Last visit was: 18 Jul 2024, 10:22 It is currently 18 Jul 2024, 10:22

Close

GRE Prep 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 GRE 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
Verbal Expert
Joined: 18 Apr 2015
Posts: 29119
Own Kudos [?]: 34136 [24]
Given Kudos: 25510
Send PM
Most Helpful Community Reply
avatar
Retired Moderator
Joined: 16 Oct 2019
Posts: 63
Own Kudos [?]: 173 [7]
Given Kudos: 21
Send PM
General Discussion
Verbal Expert
Joined: 18 Apr 2015
Posts: 29119
Own Kudos [?]: 34136 [2]
Given Kudos: 25510
Send PM
avatar
Intern
Intern
Joined: 08 Apr 2020
Posts: 20
Own Kudos [?]: 35 [12]
Given Kudos: 0
Send PM
Re: Within rectangle ACDF, both ABGH and BCDE are squares, and 3 [#permalink]
10
2
Bookmarks
Here's my work.
Attachments

x.PNG
x.PNG [ 220.46 KiB | Viewed 7718 times ]


Originally posted by 7jdjones7 on 31 May 2020, 17:39.
Last edited by 7jdjones7 on 31 May 2020, 20:00, edited 2 times in total.
avatar
Retired Moderator
Joined: 16 Oct 2019
Posts: 63
Own Kudos [?]: 173 [1]
Given Kudos: 21
Send PM
Re: Within rectangle ACDF, both ABGH and BCDE are squares, and 3 [#permalink]
1
7jdjones7 wrote:
Here's my work


Sir, recheck your calculations
avatar
Intern
Intern
Joined: 08 Apr 2020
Posts: 20
Own Kudos [?]: 35 [0]
Given Kudos: 0
Send PM
Re: Within rectangle ACDF, both ABGH and BCDE are squares, and 3 [#permalink]
vndnjn wrote:
7jdjones7 wrote:
Here's my work


Sir, recheck your calculations


Did it right when I solved it the first time around, rewrote it wrong for answer I posted. It's been revised.
Manager
Manager
Joined: 16 Aug 2021
Posts: 139
Own Kudos [?]: 46 [1]
Given Kudos: 86
Send PM
Re: Within rectangle ACDF, both ABGH and BCDE are squares, and 3 [#permalink]
1
Bookmarks
vndnjn wrote:
Area of ACDF: AF*DF = (x+y)*(2x+y)


how did you know that AF =x+y
and DF = 2x+y
where in the question this info is stated ??????????
Intern
Intern
Joined: 23 Aug 2021
Posts: 5
Own Kudos [?]: 7 [1]
Given Kudos: 1
Location: United States
Concentration: Entrepreneurship, Leadership
GRE 1: Q155 V156
Send PM
Re: Within rectangle ACDF, both ABGH and BCDE are squares, and 3 [#permalink]
1
mustafaaldory079 wrote:
vndnjn wrote:
Area of ACDF: AF*DF = (x+y)*(2x+y)


how did you know that AF =x+y
and DF = 2x+y
where in the question this info is stated ??????????


you can tell if you look at the bottom of the photo. y is one piece and x is the other and since the figure is a square that's how you know
Intern
Intern
Joined: 08 Aug 2022
Posts: 49
Own Kudos [?]: 33 [1]
Given Kudos: 98
Send PM
Re: Within rectangle ACDF, both ABGH and BCDE are squares, and 3 [#permalink]
1
Area of HGEF = xy
Since y is between 3x and 2x, we get
3x^2 > Area of HGEF > 2x^2

Now let's look at area of ACDF. It helps to break this into 3 pieces.
Area of the tiny square = x^2
Area of the tiny rectangle HGEF = xy
Area of the large square = (x+y)^2 = x^2 + 2xy + y^2
Total area of ACDF = 2x^2 + 3xy + y^2
Now we plug in our possible values of y, and we get: 20x^2 > area ACDF > 12x^2

Finally, we can look at the ratios:
20x^2 / 3X^2 > ACDF / HGEF < 12x^2 / 2x^2
6.67 > ACDF / HGEF < 6 --> This range is all greater than 5, so A is greater.
Intern
Intern
Joined: 08 Jun 2022
Posts: 8
Own Kudos [?]: 3 [0]
Given Kudos: 12
Send PM
Re: Within rectangle ACDF, both ABGH and BCDE are squares, and 3 [#permalink]
7jdjones7 wrote:
Here's my work.

can anyone please explain how DE is x+y?
Verbal Expert
Joined: 18 Apr 2015
Posts: 29119
Own Kudos [?]: 34136 [0]
Given Kudos: 25510
Send PM
Re: Within rectangle ACDF, both ABGH and BCDE are squares, and 3 [#permalink]
Expert Reply
Attachment:
#greprepclub Within rectangle ACDF, both ABGH and BCDE are squares.jpg
#greprepclub Within rectangle ACDF, both ABGH and BCDE are squares.jpg [ 11 KiB | Viewed 2243 times ]


The figure looks like above

Now , in this question is just to follow the wire until the solution. It is just a consequence or chain

We do know that ACDF is a rectangle so the side AC > CD

We do know that square ABGH have all sides =

we do know that 3x>y>2x

Suppose x= 2 then y =5

From this All sides of ABGH are 2

The parallel side CD is 2+5=7

because ACDF is a rectangle side AF =2+5=7 and CD as well =7

Moreover, we have a rectangle so the side AC must be AT LEAST 8 because it is longer than side CD which is 7

So AC is 8 and because AB is 2, the side portion labeled Z must be 6

The area or the entire rectangle is 8*7=56

HGEF must be also a rectangle because we do know that x = 2 BUT y=5

The area is 2*5=10

So the ratio ACDF to HGEF is = 56/10 and this must be greater than 5

The answer is A
User avatar
GRE Prep Club Legend
GRE Prep Club Legend
Joined: 07 Jan 2021
Posts: 4665
Own Kudos [?]: 69 [0]
Given Kudos: 0
Send PM
Re: Within rectangle ACDF, both ABGH and BCDE are squares, and 3 [#permalink]
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep 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.
Prep Club for GRE Bot
[#permalink]
Moderators:
GRE Instructor
48 posts
GRE Forum Moderator
25 posts
Moderator
1091 posts
GRE Instructor
218 posts

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