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

 It is currently 22 Sep 2018, 06:10

### 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

# In the figure above, the measure of angle EAB in triangle ABE is 90...

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 12 Feb 2015
Posts: 431
In the figure above, the measure of angle EAB in triangle ABE is 90...  [#permalink]

### Show Tags

Updated on: 29 Jun 2018, 11:05
4
00:00

Difficulty:

95% (hard)

Question Stats:

46% (01:44) correct 54% (02:10) wrong based on 67 sessions

### HideShow timer Statistics

In the figure above, the measure of angle EAB in triangle ABE is 90 degrees, and BCDE is a square. What is the length of AB?

(1) The length of AE is 12, and the ratio of the area of triangle ABE to the area of square BCDE is $$\frac{6}{25}$$.

(2) The perimeter of square BCDE is 80 and the ratio of the length of AE to the length of AB is 3 to 4.

Attachment:

ZZ1.jpg [ 12.5 KiB | Viewed 645 times ]

_________________

"Please hit +1 Kudos if you like this post"

_________________
Manish

"Only I can change my life. No one can do it for me"

Originally posted by CAMANISHPARMAR on 29 Jun 2018, 11:00.
Last edited by Bunuel on 29 Jun 2018, 11:05, edited 1 time in total.
Formatted.
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 857
WE: Supply Chain Management (Energy and Utilities)
Re: In the figure above, the measure of angle EAB in triangle ABE is 90...  [#permalink]

### Show Tags

29 Jun 2018, 12:20
CAMANISHPARMAR wrote:

In the figure above, the measure of angle EAB in triangle ABE is 90 degrees, and BCDE is a square. What is the length of AB?

(1) The length of AE is 12, and the ratio of the area of triangle ABE to the area of square BCDE is $$\frac{6}{25}$$.

(2) The perimeter of square BCDE is 80 and the ratio of the length of AE to the length of AB is 3 to 4.

Attachment:
ZZ1.jpg

Question stem:- AB=?
Statement1:-

Given $$\frac{0.5*AE *AB}{EB^2}=\frac{6}{25}$$
Let AB=x unit , hence $$x^2+12^2=EB^2$$
Substituting , we have, $$\frac{0.5*12*x}{x^2+12^2}=\frac{6}{25}$$
Or,$$x^2-25x+12^2=0$$
Since we have two positive roots which implies more than one value of AB. So, st1 is insufficient.

Statement2:-
Given,$$\frac{AE}{AB}=\frac{3}{4}$$ & $$BE=\frac{perimeter}{4}=\frac{80}{4}=20$$
Now, we can definitely obtain the length of AB by using Pythagoras property in the right angled triangle AEB.($$(3k)^2+(4k)^2=20^2$$, k can be calculated , so AB=4k)
Therefore, st2 is sufficient.

Ans. (B)
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Senior Manager
Joined: 04 Aug 2010
Posts: 276
Schools: Dartmouth College
In the figure above, the measure of angle EAB in triangle ABE is 90...  [#permalink]

### Show Tags

29 Jun 2018, 12:41
CAMANISHPARMAR wrote:

In the figure above, the measure of angle EAB in triangle ABE is 90 degrees, and BCDE is a square. What is the length of AB?

(1) The length of AE is 12, and the ratio of the area of triangle ABE to the area of square BCDE is $$\frac{6}{25}$$.

(2) The perimeter of square BCDE is 80 and the ratio of the length of AE to the length of AB is 3 to 4.

Attachment:
ZZ1.jpg

Always look for SPECIAL TRIANGLES.

Statement 1:
Since the length of AE is divisible by 3 and 4, test whether it's possible that ABE is a multiple of a 3:4:5 triangle.

Case 1: AE=12, AB=16 and BE=20, with the result that AE:AB:BE = 3:4:5
In this case:
$$\frac{ABE}{BCDE} = \frac{(0.5 * 12 *16)}{20^2} = \frac{96}{400} = \frac{6}{25}$$.

Case 2: AE=12, AB=9 and BE=15. with the result that AB:AE:BE = 3:4:5
In this case:
$$\frac{ABE}{BCDE} = \frac{(0.5 * 12 * 9)}{15^2} = \frac{54}{225} = \frac{6}{25}$$.

Statement 1 is satisfied by both cases.
Since AB can be different values, INSUFFICIENT.

Statement 2:
Statement 2 is satisfied only by Case 1.
Thus, AB=16.
SUFFICIENT.

_________________

GMAT and GRE Tutor
Over 1800 followers
GMATGuruNY@gmail.com
New York, NY
If you find one of my posts helpful, please take a moment to click on the "Kudos" icon.
Available for tutoring in NYC and long-distance.

Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 857
WE: Supply Chain Management (Energy and Utilities)
Re: In the figure above, the measure of angle EAB in triangle ABE is 90...  [#permalink]

### Show Tags

29 Jun 2018, 12:52
GMATGuruNY wrote:
CAMANISHPARMAR wrote:

In the figure above, the measure of angle EAB in triangle ABE is 90 degrees, and BCDE is a square. What is the length of AB?

