GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 15 Aug 2018, 08:20

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.

Close

Request Expert Reply

Confirm Cancel

If a rectangular region has perimeter P inches and area A sq

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
Joined: 06 Jul 2013
Posts: 1
If a rectangular region has perimeter P inches and area A sq  [#permalink]

Show Tags

New post Updated on: 21 Sep 2013, 08:58
14
70
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

67% (00:54) correct 33% (00:58) wrong based on 1254 sessions

HideShow timer Statistics

If a rectangular region has perimeter P inches and area A square inches, is the region square?

(1) P = 4/3*A
(2) P = 4√A

Originally posted by olifurlong on 21 Sep 2013, 07:03.
Last edited by Bunuel on 21 Sep 2013, 08:58, edited 2 times in total.
Renamed the topic and edited the question.
Most Helpful Community Reply
Intern
Intern
avatar
Joined: 08 Aug 2011
Posts: 22
GMAT ToolKit User
Re: If a rectangular region has perimeter P inches and area A sq  [#permalink]

Show Tags

New post 24 Mar 2014, 01:30
38
15
olifurlong wrote:
If a rectangular region has perimeter \(P\) inches and area \(A\) square inches, is the region square?

(1) \(P = \frac{4}{3}*A\)
(2) \(P = 4\sqrt{A}\)


Let the rectangular region have sides \(x\) and \(y\).
--> \(Perimeter = P = 2(x+y)\)
--> \(Area = A = xy\)

Question: Is \(x = y\) ?

(1) \(P = \frac{4}{3}*A\)

\(2(x+y) = (\frac{4}{3})xy\)

\(\frac{x+y}{xy} = \frac{4}{6} = \frac{2}{3}\)

\(\frac{1}{x} + \frac{1}{y} = \frac{4}{6} = \frac{2}{3}\)

So we have that the sum of two values equals \(\frac{2}{3}\)

If \(\frac{1}{x} = \frac{1}{y} = \frac{1}{3}\), then the answer is YES

If \(\frac{1}{x} = \frac{1}{6}\) and \(\frac{1}{y} =\frac{3}{6}\), then the answer is NO

Two different answers --> INSUFFICIENT


(2) \(P = 4\sqrt{A}\)

\(2(x + y) = 4\sqrt{xy}\)

\(x + y = 2\sqrt{xy}\)

\(x + y - 2\sqrt{xy} = 0\)

\((\sqrt{x} - \sqrt{y})^2 = 0\)

\(\sqrt{x} - \sqrt{y} = 0\)

\(\sqrt{x} = \sqrt{y}\)

\(x = y\)

--> SUFFICIENT
General Discussion
Manager
Manager
avatar
Joined: 10 Sep 2013
Posts: 79
Concentration: Sustainability, International Business
Re: PS- Gmat Prep exam pack 1- If a rectangular region has  [#permalink]

Show Tags

New post 21 Sep 2013, 07:29
37
10
olifurlong wrote:
If a rectangular region has perimeter P inches and area A square inches, is the region square?
1) P=4/3A
2)P=4√A


Lets try finding the relation between area and perimeter of a square.
We know the area of a square with length x (A) = x^2
The perimeter of the square (P) = 4x

Since P = 4x --> x = P/4

So, A = (P/4)^2
A =(P^2)/16
Therefore, P^2 = 16A
and P = 4*sqrtA

Therefore, B is suff to answer this question
_________________

Kudos if I helped :)

Intern
Intern
avatar
Joined: 09 Sep 2013
Posts: 4
Re: PS- Gmat Prep exam pack 1- If a rectangular region has  [#permalink]

Show Tags

New post 21 Sep 2013, 07:34
I think 2) is pretty obvious, it satisfies length = breadth condition.
For 1) if you substitute length = P/2 - breadth,
it can be written as
length = 2/3A - breadth.
Now substitute in Area formula A = length * breadth
the equation looks like this:

