Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 26 May 2017, 05:43

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# ABCD is a square with a side y, and JKLM is a side x.

Author Message
TAGS:

### Hide Tags

Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4038
Followers: 1416

Kudos [?]: 6776 [2] , given: 84

ABCD is a square with a side y, and JKLM is a side x. [#permalink]

### Show Tags

02 May 2013, 11:42
2
KUDOS
Expert's post
00:00

Difficulty:

5% (low)

Question Stats:

89% (01:56) correct 11% (01:01) wrong based on 82 sessions

### HideShow timer Statistics

Attachment:

square in a square.png [ 14.6 KiB | Viewed 1999 times ]

ABCD is a square with a side y, and JKLM is a side x. If Rectangle S (not shown) with length (x + y) has the same area as the shaded region above, what is the width of Rectangle S?
(A) x
(B) y
(C) y + x
(D) y - x
(E) $$y^2 - x^2$$

For a complete solution, see this post:
http://magoosh.com/gmat/2013/three-alge ... -the-gmat/
[Reveal] Spoiler: OA

_________________

Mike McGarry
Magoosh Test Prep

 Magoosh Discount Codes Optimus Prep Discount Codes Manhattan GMAT Discount Codes
Intern
Joined: 06 Jan 2013
Posts: 24
GPA: 3
WE: Engineering (Transportation)
Followers: 0

Kudos [?]: 60 [1] , given: 9

Re: ABCD is a square with a side y, and JKLM is a side x. [#permalink]

### Show Tags

02 May 2013, 11:52
1
KUDOS
We have the area of the shaded region:-(y^2)-(x^2)
Now the shaded area can be factorised as (y+x)(y-x).
The question tells us that a rectangle of length (x+y) has the same area (y^2-x^2).
Hence, the width of the rectangle has to be (y-x)

_________________

If you shut your door to all errors, truth will be shut out.

Manager
Status: Pushing Hard
Affiliations: GNGO2, SSCRB
Joined: 30 Sep 2012
Posts: 89
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.33
WE: Analyst (Health Care)
Followers: 1

Kudos [?]: 84 [1] , given: 11

Re: ABCD is a square with a side y, and JKLM is a side x. [#permalink]

### Show Tags

02 May 2013, 21:14
1
KUDOS
mikemcgarry wrote:
Attachment:
square in a square.png

ABCD is a square with a side y, and JKLM is a side x. If Rectangle S (not shown) with length (x + y) has the same area as the shaded region above, what is the width of Rectangle S?
(A) x
(B) y
(C) y + x
(D) y - x
(E) $$y^2 - x^2$$

For a complete solution, see this post:
http://magoosh.com/gmat/2013/three-alge ... -the-gmat/

Hi Mike,

Sorry for Question ....but do you really think ?? This is a 700- level Question ??? I did this in around 30 seconds .......... Pls advise. Thanks !! in Advance ............
_________________

If you don’t make mistakes, you’re not working hard. And Now that’s a Huge mistake.

Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4038
Followers: 1416

Kudos [?]: 6776 [1] , given: 84

Re: ABCD is a square with a side y, and JKLM is a side x. [#permalink]

### Show Tags

03 May 2013, 11:07
1
KUDOS
Expert's post
manishuol wrote:
Hi Mike,
Sorry for Question ....but do you really think ?? This is a 700- level Question ??? I did this in around 30 seconds .......... Pls advise. Thanks !! in Advance ............

To be perfectly honest, many of the questions I post are ones I have recently written. I like to share brand new content with folks who are studying for the GMAT. If a question has been in the Magoosh product for a while, then hundreds of people will have answered it, and we can see the percentage correct and thus judge with considerable accuracy the difficulty of the question. By contrast, when I write a brand new question and post it on GC, the system requires me to estimate a difficulty level, and I have to take my best guess. To be perfectly blunt, I am conversant in multivariable calculus and advanced statistics, so pretty much all GMAT math looks easy to me ---- it's very hard for me to guess what other folks are going to find easy or difficult. I am estimating from my experience of the wide array of GMAT students I have encountered.

