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

It is currently 22 Sep 2018, 18:04

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

The area of one square is x 2 + 10x + 25 and the area of another squar

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49303
The area of one square is x 2 + 10x + 25 and the area of another squar  [#permalink]

Show Tags

New post 14 Feb 2016, 03:15
1
10
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

59% (02:05) correct 41% (02:11) wrong based on 374 sessions

HideShow timer Statistics

The area of one square is x^2 + 10x + 25 and the area of another square is 4x^2 − 12x + 9. If the sum of the perimeters of both squares is 32, what is the value of x?

A. 0
B. 2
C. 2.5
D. 4.67
E. 10

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Most Helpful Community Reply
SVP
SVP
User avatar
D
Joined: 26 Mar 2013
Posts: 1808
Reviews Badge CAT Tests
The area of one square is x 2 + 10x + 25 and the area of another squar  [#permalink]

Show Tags

New post 15 Feb 2016, 15:07
3
3
Bunuel wrote:
The area of one square is x^2 + 10x + 25 and the area of another square is 4x^2 − 12x + 9. If the sum of the perimeters of both squares is 32, what is the value of x?

A. 0
B. 2
C. 2.5
D. 4.67
E. 10



spotting the pattern of equations both are in form of (X+C)^2 so

A1= (x+5)^2 & A2= (2x-3)^2

L1= x+5 & L2= 2x-3

P1 = 4( x+5) & P2=4(2x-3)

P1+P2=32

4( x+5) +4(2x-3)=32..............> X=2

Answer: B
General Discussion
Current Student
User avatar
B
Status: DONE!
Joined: 05 Sep 2016
Posts: 390
Re: The area of one square is x 2 + 10x + 25 and the area of another squar  [#permalink]

Show Tags

New post 24 Oct 2016, 10:52
x^2 + 10x + 25 = (x+5)^2
Perimeter = 4(x+5)

4x^2 − 12x + 9 = (2x-3)^2
Perimeter = 4(2x-3)

4(x+5)+4(2x-3) = 32
x =2
Board of Directors
User avatar
P
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4033
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
Re: The area of one square is x 2 + 10x + 25 and the area of another squar  [#permalink]

Show Tags

New post 24 Oct 2016, 12:18
1
Bunuel wrote:
The area of one square is x^2 + 10x + 25 and the area of another square is 4x^2 − 12x + 9. If the sum of the perimeters of both squares is 32, what is the value of x?

A. 0
B. 2
C. 2.5
D. 4.67
E. 10

\(x^2 + 10x + 25\) = \(( x + 5 )^2\)

\(4x^2 − 12x + 9\) = \(( 2x - 3 )^2\)

Now, \(( x + 5 ) + ( 2x - 3 ) = 32\)

Or, \(3x + 2 = 32\)

Or, \(x = 10\)

Hence , answer will be (E)

_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Board of Directors
User avatar
P
Joined: 17 Jul 2014
Posts: 2683
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Premium Member Reviews Badge
Re: The area of one square is x 2 + 10x + 25 and the area of another squar  [#permalink]

Show Tags

New post 25 Nov 2016, 09:54
yep...agree...it's B - x=2

(x+5)^2 = Y(side of first sqare) ^2
y=x+5

(2x-3)^2 = z(side of the seconds quared)^2
z=2x-3

4y+4z = 32
y+z=8

2x-3+x+5=3x-2=8
3x=6
x=2

but 0 works too..so something is wrong with the question...

if x=0

x^2 + 10x + 25 = y^2
25 = y^2
y=5

4x^2 − 12x + 9 = z^2
9=z^2
z=3

y+z = 8

Bunuel - can you pls check, maybe instead of 0 to put 1 or 1.5? because if we plug it in - it works too..
Director
Director
User avatar
G
Joined: 24 Nov 2015
Posts: 542
Location: United States (LA)
Reviews Badge
Re: The area of one square is x 2 + 10x + 25 and the area of another squar  [#permalink]

Show Tags

New post 13 Mar 2017, 01:43
1
Abhishek009 wrote:
Bunuel wrote:
The area of one square is x^2 + 10x + 25 and the area of another square is 4x^2 − 12x + 9. If the sum of the perimeters of both squares is 32, what is the value of x?

A. 0
B. 2
C. 2.5
D. 4.67
E. 10

\(x^2 + 10x + 25\) = \(( x + 5 )^2\)

\(4x^2 − 12x + 9\) = \(( 2x - 3 )^2\)

Now, \(( x + 5 ) + ( 2x - 3 ) = 32\)

Or, \(3x + 2 = 32\)

Or, \(x = 10\)

Hence , answer will be (E)

apologies for seeing a mistake
sum of perimeter of 2 squares is given as 32 whereas you are considering the sum of 2 sides of the square as 32 which would be wrong pls correct the answer
correct answer is 4 (x+5) + 4(2x-3) = 32
so x = 2
correct answer - B
Manager
Manager
avatar
B
Joined: 16 Jan 2017
Posts: 63
GMAT 1: 620 Q46 V29
Re: The area of one square is x 2 + 10x + 25 and the area of another squar  [#permalink]

Show Tags

New post 23 Mar 2017, 10:53
Mhmmm, yeah I used a similar approach to mvcitor. and I seems that using this method would also make option A valid. So I assume I did it wrong. But basically if we call the side of square one y, and side of square two x,

4x + 4y = 32,
x + y = 8. So we are looking for values that give us this. So we plug in the available options into the initial formulas and when x + y = 8 that is the solution.