(1) The length of AE is 12, and the ratio of the area of triangle ABE to the area of square BCDE is $$\frac{6}{25}$$.

(2) The perimeter of square BCDE is 80 and the ratio of the length of AE to the length of AB is 3 to 4.

Attachment:
ZZ1.jpg

Always look for SPECIAL TRIANGLES.

Statement 1:
Since the length of AE is divisible by 3 and 4, test whether it's possible that ABE is a multiple of a 3:4:5 triangle.

Case 1: AE=12, AB=16 and BE=20, with the result that AE:AB:BE = 3:4:5
In this case:
$$\frac{ABE}{BCDE} = \frac{(0.5 * 12 *16)}{20^2} = \frac{96}{400} = \frac{6}{25}$$.

Case 2: AE=12, AB=9 and BE=15. with the result that AB:AE:BE = 3:4:5

In this case:
$$\frac{ABE}{BCDE} = \frac{(0.5 * 12 * 9)}{15^2} = \frac{54}{225} = \frac{6}{25}$$.

Statement 1 is satisfied by both cases.
Since AB can be different values, INSUFFICIENT.

Statement 2:
Statement 2 is satisfied only by Case 1.
Thus, AB=16.
SUFFICIENT.

Hi,

How did u arrive at case 2, AB=9 unit?

Case-I is clearly understood(3x:4x:5x with x=4).
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Senior Manager
Joined: 04 Aug 2010
Posts: 276
Schools: Dartmouth College
Re: In the figure above, the measure of angle EAB in triangle ABE is 90...  [#permalink]

### Show Tags

29 Jun 2018, 13:11
PKN wrote:
Hi,

How did u arrive at case 2, AB=9 unit?

Case-I is clearly understood(3x:4x:5x with x=4).

Because AE=12 is a multiple of both 3 and 4, I tested whether it could constitute the SMALLEST side of a 3:4:5 triangle and whether it could constitute the MIDDLE side of a 3:4:5 triangle.

In Case 1, AE=12 constitutes the SMALLEST side of a 3:4:5 triangle:
AE --> 3*4 = 12
AB --> 4*4 = 16
BE --> 5*4 = 20

In Case 2, AE=12 constitutes the MIDDLE side of a 3:4:5 triangle:
AB = 3*3 = 9
AE = 4*3 = 12
BE = 5*3 = 15

As shown in my earlier solution, both cases satisfy Statement 1.
_________________

GMAT and GRE Tutor
Over 1800 followers
GMATGuruNY@gmail.com
New York, NY
If you find one of my posts helpful, please take a moment to click on the "Kudos" icon.
Available for tutoring in NYC and long-distance.

Math Expert
Joined: 02 Aug 2009
Posts: 6800
In the figure above, the measure of angle EAB in triangle ABE is 90...  [#permalink]

### Show Tags

29 Jun 2018, 19:35
CAMANISHPARMAR wrote:

In the figure above, the measure of angle EAB in triangle ABE is 90 degrees, and BCDE is a square. What is the length of AB?

(1) The length of AE is 12, and the ratio of the area of triangle ABE to the area of square BCDE is $$\frac{6}{25}$$.

(2) The perimeter of square BCDE is 80 and the ratio of the length of AE to the length of AB is 3 to 4.

Attachment:
ZZ1.jpg

Triangle ABE is right angled $$\triangle$$ and its hypotenuse BE is also the side of square ABCD..

(1) The length of AE is 12, and the ratio of the area of triangle ABE to the area of square BCDE is $$\frac{6}{25}=6x/25x$$.
area of $$\triangle {AEB}$$= $$\frac{1}{2}12*AB=6x.....AB=x$$
Area of square = $$25x=BE^2=AB^2+AE^2=12^2+x^2$$......
$$25x=x^2+144.......................x^2-25x+144=0.....................(x-9)(x-16)=0$$
so x= AB can be 16 or 9
insuff

(2) The perimeter of square BCDE is 80 and the ratio of the length of AE to the length of AB is 3 to 4.
so BE = $$\frac{80}{4}=20$$....
ratio of AE:AB = 3:4 means it is 3:4:5
so AE:AB:BE=3x:4x:5x where 5x=20....x=4
so AB=4*4=16
suff

B
_________________

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

Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 857
WE: Supply Chain Management (Energy and Utilities)
In the figure above, the measure of angle EAB in triangle ABE is 90...  [#permalink]

### Show Tags

29 Jun 2018, 19:52
1
chetan2u wrote:
CAMANISHPARMAR wrote:

In the figure above, the measure of angle EAB in triangle ABE is 90 degrees, and BCDE is a square. What is the length of AB?

(1) The length of AE is 12, and the ratio of the area of triangle ABE to the area of square BCDE is $$\frac{6}{25}$$.