(breadth)^2 - (2/3A)breadth + A = 0

This clearly is not a form of (a-b)^2.
So the above equation has 2 distinct values of breadth. Hence it is not suff.
Intern
Intern
User avatar
Joined: 14 Aug 2013
Posts: 34
Location: United States
Concentration: Finance, Strategy
GMAT Date: 10-31-2013
GPA: 3.2
WE: Consulting (Consumer Electronics)
GMAT ToolKit User
Re: PS- Gmat Prep exam pack 1- If a rectangular region has  [#permalink]

Show Tags

New post 21 Sep 2013, 07:40
21
4
olifurlong wrote:
If a rectangular region has perimeter P inches and area A square inches, is the region square?
1) P=4/3A
2)P=4√A


for a rectangle Perimeter P=2(l+b)
Area A=l*b

From 1) 2(l+b)=4/3*(l*b)
6(l+b)=4(l*b)
3(l+b)=2(l*b)
this equation satisfies for l=3 and b=3, dimensions of a square and at l=6,b=2 dimensions of a rectangle..hence not sufficient

From 2) 2(l+b)=4√(l*b)
(l+b)=2√(l*b) squaring both sides
(l+b)^2=4l*b
(l-b)^2=0
l=b,which is a square, Sufficient
SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1852
Concentration: Finance
GMAT ToolKit User
Re: If a rectangular region has perimeter P inches and area A sq  [#permalink]

Show Tags

New post 30 Mar 2014, 09:50
7
6
Let me show you what I tried to do with this one

Is the figure a square?

Well if its a square then perimeter is 4x and area is x^2, pretty obvious up to here.

Now, statement 1

P=4/3A

So if the figure is in fact a square then it must follow that 4x=4/3 (x^2)

Is 12x = 4x^2?
Is 4x (x-3) = 0?
Is x = 3?

Well we can't solve this so insufficient

Statement 2 says that P= 4 (sqrt) A

So is 4x = 4 (sqrt (x^2))?

Well is 4x = 4 abs (x)?

If x is the side of the square then x>0, so 4x = 4x, so yes this is in fact a square

Answer is B

Hope this helps
Cheers :-D
J
Intern
Intern
avatar
Joined: 08 Aug 2011
Posts: 22
GMAT ToolKit User
Re: If a rectangular region has perimeter P inches and area A sq  [#permalink]

Show Tags

New post 30 Mar 2014, 10:33
jlgdr wrote:
Let me show you what I tried to do with this one

Is the figure a square?

Well if its a square then perimeter is 4x and area is x^2, pretty obvious up to here.

Now, statement 1

P=4/3A

So if the figure is in fact a square then it must follow that 4x=4/3 (x^2)

Is 12x = 4x^2?
Is 4x (x-3) = 0?
Is x = 3?

Well we can't solve this so insufficient

Statement 2 says that P= 4 (sqrt) A

So is 4x = 4 (sqrt (x^2))?

Well is 4x = 4 abs (x)?

If x is the side of the square then x>0, so 4x = 4x, so yes this is in fact a square

Answer is B

Hope this helps
Cheers :-D
J


Dropping an "if and only if" (iff) assumption into a question and evaluating whether it holds is my favorite method.

If anyone wants some fun practice with that, try the following:

Prove that line y=mx+b is tangent to circle x^2+y^2=r^2 iff b^2=r^2(1+m^2).

This question is obviously beyond GMAT scope, but in terms of practicing for the exam, I thinks it's quite useful.

Hint: a quadratic equation in one variable has one solution iff the discriminant is zero.

Posted from my mobile device
Manager
Manager
User avatar
Joined: 10 Mar 2013
Posts: 234
GMAT 1: 620 Q44 V31
GMAT 2: 690 Q47 V37
GMAT 3: 610 Q47 V28
GMAT 4: 700 Q50 V34
GMAT 5: 700 Q49 V36
GMAT 6: 690 Q48 V35
GMAT 7: 750 Q49 V42
GMAT 8: 730 Q50 V39
Re: If a rectangular region has perimeter P inches and area A sq  [#permalink]

Show Tags

New post 03 Oct 2014, 06:40
2
2
Reinfrank2011 wrote:
olifurlong wrote:
If a rectangular region has perimeter \(P\) inches and area \(A\) square inches, is the region square?

