It is currently 21 Jan 2018, 00:56

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

For triangle ABC, angle ABC = 90 degrees, and side AC has a length of

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43334

Kudos [?]: 139638 [0], given: 12794

For triangle ABC, angle ABC = 90 degrees, and side AC has a length of [#permalink]

Show Tags

New post 02 Feb 2015, 06:20
Expert's post
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

65% (01:22) correct 35% (00:57) wrong based on 221 sessions

HideShow timer Statistics

For triangle ABC, angle ABC = 90 degrees, and side AC has a length of 15. If point D lies on side AC, and a line is drawn from point B to point D, what is the length of line segment BD?

(1) Triangle ABC is isosceles.

(2) Line segment BD is perpendicular to side AC.

Kudos for a correct solution.
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 139638 [0], given: 12794

Expert Post
1 KUDOS received
Math Expert
User avatar
D
Joined: 02 Aug 2009
Posts: 5536

Kudos [?]: 6443 [1], given: 122

Re: For triangle ABC, angle ABC = 90 degrees, and side AC has a length of [#permalink]

Show Tags

New post 02 Feb 2015, 07:28
1
This post received
KUDOS
Expert's post
ans C.. a right angle triangle given with length of hyp...
1) it tells us the other two sides are equal and gives the length of other two sides.. however D can be anywhere on line AC ..insufficient
2)it just tells us that BD is altitude.. no use unless sides are known..insufficient

combined sufficient as allsides known and alt bd can be found out
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html


BANGALORE/-

Kudos [?]: 6443 [1], given: 122

1 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 28 Feb 2014
Posts: 295

Kudos [?]: 146 [1], given: 133

Location: United States
Concentration: Strategy, General Management
Reviews Badge
Re: For triangle ABC, angle ABC = 90 degrees, and side AC has a length of [#permalink]

Show Tags

New post 02 Feb 2015, 09:34
1
This post received
KUDOS
Bunuel wrote:
For triangle ABC, angle ABC = 90 degrees, and side AC has a length of 15. If point D lies on side AC, and a line is drawn from point B to point D, what is the length of line segment BD?

(1) Triangle ABC is isosceles.

(2) Line segment BD is perpendicular to side AC.

Kudos for a correct solution.


Statement 1: We know that side AB and side BC are of the same length.
However, the segment BD can be of various lengths based on where the point D is located along side AC.
Insufficient.

Statement 2: segment BD forms a 90 deg angle with side AC. However, we still do not know how side AC is broken down or what the length is of any other side.
Insufficient.

Combined, we know right triangle ABC is isosceles with BD as its altitude and bisector. We can now apply pythagorean theorem to find the length of segment BD.

Answer: C

Kudos [?]: 146 [1], given: 133

1 KUDOS received
Manager
Manager
avatar
Joined: 17 Dec 2013
Posts: 60

Kudos [?]: 26 [1], given: 35

GMAT Date: 01-08-2015
GMAT ToolKit User
Re: For triangle ABC, angle ABC = 90 degrees, and side AC has a length of [#permalink]

Show Tags

New post 02 Feb 2015, 12:34
1
This post received
KUDOS
Quote:
For triangle ABC, angle ABC = 90 degrees, and side AC has a length of 15. If point D lies on side AC, and a line is drawn from point B to point D, what is the length of line segment BD?

(1) Triangle ABC is isosceles.

(2) Line segment BD is perpendicular to side AC.


I start with (2): since we do not know
the length of AD and CD we can not use the similar triangle theorem, (sid/alt=alt/side)
not suff.
(1)triangle is a isosceles. but we do not know where is the point D on AC.

(1/2): since BD is perpendicular, we know that the isosceles ABC with °ABC=90 has BCA=45 and CAB=45. with AC = 15 we got AD=7,5 and CD=7,5. We could either use x:x:x*root(2) to determine AB / CB and afterwars BD (with pythagoras).
or we know that the perpendicular will build 2 triangles with 45-45-90 but as the ground we will get x, and as the legs we will get 0,5*15. so its suff

Kudos [?]: 26 [1], given: 35

1 KUDOS received
Manager
Manager
avatar
B
Joined: 02 Sep 2014
Posts: 89

Kudos [?]: 261 [1], given: 32

Location: United States
Schools: Haas EWMBA '20
GMAT 1: 770 Q50 V44
GPA: 3.97
GMAT ToolKit User Reviews Badge
Re: For triangle ABC, angle ABC = 90 degrees, and side AC has a length of [#permalink]

Show Tags

New post 02 Feb 2015, 23:27
1
This post received
KUDOS
Bunuel wrote:
For triangle ABC, angle ABC = 90 degrees, and side AC has a length of 15. If point D lies on side AC, and a line is drawn from point B to point D, what is the length of line segment BD?