(2) The perimeter of square BCDE is 80 and the ratio of the length of AE to the length of AB is 3 to 4.

Attachment:
ZZ1.jpg

Triangle ABE is right angled $$\triangle$$ and its hypotenuse BE is also the side of square ABCD..

(1) The length of AE is 12, and the ratio of the area of triangle ABE to the area of square BCDE is $$\frac{6}{25}$$.
area of $$\triangle {AEB}$$= $$\frac{1}{2}12*AB=6*\sqrt{BE^2-AB^2}$$
Area of square = BE^2
ratio = $$\frac{6*square_root(BE^2-AB^2)}{BE^2}=\frac{6}{25}$$
two unknowns and there is noway any variable will get cancelled out

insuff

(2) The perimeter of square BCDE is 80 and the ratio of the length of AE to the length of AB is 3 to 4.
so BE = $$\frac{80}{4}=20$$....
ratio of AE:AB = 3:4 means it is 3:4:5
so AE:AB:BE=3x:4x:5x where 5x=20....x=4
so AB=4*4=16
suff

b

Hi chetan2u,

I think it is: AB=$$\sqrt{(BE^2-AE^2)}$$

And the ratio becomes an equation with one unknown variable.
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Math Expert
Joined: 02 Aug 2009
Posts: 6800
Re: In the figure above, the measure of angle EAB in triangle ABE is 90...  [#permalink]

### Show Tags

29 Jun 2018, 20:28
PKN wrote:
chetan2u wrote:
CAMANISHPARMAR wrote:

In the figure above, the measure of angle EAB in triangle ABE is 90 degrees, and BCDE is a square. What is the length of AB?

(1) The length of AE is 12, and the ratio of the area of triangle ABE to the area of square BCDE is $$\frac{6}{25}$$.

(2) The perimeter of square BCDE is 80 and the ratio of the length of AE to the length of AB is 3 to 4.

Attachment:
ZZ1.jpg

Triangle ABE is right angled $$\triangle$$ and its hypotenuse BE is also the side of square ABCD..

(1) The length of AE is 12, and the ratio of the area of triangle ABE to the area of square BCDE is $$\frac{6}{25}$$.
area of $$\triangle {AEB}$$= $$\frac{1}{2}12*AB=6*\sqrt{BE^2-AB^2}$$
Area of square = BE^2
ratio = $$\frac{6*square_root(BE^2-AB^2)}{BE^2}=\frac{6}{25}$$
two unknowns and there is noway any variable will get cancelled out

insuff

(2) The perimeter of square BCDE is 80 and the ratio of the length of AE to the length of AB is 3 to 4.
so BE = $$\frac{80}{4}=20$$....
ratio of AE:AB = 3:4 means it is 3:4:5
so AE:AB:BE=3x:4x:5x where 5x=20....x=4
so AB=4*4=16
suff

b

Hi chetan2u,

I think it is: AB=$$\sqrt{(BE^2-AE^2)}$$

And the ratio becomes an equation with one unknown variable.

Thanks...
typo.. Dont know what I was thinking
_________________

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

Manager
Joined: 07 Feb 2017
Posts: 179
In the figure above, the measure of angle EAB in triangle ABE is 90...  [#permalink]

### Show Tags

29 Jun 2018, 21:51
x=AB
12x/2 : 144+x^2 = 6 : 25
since Hypotenuse = sqrt(144+x^2)

6x / (6x+144+x^2)= 6/31 should cancel 6s
6x=36/31x+864/31+6/31x^2
186x=36x+864+6x^2
0=6x^2-150x+864
0=x^2-25x+144
0=(x-9)(x-16)
x=9,16 Insufficient

(2) square side=20
AE:20=3:4
AE=15
x=remaining side of right triangle side
Sufficient
Math Expert
Joined: 02 Aug 2009
Posts: 6800
Re: In the figure above, the measure of angle EAB in triangle ABE is 90...  [#permalink]

### Show Tags

29 Jun 2018, 22:11
gmatzpractice wrote:
x=AB
12x/2 : 144+x^2 = 6 : 25
since Hypotenuse = sqrt(144+x^2)

6x / (6x+144+x^2)= 6/31 should cancel 6s
6x=36/31x+864/31+6/31x^2
186x=36x+864+6x^2
0=6x^2-150x+864
0=x^2-25x+144
0=(x-9)(x-16)
x=9,16 Insufficient

(2) square side=20
AE:20=3:4
AE=15
x=remaining side of right triangle side
Sufficient

Everything is correct but you are wrong in the coloured portion..
AE:AB=3:4
So it's 3:4:5 triangle and sides are AE:AB:EB=AE:AB:20 =3:4:5
_________________

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

Re: In the figure above, the measure of angle EAB in triangle ABE is 90... &nbs [#permalink] 29 Jun 2018, 22:11
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®.