(1) \(P = \frac{4}{3}*A\)
(2) \(P = 4\sqrt{A}\)


Let the rectangular region have sides \(x\) and \(y\).
--> \(Perimeter = P = 2(x+y)\)
--> \(Area = A = xy\)

Question: Is \(x = y\) ?

(1) \(P = \frac{4}{3}*A\)

\(2(x+y) = (\frac{4}{3})xy\)

\(\frac{x+y}{xy} = \frac{4}{6} = \frac{2}{3}\)

\(\frac{1}{x} + \frac{1}{y} = \frac{4}{6} = \frac{2}{3}\)

So we have that the sum of two values equals \(\frac{2}{3}\)

If \(\frac{1}{x} = \frac{1}{y} = \frac{1}{3}\), then the answer is YES

If \(\frac{1}{x} = \frac{1}{6}\) and \(\frac{1}{y} =\frac{3}{6}\), then the answer is NO

Two different answers --> INSUFFICIENT


(2) \(P = 4\sqrt{A}\)

\(2(x + y) = 4\sqrt{xy}\)

\(x + y = 2\sqrt{xy}\)

\(x + y - 2\sqrt{xy} = 0\)

\((\sqrt{x} - \sqrt{y})^2 = 0\)

\(\sqrt{x} - \sqrt{y} = 0\)

\(\sqrt{x} = \sqrt{y}\)

\(x = y\)

--> SUFFICIENT


This is the clearest solution for this problem that I have seen! Well done, mate!
Retired Moderator
avatar
B
Joined: 17 Sep 2013
Posts: 369
Concentration: Strategy, General Management
GMAT 1: 730 Q51 V38
WE: Analyst (Consulting)
GMAT ToolKit User Premium Member Reviews Badge
Re: If a rectangular region has perimeter P inches and area A sq  [#permalink]

Show Tags

New post 03 Nov 2014, 00:58
2
My approach here :

From 1: 3(l+b)= 2lb

Put in
b= 10L (or anything that makes it a non square)

33L=20L^2
33=20L

There definitely is some value of L that will satisfy this..So a rectangle does exist..

b=l

6L = 2L^2
6=2L
L=3

So a square too exists...Done A is insuff

For B

the equation comes to: 2(L+B)=4\sqrt{LB}
Square and simplify
L^2 + B^2 - 2 LB = 0
which is (L-B)^2

you can also try the above approach here:
B=10 L
101L^2- 20L^2 = 0

Which aint true..So B is suff to say that it is indeed a square
_________________

Appreciate the efforts...KUDOS for all
Don't let an extra chromosome get you down..:P

Intern
Intern
User avatar
B
Status: Going the extra mile
Joined: 08 Feb 2014
Posts: 18
Location: Netherlands
Concentration: Strategy, International Business
GMAT 1: 470 Q37 V18
GMAT 2: 570 Q36 V32
GMAT 3: 560 Q37 V30
GMAT 4: 610 Q41 V34
Reviews Badge
If a rectangular region has perimeter P inches and area A sq  [#permalink]

Show Tags

New post 16 Dec 2014, 13:56
2
1
olifurlong wrote:
If a rectangular region has perimeter P inches and area A square inches, is the region square?

(1) P = 4/3*A
(2) P = 4√A


I would solve this question by simply plugging in numbers.

1. Let's assume the rectangular is indeed a square.
2. Let's assume the side of the square is 4.

If the side of this square is 4:
The perimeter would be 16 and the area would be 16 as well.

(S1) P = 4/3√A
If the rectangular is a square, all values for A area should correspond with the right value for P.
In my assumed case: if the perimeter is 16 , the area should be 16 too.
In this case : 16 is not equal to 4/3*16 , so we can't say for sure that this rectangle indeed is a square.

(S2) P = 4√A
16=4*√16
We got a match!

If you want to be sure , try any other plugin for a square.
Lets say the side of the rectangle is 2.
For it to be a square the perimeter should be 8(2+2+2+2) and the area is 4(2*2)
8=4√4
So as you can see , S2 will hold true for any plugin.A
_________________

Structural persistence is the key to succes .
Party hard, study harder.

