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

 It is currently 22 Sep 2018, 06:43

### 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

# ABCD is a square, and EFGH is a square, each vertex of which is on a s

Author Message
TAGS:

### Hide Tags

Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4664
ABCD is a square, and EFGH is a square, each vertex of which is on a s  [#permalink]

### Show Tags

27 May 2016, 17:05
00:00

Difficulty:

65% (hard)

Question Stats:

59% (02:03) correct 41% (02:25) wrong based on 97 sessions

### HideShow timer Statistics

Attachment:

Square inside square.png [ 4.88 KiB | Viewed 2143 times ]

ABCD is a square, and EFGH is a square, each vertex of which is on a side of ABCD. What is the ratio of the area of square EFGH to the area of square ABCD?

Statement #1: AE:AB = 4:7

Statement #2: The ratio of the area of triangle AHE to the area of square EFGH is 0.24

Geometry is a truly beautiful subject! This question is one of a set of ten practice DS questions about geometry. To see the others, as well as the OE for this particular question, see:
GMAT Data Sufficiency Geometry Practice Questions

Mike

_________________

Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

 Magoosh Discount Codes Economist GMAT Tutor Discount Codes e-GMAT Discount Codes
Math Expert
Joined: 02 Aug 2009
Posts: 6800
Re: ABCD is a square, and EFGH is a square, each vertex of which is on a s  [#permalink]

### Show Tags

27 May 2016, 19:53
mikemcgarry wrote:
Attachment:
Square inside square.png

ABCD is a square, and EFGH is a square, each vertex of which is on a side of ABCD. What is the ratio of the area of square EFGH to the area of square ABCD?

Statement #1: AE:AB = 4:7

Statement #2: The ratio of the area of triangle AHE to the area of square EFGH is 0.24

Geometry is a truly beautiful subject! This question is one of a set of ten practice DS questions about geometry. To see the others, as well as the OE for this particular question, see:
GMAT Data Sufficiency Geometry Practice Questions

Mike

we have two squares...
the one inside, EFGH, will have least area when its vertex is in center of the sides.....
and will become max as it moves closer to the vertex of the bigger square ABCD..

Second point is that all the triangles formed on the vertex of ABCD will be similar...

lets see the statement

Statement #1: AE:AB = 4:7
let the common ratio be x....
so AE = 4x and AB = 7x, so BE = 3x...

side of ABCD = 7x and side of EFGH = HYP of triangle whose sides are 3x and 4x = $$\sqrt{(3x)^2+(4x)^2}$$..
ratio =$$\frac{7x*7x}{\sqrt{(3x)^2+(4x)^2}^2}$$..
variable x will get cancelled out and we will have a numeric value...
Suff

Statement #2: The ratio of the area of triangle AHE to the area of square EFGH is 0.24
all triangles are similar so their Area = 0.24*Area of EFGH*4.....
Let area of square EFGH = x
Area of ABCD = Area of 4 triangles + area of EFGH = 0.24*x*4 + x...

ratio =$$\frac{0.24*x*4 + x}{x}$$ = 1.96/1
Suff

D
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Intern
Joined: 28 Dec 2015
Posts: 40
Re: ABCD is a square, and EFGH is a square, each vertex of which is on a s  [#permalink]

### Show Tags

05 Jul 2016, 03:13
chetan2u wrote:
mikemcgarry wrote:
Attachment:
Square inside square.png

ABCD is a square, and EFGH is a square, each vertex of which is on a side of ABCD. What is the ratio of the area of square EFGH to the area of square ABCD?

Statement #1: AE:AB = 4:7

Statement #2: The ratio of the area of triangle AHE to the area of square EFGH is 0.24

Geometry is a truly beautiful subject! This question is one of a set of ten practice DS questions about geometry. To see the others, as well as the OE for this particular question, see:
GMAT Data Sufficiency Geometry Practice Questions

Mike

we have two squares...
the one inside, EFGH, will have least area when its vertex is in center of the sides.....
and will become max as it moves closer to the vertex of the bigger square ABCD..

Second point is that all the triangles formed on the vertex of ABCD will be similar...

lets see the statement

Statement #1: AE:AB = 4:7
let the common ratio be x....
so AE = 4x and AB = 7x, so BE = 3x...

side of ABCD = 7x and side of EFGH = HYP of triangle whose sides are 3x and 4x = $$\sqrt{(3x)^2+(4x)^2}$$..
ratio =$$\frac{7x*7x}{\sqrt{(3x)^2+(4x)^2}^2}$$..
variable x will get cancelled out and we will have a numeric value...
Suff

Statement #2: The ratio of the area of triangle AHE to the area of square EFGH is 0.24
all triangles are similar so their Area = 0.24*Area of EFGH*4.....
Let area of square EFGH = x
Area of ABCD = Area of 4 triangles + area of EFGH = 0.24*x*4 + x...

ratio =$$\frac{0.24*x*4 + x}{x}$$ = 1.96/1
Suff

D

Dear sir,

I don't get the first part...
AE/AB=4/7
AE/AE+EB=4/7
AE/EB=4/3

So,AE=4x and EB=3x
But then how EBF or any other triangle is a 3-4-5 triangle??
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4664
Re: ABCD is a square, and EFGH is a square, each vertex of which is on a s  [#permalink]

### Show Tags

05 Jul 2016, 10:31
1
Ashishsteag wrote:
Dear sir,

I don't get the first part...
AE/AB=4/7
AE/AE+EB=4/7
AE/EB=4/3

So,AE=4x and EB=3x
But then how EBF or any other triangle is a 3-4-5 triangle??

Dear Ashishsteag

This is Mike McGarry, the author of this question. I'm happy to respond.

So I believe you get that, for some unknown x, AE = 4x and EB = 3x.

You see, the entire figure has four-fold symmetry. We could rotate the entire shape by 90 degrees and it would be the same. The four triangles, {AEH, BFE, CGF, and DHG} have to be entirely congruent. Thus,

AE = BF = CG = DH = 4x
AH = BE = CF = GD = 3x

Thus, all of them are 3-4-5 triangles.

Does this make sense?
Mike
_________________

Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Intern
Joined: 28 Dec 2015
Posts: 40
Re: ABCD is a square, and EFGH is a square, each vertex of which is on a s  [#permalink]

### Show Tags

05 Jul 2016, 22:30
mikemcgarry wrote:
Ashishsteag wrote:
Dear sir,

I don't get the first part...
AE/AB=4/7
AE/AE+EB=4/7
AE/EB=4/3

So,AE=4x and EB=3x
But then how EBF or any other triangle is a 3-4-5 triangle??

Dear Ashishsteag

This is Mike McGarry, the author of this question. I'm happy to respond.

So I believe you get that, for some unknown x, AE = 4x and EB = 3x.

You see, the entire figure has four-fold symmetry. We could rotate the entire shape by 90 degrees and it would be the same. The four triangles, {AEH, BFE, CGF, and DHG} have to be entirely congruent. Thus,

AE = BF = CG = DH = 4x
AH = BE = CF = GD = 3x

Thus, all of them are 3-4-5 triangles.

Does this make sense?
Mike

Thanx a lot mike....:D
Non-Human User
Joined: 09 Sep 2013
Posts: 8145
Re: ABCD is a square, and EFGH is a square, each vertex of which is on a s  [#permalink]

### Show Tags

12 Jul 2018, 12:03
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, and EFGH is a square, each vertex of which is on a s &nbs [#permalink] 12 Jul 2018, 12:03
Display posts from previous: Sort by

# Events & Promotions

 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®.