But as Victor has said option A would also work in this case too... So I assume that getting the correct solution was out of luck
Intern
Intern
avatar
B
Joined: 22 Oct 2016
Posts: 22
Re: The area of one square is x 2 + 10x + 25 and the area of another squar  [#permalink]

Show Tags

New post 28 Mar 2017, 08:09
hi vmelgargalan,

rhine29388 has correctly pointed.
4x+4y=32
4(x+5)+4(2x-3)=32
Upon simplifying x=2
I guess you and mvictor are trying to equate the values of x in both squares which has different roots.

_________________

Regards,
Sarugiri

Senior Manager
Senior Manager
User avatar
S
Joined: 24 Oct 2016
Posts: 285
Location: India
Concentration: Finance, International Business
Schools: IIMB
GMAT 1: 550 Q42 V28
GPA: 3.96
WE: Human Resources (Retail Banking)
Re: The area of one square is x 2 + 10x + 25 and the area of another squar  [#permalink]

Show Tags

New post 03 Apr 2017, 04:31
vmelgargalan wrote:
Mhmmm, yeah I used a similar approach to mvcitor. and I seems that using this method would also make option A valid. So I assume I did it wrong. But basically if we call the side of square one y, and side of square two x,

4x + 4y = 32,
x + y = 8. So we are looking for values that give us this. So we plug in the available options into the initial formulas and when x + y = 8 that is the solution.

But as Victor has said option A would also work in this case too... So I assume that getting the correct solution was out of luck


Hi,
i tried back solving , putting value of X in the equations ,
and getting A and B as a answer , like in option A put x=0 then equ.1 would be have 25 and equation 2, would have 9 then perimeter will be 5*4+3*4=32 :shock:
same process for option B , we get perimeter 7*4+4*1=32 :oops:
what's wrong in this can you clarify

thanks
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2835
Re: The area of one square is x 2 + 10x + 25 and the area of another squar  [#permalink]

Show Tags

New post 06 Apr 2017, 09:31
Bunuel wrote:
The area of one square is x^2 + 10x + 25 and the area of another square is 4x^2 − 12x + 9. If the sum of the perimeters of both squares is 32, what is the value of x?

A. 0
B. 2
C. 2.5
D. 4.67
E. 10


We have to determine the side length of each square. Since the area of the first square is x^2 + 10x + 25 = (x + 5)^2, its side is x + 5. Similarly, since the area of the second square is 4x^2 − 12x + 9 = (2x - 3)^2, its side is 2x - 3. Furthermore, the perimeter of the first square is 4(x + 5) and that of the second square is 4(2x - 3). Since the sum of the perimeters of the two squares is 32, we can create the following equation:

4(x + 5) + 4(2x - 3) = 32

4x + 20 + 8x - 12 = 32

12x + 8 = 32

12x = 24

x = 2

Answer: B
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Intern
Intern
avatar
B
Joined: 24 May 2016
Posts: 1
Location: India
Schools: CBS '21
GMAT 1: 740 Q50 V40
GPA: 3.63
Re: The area of one square is x 2 + 10x + 25 and the area of another squar  [#permalink]

Show Tags

New post 26 Aug 2018, 05:58
nks2611 wrote:
vmelgargalan wrote:
Mhmmm, yeah I used a similar approach to mvcitor. and I seems that using this method would also make option A valid. So I assume I did it wrong. But basically if we call the side of square one y, and side of square two x,

4x + 4y = 32,
x + y = 8. So we are looking for values that give us this. So we plug in the available options into the initial formulas and when x + y = 8 that is the solution.

But as Victor has said option A would also work in this case too... So I assume that getting the correct solution was out of luck


Hi,
i tried back solving , putting value of X in the equations ,
and getting A and B as a answer , like in option A put x=0 then equ.1 would be have 25 and equation 2, would have 9 then perimeter will be 5*4+3*4=32 :shock:
same process for option B , we get perimeter 7*4+4*1=32 :oops:
what's wrong in this can you clarify

thanks


I too plugged in values in haste and marked the option as A.
Side of a square cannot be negative so 4x^2-12x+9 which is (2x-3) has to be more than than 1.5.
GMAT Club Bot
Re: The area of one square is x 2 + 10x + 25 and the area of another squar &nbs [#permalink] 26 Aug 2018, 05:58
Display posts from previous: Sort by

The area of one square is x 2 + 10x + 25 and the area of another squar

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

Events & Promotions

PREV
NEXT


Copyright

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®.