Still bashing, will continue to do so , although it's important to chill aswell ; )
STUDY+CHILL=VICTORY

Manager
Manager
avatar
Joined: 14 Jul 2014
Posts: 94
If a rectangular region has perimeter P inches and area A sq  [#permalink]

Show Tags

New post 30 Mar 2015, 12:01
kusena wrote:
olifurlong wrote:
If a rectangular region has perimeter P inches and area A square inches, is the region square?
1) P=4/3A
2)P=4√A


for a rectangle Perimeter P=2(l+b)
Area A=l*b

From 1) 2(l+b)=4/3*(l*b)
6(l+b)=4(l*b)
3(l+b)=2(l*b)
this equation satisfies for l=3 and b=3, dimensions of a square and at l=6,b=2 dimensions of a rectangle..hence not sufficient

From 2) 2(l+b)=4√(l*b)
(l+b)=2√(l*b) squaring both sides
(l+b)^2=4l*b
(l-b)^2=0
l=b,which is a square,Sufficient



This can be Rhombus as well right?Even Rhombus has all sides equal. So how can we confidently say that it is a square. We dont know whether the diagonals are equal

Would really appreciate if someone can clear my doubt

Thanks
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12175
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If a rectangular region has perimeter P inches and area A sq  [#permalink]

Show Tags

New post 30 Mar 2015, 18:36
3
Hi buddyisraelgmat,

The prompt refers to a RECTANGULAR REGION, so the four corners must be 90 degrees each. Thus, we're dealing with either a rectangle of some kind or a square.

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Director
Director
User avatar
G
Joined: 23 Jan 2013
Posts: 598
Schools: Cambridge'16
Re: If a rectangular region has perimeter P inches and area A sq  [#permalink]

Show Tags

New post 30 Mar 2015, 22:12
Test scenarios

St.1 P=(4/3)A

take 2 as square side, we get P=8, A=4 - NO as square
take 3 as quare side, we get P=12, A=9 - YES as square

INSUFF

St.2 P=4√A

both 2 and 3 confirms this relation

SUFF

B
Retired Moderator
avatar
Joined: 29 Apr 2015
Posts: 862
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
GMAT ToolKit User Premium Member
Re: If a rectangular region has perimeter P inches and area A sq  [#permalink]

Show Tags

New post 19 Oct 2015, 11:58
4
1
olifurlong wrote:
If a rectangular region has perimeter P inches and area A square inches, is the region square?

(1) P = 4/3*A
(2) P = 4√A


I would also solve by plugging in values:

Let's create two rectangular regions which are squares:

Generally: P = 4s (where s is the side of a square) and \(A = s^2\)

First square with side 2:
P = 8 and A = 4

Second square with side 3:
P = 12 and A = 9

Statement 1: Gives you a yes on the square with side 3 because P = 4/3 * A but a no for the square with side 2.
Statement 2: \(P = 4*\sqrt{A}\) - this is true for both squares we created. Fair enough, Answer B.
_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

Senior Manager
Senior Manager
avatar
S
Joined: 18 Aug 2014
Posts: 325
GMAT ToolKit User Reviews Badge
Re: If a rectangular region has perimeter P inches and area A sq  [#permalink]

Show Tags

New post 03 Feb 2016, 12:48
kusena wrote:
olifurlong wrote:
From 2) 2(l+b)=4√(l*b)
(l+b)=2√(l*b) squaring both sides
(l+b)^2=4l*b
(l-b)^2=0
l=b,which is a square, Sufficient


What is happening at: (l+b)^2=4l*b to entirely get rid of the right hand side and flip the sign on the left hand side?
_________________

Please help me find my lost Kudo's bird

Current Student
avatar
S
Joined: 20 Mar 2014
Posts: 2643
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
Re: If a rectangular region has perimeter P inches and area A sq  [#permalink]

Show Tags

New post 03 Feb 2016, 13:34
1
redfield wrote:
kusena wrote:
olifurlong wrote:
From 2) 2(l+b)=4√(l*b)
(l+b)=2√(l*b) squaring both sides
(l+b)^2=4l*b
(l-b)^2=0
l=b,which is a square, Sufficient


What is happening at: (l+b)^2=4l*b to entirely get rid of the right hand side and flip the sign on the left hand side?


