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

It is currently 12 Dec 2019, 01:21

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

A rectangular yard (white area) is surrounded by a hedge (shaded regio

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59685
A rectangular yard (white area) is surrounded by a hedge (shaded regio  [#permalink]

Show Tags

New post 13 Nov 2014, 09:37
2
17
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

69% (03:04) correct 31% (03:30) wrong based on 180 sessions

HideShow timer Statistics

Tough and Tricky questions: Geometry.



Image
Note: Figure not drawn to scale.

A rectangular yard (white area) is surrounded by a hedge (shaded region) with a length of 15 meters and a width of 12 meters, as shown in the figure above. The area of the yard is equal to the area of the hedge. If the ratio of the length of the hedge to the width of the hedge is the same as the ratio of the length of the yard to the width of the yard, what is the width, in meters, of the yard?


A. \(6\sqrt{2}\)

B. \(\frac{5}{4}\)

C. \(\frac{6}{\sqrt{2}}\)

D. \(7\frac{\sqrt{2}}{2}\)

E. \(\frac{6}{2}\)

Kudos for a correct solution.


Attachment:
s95-22.png
s95-22.png [ 5.19 KiB | Viewed 9174 times ]

_________________
Most Helpful Community Reply
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1727
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: A rectangular yard (white area) is surrounded by a hedge (shaded regio  [#permalink]

Show Tags

New post 13 Nov 2014, 19:26
20
2
Answer = A \(= 6\sqrt{2}\)

Total Area = 15*12 = 180

Given that Area of rectangular yard = Area of Hedge (shaded region) \(= \frac{180}{2} = 90\)

Lets say width of the yard = a

then length of the yard \(= \frac{90}{a}\)

Equating the ratios:

\(\frac{15}{12} = \frac{\frac{90}{a}}{a}\)

\(a^2 = 72\)

\(a = 6\sqrt{2}\)
General Discussion
Manager
Manager
avatar
Joined: 10 Sep 2014
Posts: 96
Re: A rectangular yard (white area) is surrounded by a hedge (shaded regio  [#permalink]

Show Tags

New post 13 Nov 2014, 12:39
5
3
Given a ratio of 5:4 I used length of 10 and width of 8 for the yard as a starting point. The area of the yard would then be 10x8=80m and the area of the hedge would be (15x12)-80 = 180-80=100. This tells us that with length 10 and width 8, the yard is not as big as the hedge. Therefore, the width must be larger than 8.

A. knowing that the square root of 2 is roughly 1.4, this answer is approx. 8.4. this is what we are looking for but we need to check to see if any other choices are larger than 8
B. too small
C. too small
D. too small
E. too small

Answer A!
Manager
Manager
User avatar
Joined: 23 Oct 2014
Posts: 84
Concentration: Marketing
Re: A rectangular yard (white area) is surrounded by a hedge (shaded regio  [#permalink]

Show Tags

New post 13 Nov 2014, 15:41
DangerPenguin wrote:
Given a ratio of 5:4 I used length of 10 and width of 8 for the yard as a starting point. The area of the yard would then be 10x8=80m and the area of the hedge would be (15x12)-80 = 180-80=100. This tells us that with length 10 and width 8, the yard is not as big as the hedge. Therefore, the width must be larger than 8.

A. knowing that the square root of 2 is roughly 1.4, this answer is approx. 8.4. this is what we are looking for but we need to check to see if any other choices are larger than 8
B. too small
C. too small
D. too small
E. too small

Answer A!


This was majorly brilliant. I was going through a ridiculous quadratic equation only to think, "There has to be an easier way to solve this," and here it is.
Manager
Manager
avatar
Joined: 22 Sep 2012
Posts: 121
Concentration: Strategy, Technology
WE: Information Technology (Computer Software)
Re: A rectangular yard (white area) is surrounded by a hedge (shaded regio  [#permalink]

Show Tags

New post 13 Nov 2014, 20:51
4
The ratio of the length to width of the yard = 5: 4

Let length = 5x and width = 4x

therefore we know , 5x * 4x = 15*12 - 5x*4x
=> x^2 = 4.5
Therefore, x = 3 * sqrt (1/2)

Therefore, width of the the yard = 4x = 4 * 3 * sqrt (1/2) = 6 * sqrt(2)

Hence A) is the answer
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59685
Re: A rectangular yard (white area) is surrounded by a hedge (shaded regio  [#permalink]

Show Tags

New post 14 Nov 2014, 09:37
2
Official Solution:

Image
Note: Figure not drawn to scale.

A rectangular yard (white area) is surrounded by a hedge (shaded region) with a length of 15 meters and a width of 12 meters, as shown in the figure above. The area of the yard is equal to the area of the hedge. If the ratio of the length of the hedge to the width of the hedge is the same as the ratio of the length of the yard to the width of the yard, what is the width, in meters, of the yard?

A. \(6\sqrt{2}\)
B. \(\frac{5}{4}\)
C. \(\frac{6}{\sqrt{2}}\)
D. \(7\frac{\sqrt{2}}{2}\)
E. \(\frac{6}{2}\)


Let the length of the yard be \(x\), and let the width of the yard be \(y\).

