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

 It is currently 15 Oct 2019, 14:57 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  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 V
Joined: 02 Sep 2009
Posts: 58340
The area of one square is x 2 + 10x + 25 and the area of another squar  [#permalink]

Show Tags

1
11 00:00

Difficulty:   75% (hard)

Question Stats: 58% (02:22) correct 42% (02:37) wrong based on 397 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

_________________
SVP  V
Joined: 26 Mar 2013
Posts: 2345
The area of one square is x 2 + 10x + 25 and the area of another squar  [#permalink]

Show Tags

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

General Discussion
Current Student B
Status: DONE!
Joined: 05 Sep 2016
Posts: 358
Re: The area of one square is x 2 + 10x + 25 and the area of another squar  [#permalink]

Show Tags

1
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 D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4778
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
Re: The area of one square is x 2 + 10x + 25 and the area of another squar  [#permalink]

Show Tags

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 P
Joined: 17 Jul 2014
Posts: 2514
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30 GPA: 3.92
WE: General Management (Transportation)
Re: The area of one square is x 2 + 10x + 25 and the area of another squar  [#permalink]

Show Tags

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..
Senior Manager  G
Joined: 24 Nov 2015
Posts: 490
Location: United States (LA)
Re: The area of one square is x 2 + 10x + 25 and the area of another squar  [#permalink]

Show Tags

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  B
Joined: 16 Jan 2017
Posts: 60
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

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  B
Joined: 22 Oct 2016
Posts: 21
Re: The area of one square is x 2 + 10x + 25 and the area of another squar  [#permalink]

Show Tags

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  S
Joined: 24 Oct 2016
Posts: 251
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

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 same process for option B , we get perimeter 7*4+4*1=32 what's wrong in this can you clarify

thanks
Target Test Prep Representative G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2817
Re: The area of one square is x 2 + 10x + 25 and the area of another squar  [#permalink]

Show Tags

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

_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern  B
Joined: 24 May 2016
Posts: 14
Location: India
Schools: Yale '21 (D)
GMAT 1: 760 Q51 V42 GPA: 3.63
Re: The area of one square is x 2 + 10x + 25 and the area of another squar  [#permalink]

Show Tags

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 same process for option B , we get perimeter 7*4+4*1=32 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. Re: The area of one square is x 2 + 10x + 25 and the area of another squar   [#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

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