With this particular question, one has to see, first of all, that the shaded area is the big square minus the small square, y^2 - x^2. Then, one has to see one can factor y^2 - x^2 = (y + x)(y - x). If one sees both of those right away, this problem is trivially easy. I would say, though, not all GMAT test takers will have both of those observations right at their fingertips. For some folks, either one or both of those will be completely befuddling. It's always the case, in any GMAT math problem --- if you see all the things that are necessary to see, the problem becomes quite easy. All of math has the quality that it's impossibly difficulty when you don't know what to do and trivially easy when you do know what to do. Does all this make this question an 700 question? I don't know, but I will say, I believe it says good things about your mathematical abilities that you were able to solve it so easily. Congratulations.

Mike
_________________

Mike McGarry
Magoosh Test Prep

Senior Manager
Joined: 21 Jan 2010
Posts: 329
Followers: 3

Kudos [?]: 195 [0], given: 12

Re: ABCD is a square with a side y, and JKLM is a side x. [#permalink]

### Show Tags

03 May 2013, 11:34
Just think on the lines of the question. You have to find the other side and you are given the area of the rectangle.
Area = L x B
L = x+ y
Area = y^2 - x^2
Hence B = y -x.
Manager
Status: Pushing Hard
Affiliations: GNGO2, SSCRB
Joined: 30 Sep 2012
Posts: 89
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.33
WE: Analyst (Health Care)
Followers: 1

Kudos [?]: 84 [0], given: 11

Re: ABCD is a square with a side y, and JKLM is a side x. [#permalink]

### Show Tags

03 May 2013, 18:46
mikemcgarry wrote:
manishuol wrote:
Hi Mike,
Sorry for Question ....but do you really think ?? This is a 700- level Question ??? I did this in around 30 seconds .......... Pls advise. Thanks !! in Advance ............

To be perfectly honest, many of the questions I post are ones I have recently written. I like to share brand new content with folks who are studying for the GMAT. If a question has been in the Magoosh product for a while, then hundreds of people will have answered it, and we can see the percentage correct and thus judge with considerable accuracy the difficulty of the question. By contrast, when I write a brand new question and post it on GC, the system requires me to estimate a difficulty level, and I have to take my best guess. To be perfectly blunt, I am conversant in multivariable calculus and advanced statistics, so pretty much all GMAT math looks easy to me ---- it's very hard for me to guess what other folks are going to find easy or difficult. I am estimating from my experience of the wide array of GMAT students I have encountered.

With this particular question, one has to see, first of all, that the shaded area is the big square minus the small square, y^2 - x^2. Then, one has to see one can factor y^2 - x^2 = (y + x)(y - x). If one sees both of those right away, this problem is trivially easy. I would say, though, not all GMAT test takers will have both of those observations right at their fingertips. For some folks, either one or both of those will be completely befuddling. It's always the case, in any GMAT math problem --- if you see all the things that are necessary to see, the problem becomes quite easy. All of math has the quality that it's impossibly difficulty when you don't know what to do and trivially easy when you do know what to do. Does all this make this question an 700 question? I don't know, but I will say, I believe it says good things about your mathematical abilities that you were able to solve it so easily. Congratulations.

Mike

Thanks !! for your Detailed Genuine reply ... Mike !! I appreciate that.
_________________

If you don’t make mistakes, you’re not working hard. And Now that’s a Huge mistake.

MBA Section Director
Status: Back to work...
Affiliations: GMAT Club
Joined: 22 Feb 2012
Posts: 4319
Location: India
City: Pune
GMAT 1: 680 Q49 V34
GPA: 3.4
Followers: 440

Kudos [?]: 3179 [0], given: 2301

Re: ABCD is a square with a side y, and JKLM is a side x. [#permalink]

### Show Tags

04 May 2013, 09:32
mikemcgarry wrote:
manishuol wrote:
Hi Mike,
Sorry for Question ....but do you really think ?? This is a 700- level Question ??? I did this in around 30 seconds .......... Pls advise. Thanks !! in Advance ............

To be perfectly honest, many of the questions I post are ones I have recently written. I like to share brand new content with folks who are studying for the GMAT. If a question has been in the Magoosh product for a while, then hundreds of people will have answered it, and we can see the percentage correct and thus judge with considerable accuracy the difficulty of the question. By contrast, when I write a brand new question and post it on GC, the system requires me to estimate a difficulty level, and I have to take my best guess. To be perfectly blunt, I am conversant in multivariable calculus and advanced statistics, so pretty much all GMAT math looks easy to me ---- it's very hard for me to guess what other folks are going to find easy or difficult. I am estimating from my experience of the wide array of GMAT students I have encountered.