We are told that the length of the hedge is 15 meters and that the width of the hedge is 12 meters, so we can find the area of the yard and hedge combined using the formula for area of a rectangle: \(A_{\text{yard and hedge}} = \text{length} \times \text{width} = 15 \times 12 = 180\). Similarly, we can find the area of the yard: \(A_{yard} = xy\).

We are told that the area of the yard and the hedge are equal, so the area of the hedge must also be \(A_{hedge} = A_{yard} = xy\). We can use this information to write \(xy + xy = 2xy = 180\), or \(xy = 90\).

We know that the length and width of the yard are in the same ratio as the length and width of the hedge. We express this with a proportion: \(\frac{15}{12} = \frac{x}{y}\). Cross-multiply to get \(15y = 12x\). Simplify to get \(5y = 4x\).

Now we have two equations for \(x\) and \(y\). We will solve for these unknowns using substitution. Since we want to find the width, \(y\), we first solve for \(x\) in terms of \(y\). From the equation \(xy = 90\), we get \(x = \frac{90}{y}\). We plug this into \(5y = 4x\) and get \(5y = 4 \times \frac{90}{y} = \frac{360}{y}\). Dividing both sides by 5 and multiplying by \(y\), we find \(y^2 = 72\). We now take the square root of both sides to get \(y = \sqrt{72}\).

To simplify this square root, we look for a perfect square that is a factor of 72. We note that \(72 = 36 \times 2\), and so \(y = \sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2}\).

Answer: A.
_________________
Director
Director
User avatar
G
Joined: 23 Jan 2013
Posts: 522
Schools: Cambridge'16
Re: A rectangular yard (white area) is surrounded by a hedge (shaded regio  [#permalink]

Show Tags

New post 14 Nov 2014, 21:46
I missed the fact that one should 180/2=90, so

5x*4x=90
20x^2=90
x^2=90/20 --> x=3*sqrt2/2

finally, 3*sqrt2*4/2=6*sqrt2

A
Manager
Manager
avatar
B
Joined: 21 Dec 2014
Posts: 67
Re: A rectangular yard (white area) is surrounded by a hedge (shaded regio  [#permalink]

Show Tags

New post 05 Jun 2015, 06:13
I don't get it. Why is everyone taking the length and breadth of the hedge as 15 and 12? Wouldn't the area be 180 then? And we know the area is 90. So, shouldn't we equate X/Y = 15-X/12-Y??
Can anyone tell me what silly mistake i am doing?
Manager
Manager
avatar
B
Joined: 21 Dec 2014
Posts: 67
Re: A rectangular yard (white area) is surrounded by a hedge (shaded regio  [#permalink]

Show Tags

New post 05 Jun 2015, 06:16
I don't get it. Why is everyone taking the length and breadth of the hedge as 15 and 12? Wouldn't the area be 180 then? And we know the area is 90. So, shouldn't we equate X/Y = 15-X/12-Y??
Can anyone tell me what silly mistake i am doing?
Bunuel
PareshGmat
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59685
Re: A rectangular yard (white area) is surrounded by a hedge (shaded regio  [#permalink]

Show Tags

New post 05 Jun 2015, 06:36
AnubhavRao wrote:
I don't get it. Why is everyone taking the length and breadth of the hedge as 15 and 12? Wouldn't the area be 180 then? And we know the area is 90. So, shouldn't we equate X/Y = 15-X/12-Y??
Can anyone tell me what silly mistake i am doing?
Bunuel
PareshGmat


The ratio of the length of the hedge (15) to the width of the hedge (12) is the same as the ratio of the length of the yard (x) to the width of the yard (y): 15/12 = x/y

Attachment:
Untitled.png
Untitled.png [ 8.3 KiB | Viewed 7372 times ]

_________________
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59685
Re: A rectangular yard (white area) is surrounded by a hedge (shaded regio  [#permalink]

Show Tags

New post 05 Jun 2015, 06:41
AnubhavRao wrote:
I don't get it. Why is everyone taking the length and breadth of the hedge as 15 and 12? Wouldn't the area be 180 then? And we know the area is 90. So, shouldn't we equate X/Y = 15-X/12-Y??
Can anyone tell me what silly mistake i am doing?
Bunuel
PareshGmat


Similar questions to practice about rectangles:
a-square-wooden-plaque-has-a-square-brass-inlay-in-the-89215.html
a-border-of-uniform-width-is-placed-around-a-rectangular-144434.html
a-rectangular-yard-is-20-yards-wide-and-40-yards-long-it-is-8453.html
the-figure-above-represents-a-square-plot-measuring-x-feet-o-160568.html
a-rectangular-photograph-is-surrounded-by-a-border-that-is-72686.html
harriet-wants-to-put-up-fencing-around-three-sides-of-her-127082.html