Once you get,\((l+b)^2=4l*b\) ---> open the brackets by employing the relation \((a+b)^2=a^2+b^2+2ab\),

You get, \(l^2+b^2+2lb=4lb\)---> \(l^2+b^2-2lb =0\) ---> recognize that this =\((l-b)^2\) as \((l-b)^2 = l^2+b^2-2lb\)

Thus, \((l-b)^2=0\)---> l=b. Hence, the given rectangle is a Square. Sufficient.

Hope this helps.
Intern
Intern
avatar
B
Joined: 13 Jan 2016
Posts: 46
GMAT 1: 710 Q47 V40
Reviews Badge
Re: If a rectangular region has perimeter P inches and area A sq  [#permalink]

Show Tags

New post 04 Sep 2016, 10:42
Can this problem be solved by picking numbers? Can someone show me how to? I tried to solve this by picking numbers and ended up getting into a rut. Thanks!
Board of Directors
User avatar
V
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3692
Premium Member Reviews Badge CAT Tests
Re: If a rectangular region has perimeter P inches and area A sq  [#permalink]

Show Tags

New post 04 Sep 2016, 11:03
ruggerkaz wrote:
Can this problem be solved by picking numbers? Can someone show me how to? I tried to solve this by picking numbers and ended up getting into a rut. Thanks!


How can you take the real values of length and breath unless you know if they are equal or not? I don't think this question could be solved picking real numbers.
_________________

My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub | Importance of an Error Log!
Verbal Resources: All SC Resources at one place | All CR Resources at one place
Blog: Subscribe to Question of the Day Blog

GMAT Club Inbuilt Error Log Functionality - View More.
New Visa Forum - Ask all your Visa Related Questions - here.

New! Best Reply Functionality on GMAT Club!



Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free

Manager
Manager
avatar
Joined: 24 May 2016
Posts: 163
Re: If a rectangular region has perimeter P inches and area A sq  [#permalink]

Show Tags

New post 20 Sep 2016, 11:14
reto wrote:
olifurlong wrote:
If a rectangular region has perimeter P inches and area A square inches, is the region square?

(1) P = 4/3*A
(2) P = 4√A


I would also solve by plugging in values:

Let's create two rectangular regions which are squares:

Generally: P = 4s (where s is the side of a square) and \(A = s^2\)

First square with side 2:
P = 8 and A = 4

Second square with side 3:
P = 12 and A = 9

Statement 1: Gives you a yes on the square with side 3 because P = 4/3 * A but a no for the square with side 2.
Statement 2: \(P = 4*\sqrt{A}\) - this is true for both squares we created. Fair enough, Answer B.


When you plug in numbers, you have to make sure that the numbers that you plug in lead you to a perimeter and an area that satisfy the condition mandated by the statement.

In the first statement, the values P = 8 and A = 4 do not satisfy the condition P = 4/3*A.

Hence, your approach is wrong.
Manager
Manager
avatar
B
Joined: 26 Mar 2017
Posts: 145
If a rectangular region has perimeter P inches and area A sq  [#permalink]

Show Tags

New post 15 Jun 2017, 11:35
1
mh not quite satisfied with the explanations :(

So Ill give it a try


If a rectangular region has perimeter P inches and area A square inches, is the region square?


Perimeter of a Square = 4x
Area of a Square = x^2

(1) P = 4/3*A

4x = 4/3*x^2
3x=x^2
x=3

so in order to be a square x has to be 3, but we don't know --> insufficient



(2) P = 4√A

4x=4√x^2
x=x


--> sufficient


cheers
_________________

I hate long and complicated explanations!

If a rectangular region has perimeter P inches and area A sq &nbs [#permalink] 15 Jun 2017, 11:35

Go to page    1   2    Next  [ 27 posts ] 

Display posts from previous: Sort by

If a rectangular region has perimeter P inches and area A sq

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.