With this particular question, one has to see, first of all, that the shaded area is the big square minus the small square, y^2 - x^2. Then, one has to see one can factor y^2 - x^2 = (y + x)(y - x). If one sees both of those right away, this problem is trivially easy. I would say, though, not all GMAT test takers will have both of those observations right at their fingertips. For some folks, either one or both of those will be completely befuddling. It's always the case, in any GMAT math problem --- if you see all the things that are necessary to see, the problem becomes quite easy. All of math has the quality that it's impossibly difficulty when you don't know what to do and trivially easy when you do know what to do. Does all this make this question an 700 question? I don't know, but I will say, I believe it says good things about your mathematical abilities that you were able to solve it so easily. Congratulations.

Mike

100% agree with the highlighted portion.

It is because, these things are fitted in our brain so firmly that whenever we see $$y^2$$ - $$x^2$$, we quickly go on to factories it as (y+x)(y-x). but this may not so easy for some students.

By the way, the equation (y+x)(y-x) = (x+y)W would have become a dangerous trap in if y and x had not been the lengths.
In that case we would not be able to divide both sides of the equation by (x+y) without knowing the exact values of x and y.
Consider if y=-x
I initially considered this possibility assuming that Mike sir will not give us such an easy task.

Regards,

Narenn
_________________
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4038
Followers: 1416

Kudos [?]: 6776 [0], given: 84

Re: ABCD is a square with a side y, and JKLM is a side x. [#permalink]

### Show Tags

06 May 2013, 12:59
manishuol wrote:
Thanks !! for your Detailed Genuine reply ... Mike !! I appreciate that.

You are quite welcome.
Mike
_________________

Mike McGarry
Magoosh Test Prep

Intern
Status: Attending Duke in May!
Joined: 08 Jan 2013
Posts: 31
Location: United States (NC)
GMAT 1: 640 Q42 V35
Followers: 1

Kudos [?]: 35 [0], given: 18

Re: ABCD is a square with a side y, and JKLM is a side x. [#permalink]

### Show Tags

09 May 2013, 00:34
mikemcgarry wrote:
Attachment:
square in a square.png

ABCD is a square with a side y, and JKLM is a side x. If Rectangle S (not shown) with length (x + y) has the same area as the shaded region above, what is the width of Rectangle S?
(A) x
(B) y
(C) y + x
(D) y - x
(E) $$y^2 - x^2$$

For a complete solution, see this post:
http://magoosh.com/gmat/2013/three-alge ... -the-gmat/

Agree with everything Mike said above. My brain didn't even jump to factoring $$y^2-x^2$$, it wanted to plug numbers in right away.

I set y=4
and x=1

y+x=5
Area of shaded region equals 15

$$15 = 5 x (z)$$

z = 3 = y-x, Answer D

MUCH longer than factoring $$y^2-x^2$$ out, but I still got there in under 2 minutes.
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15459
Followers: 649

Kudos [?]: 209 [0], given: 0

Re: ABCD is a square with a side y, and JKLM is a side x. [#permalink]

### Show Tags

14 Sep 2015, 05:50
Hello from the GMAT Club BumpBot!

Thanks to another GMAT 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.
_________________
Re: ABCD is a square with a side y, and JKLM is a side x.   [#permalink] 14 Sep 2015, 05:50
Similar topics Replies Last post
Similar
Topics:
2 ABCD is a square of side 3, and E and F are the mid points of sides AB 3 27 Mar 2017, 10:27
4 ABCD is a square. If the shaded area is A, the side of the s 5 28 Apr 2016, 20:58
12 In the figure, each side of square ABCD has length 1, the length of li 8 30 Sep 2014, 00:40
17 In the figure, each side of square ABCD has length 1, the 10 08 Sep 2014, 04:57
209 In the figure, each side of square ABCD has length 1, the length of li 30 13 May 2017, 14:13
Display posts from previous: Sort by