Similar questions to practice about circles:
marty-s-pizza-shop-guarantees-that-their-pizzas-all-have-a-148428.html
a-circular-lawn-with-a-radius-of-5-meters-is-surrounded-by-a-154737.html
the-figure-above-shows-a-circular-flower-bed-with-its-cente-144448.html
the-figure-shows-the-top-side-of-a-circular-medallion-made-o-101845.html
_________________
Manager
Manager
avatar
B
Joined: 21 Dec 2014
Posts: 67
Re: A rectangular yard (white area) is surrounded by a hedge (shaded regio  [#permalink]

Show Tags

New post 05 Jun 2015, 06:44
Ohhh so those aren't the actual dimensions but their ratios. Dimensions will be less than those so as to have an area of 90.
My bad.
Thank you for swift response, Bunuel :)
Board of Directors
User avatar
P
Joined: 17 Jul 2014
Posts: 2491
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Reviews Badge
Re: A rectangular yard (white area) is surrounded by a hedge (shaded regio  [#permalink]

Show Tags

New post 28 Dec 2015, 16:41
180-lw=lw or 180=2lw or lw=90.

now l/w=5/4

5l/4 * l = 90
l^2 = 90*4/5
l^2 = 72
l= sqrt(72)
sqrt(72) = 6(sqrt2)

A.
VP
VP
avatar
P
Joined: 07 Dec 2014
Posts: 1217
Re: A rectangular yard (white area) is surrounded by a hedge (shaded regio  [#permalink]

Show Tags

New post 01 Jan 2016, 13:37
let L,W=length and width of hedge
let l,w=length and width of yard
LW=180m^2
lw=LW-lw=90m^2
15/12=5/4
(5x)(4x)=90
x^2=9/2
x=3/sqrt2
4x=(6)(sqrt2) meters width of yard
Senior Manager
Senior Manager
User avatar
S
Joined: 08 Jun 2015
Posts: 418
Location: India
GMAT 1: 640 Q48 V29
GMAT 2: 700 Q48 V38
GPA: 3.33
Reviews Badge
Re: A rectangular yard (white area) is surrounded by a hedge (shaded regio  [#permalink]

Show Tags

New post 11 May 2016, 10:20
A it is well explained above !
_________________
" The few , the fearless "
Manager
Manager
User avatar
S
Joined: 29 Dec 2018
Posts: 82
Location: India
WE: Marketing (Real Estate)
A rectangular yard (white area) is surrounded by a hedge (shaded regio  [#permalink]

Show Tags

New post 13 Jul 2019, 22:55
PareshGmat wrote:
Answer = A \(= 6\sqrt{2}\)

Total Area = 15*12 = 180

Given that Area of rectangular yard = Area of Hedge (shaded region) \(= \frac{180}{2} = 90\)



Dear Moderators chetan2u, VeritasKarishma gmatbusters
Can you help ? I am unable to understand why did we divide the area of 180 by 2 to get 90
_________________
Keep your eyes on the prize: 750
Retired Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1321
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
CAT Tests
Re: A rectangular yard (white area) is surrounded by a hedge (shaded regio  [#permalink]

Show Tags

New post 13 Jul 2019, 23:23
Total Area = 15*12 = 180

Given that Area of rectangular yard = Area of Hedge (shaded region)
So, let Area of rectangular yard = Area of Hedge (shaded region) = x
hence, x+x = total area = 180,
2x = 180,
or x = 180/2 = 90.

Area of rectangular yard = Area of Hedge (shaded region) \(= \frac{180}{2} = 90\)

DarkHorse2019 wrote:
PareshGmat wrote:
Answer = A \(= 6\sqrt{2}\)

Total Area = 15*12 = 180

Given that Area of rectangular yard = Area of Hedge (shaded region) \(= \frac{180}{2} = 90\)



Dear Moderators chetan2u, VeritasKarishma gmatbusters
Can you help ? I am unable to understand why did we divide the area of 180 by 2 to get 90

_________________
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9871
Location: Pune, India
Re: A rectangular yard (white area) is surrounded by a hedge (shaded regio  [#permalink]

Show Tags

New post 15 Jul 2019, 04:53
DarkHorse2019 wrote:
PareshGmat wrote:
Answer = A \(= 6\sqrt{2}\)

Total Area = 15*12 = 180

Given that Area of rectangular yard = Area of Hedge (shaded region) \(= \frac{180}{2} = 90\)



Dear Moderators chetan2u, VeritasKarishma gmatbusters
Can you help ? I am unable to understand why did we divide the area of 180 by 2 to get 90


Area of yard (white rectangle) = Area of hedge (shaded region)

Total area of yard + hedge = 15*12 = 180 (Area of the complete big rectangle)

So area of just the yard = 180/2 = 90

Ratio of length:width = 5:4. Say the length and width are 5x and 4x.

\(5x*4x = 90\)
\(x = 3/\sqrt{2}\)

\(Width = 4x = 4*3/\sqrt{2} = 6\sqrt{2}\)
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT Club Bot
Re: A rectangular yard (white area) is surrounded by a hedge (shaded regio   [#permalink] 15 Jul 2019, 04:53
Display posts from previous: Sort by

A rectangular yard (white area) is surrounded by a hedge (shaded regio

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





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