010
Posts: 18
Followers: 1

Kudos [?]: 18 [0], given: 9

### Show Tags

29 Jul 2010, 11:13
I always love when the OP uses a [Reveal] Spoiler: but posts the OA in the question anyway...
_________________

If you find my posts useful, please award me some Kudos!

Intern
Joined: 09 Dec 2008
Posts: 28
Location: Vietnam
Schools: Somewhere
Followers: 0

Kudos [?]: 70 [0], given: 2

### Show Tags

31 Jul 2010, 21:53
Bunuel wrote:
tt11234 wrote:
hello all,
here's the question...
does rectangle A have a greater perimeter than rectangle B?
1) the length of a side of rectangle A is twice the length of a side of rectangle B
2) the area of rectangle A is twice the area of rectangle B

Let the sides of rectangle A be $$s$$ and $$t$$ and the side of rectangle B $$m$$ and $$n$$.

Question: is $$2(s+t)>2(m+n)$$? --> or is $$s+t>m+n$$?

(1) $$s=2m$$, clearly insufficient as no info about the other side of rectangles.

(2) $$st=2mn$$, also insufficient as if $$s=t=2$$, $$m=1$$ and $$n=2$$ then the answer would be YES, but if $$s=t=2$$, $$m=\frac{1}{2}$$ and $$n=4$$ then the answer would be NO.

(1)+(2) $$s=2m$$ and $$st=2mn$$ --> substitute $$s$$: $$2m*t=2mn$$, so $$t=n$$. Thus as $$s=2m$$ and $$t=n$$: $$s+t=2m+n$$ which is obviously more than $$m+n$$. Sufficient.

Nice explanation, Bunuel! Thanks a lot
Current Student
Joined: 06 Sep 2013
Posts: 2035
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 64

Kudos [?]: 604 [0], given: 355

Re: Does rectangle A have a greater perimeter than rectangle B? [#permalink]

### Show Tags

27 Dec 2013, 15:25
tt11234 wrote:
Does rectangle A have a greater perimeter than rectangle B?

(1) The length of a side of rectangle A is twice the length of a side of rectangle B
(2) The area of rectangle A is twice the area of rectangle B

Nice question, let me chip in

Let's call L,W of rectangle A (A,B) and LW, of rectangle B (C,D)

So question is is 2(A+B) > 2(C+D) or if you will A+B>C+D?

(1) A = 2C Insuff

(2) AB > CD Insuff too

(1) + (2) One ends up with 4C + 2B > 2B + CD (1)

On the other hand 2CB>CD so then 2B>D (2)

Now rearranging (1)

Is 2C + 2B > CD?

Well 2B > CD from (2) So given that sides have to be positive then yes

So C is our best choice

Hope it helps

Kudos rain!

Cheers!
J
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13932
Followers: 589

Kudos [?]: 167 [0], given: 0

Re: Does rectangle A have a greater perimeter than rectangle B? [#permalink]

### Show Tags

16 Apr 2015, 11:14
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Does rectangle A have a greater perimeter than rectangle B?   [#permalink] 16 Apr 2015, 11:14
Similar topics Replies Last post
Similar
Topics:
What is the perimeter of rectangle M? 1 11 Oct 2016, 01:25
3 What is the perimeter of rectangle ABCD ? 9 29 Sep 2011, 05:05
1 Is the value of the perimeter of rectangle R greater than 3 19 Jun 2011, 22:20
9 What is the perimeter of rectangle R? 11 26 Jun 2010, 06:58
7 Does the rectangle have an area less than 30? 8 18 Aug 2009, 17:43
Display posts from previous: Sort by