(1) Triangle ABC is isosceles.

(2) Line segment BD is perpendicular to side AC.

Kudos for a correct solution.



Answer C
1) If ABC is isosceles AB=BC but doesnt help us calculate BD.
2) If BD is perpendicular to AC we still dont know BD.

Combining, we know AB = BC from one so each of them can be calculated and the triangle is defined. So BD is calculable.
Or since area of triangle is constant AB*BC=AC*BD so BD can be calculated.

Answer =C.

Press kudos if I am right.

Kudos [?]: 261 [1], given: 32

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43334

Kudos [?]: 139638 [2], given: 12794

Re: For triangle ABC, angle ABC = 90 degrees, and side AC has a length of [#permalink]

Show Tags

New post 09 Feb 2015, 03:21
2
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
Bunuel wrote:
For triangle ABC, angle ABC = 90 degrees, and side AC has a length of 15. If point D lies on side AC, and a line is drawn from point B to point D, what is the length of line segment BD?

(1) Triangle ABC is isosceles.

(2) Line segment BD is perpendicular to side AC.

Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION:

C. For statement 1, it's helpful to just draw the triangle and several variations of line BD - you should see that point D can be extremely close to point A, right down the middle, or extremely close to point C, all with different lengths. This demonstrates that statement 1 is not sufficient.

For statement 2, recognize that triangle ABC and be a right angle with an extremely long side AB and an extremely short side BC, or (as alluded to in statement 1) it could be isosceles in which both sides are the same length. And in either case, the length of line BD will differ dramatically.

If both statements are taken together, however, you can find the length of BD. Since ABC is an isosceles right triangle with a hypotenuse of 15, sides AB and BC will each have a length equal to 15 divided by the square root of 2. And since line BD will bisect triangle ABC into two identical right triangles, each with either side AB or BC as the hypotenuse, you should note that side BD will have to equal the other "short" leg of each triangle (either AD or DC), and each of those is half of the long side AC, which is 15. So the length of BD is half of 15, which is 7.5
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 139638 [2], given: 12794

Intern
Intern
avatar
B
Joined: 07 Mar 2011
Posts: 32

Kudos [?]: 7 [0], given: 5

GMAT ToolKit User Premium Member
Re: For triangle ABC, angle ABC = 90 degrees, and side AC has a length of [#permalink]

Show Tags

New post 29 Jun 2016, 20:55
Hi Bunuel,

I have understood your explanation. But I need one clarification.
What If I say, statement 2 alone is sufficient. Because we know hypotenuse is 15 and ABC is a right angled triangle and right angled at B. with Pythagoras tripplets, other two sides are 12 and 9. We know if we know 3 sides we can find out BD length.

with formula BD = (AB * BC) / AC.

With this I feel something I am missing. either I am assuming more than the required or carrying extra information. Can you tell me what is my mistake ?

Kudos [?]: 7 [0], given: 5

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43334

Kudos [?]: 139638 [0], given: 12794

Re: For triangle ABC, angle ABC = 90 degrees, and side AC has a length of [#permalink]

Show Tags

New post 30 Jun 2016, 07:14
dharan wrote:
Hi Bunuel,

I have understood your explanation. But I need one clarification.
What If I say, statement 2 alone is sufficient. Because we know hypotenuse is 15 and ABC is a right angled triangle and right angled at B. with Pythagoras tripplets, other two sides are 12 and 9. We know if we know 3 sides we can find out BD length.

with formula BD = (AB * BC) / AC.

With this I feel something I am missing. either I am assuming more than the required or carrying extra information. Can you tell me what is my mistake ?


Why do you assume that the sides should be Pythagorean Triples? Why do you assume that the sides should be integers at all?
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 139638 [0], given: 12794

Director
Director
User avatar
Joined: 04 Jun 2016
Posts: 645

Kudos [?]: 410 [0], given: 36

GMAT 1: 750 Q49 V43
For triangle ABC, angle ABC = 90 degrees, and side AC has a length of [#permalink]

Show Tags

New post 30 Jun 2016, 08:57
Bunuel wrote:
For triangle ABC, angle ABC = 90 degrees, and side AC has a length of 15. If point D lies on side AC, and a line is drawn from point B to point D, what is the length of line segment BD?

(1) Triangle ABC is isosceles.

(2) Line segment BD is perpendicular to side AC.

Kudos for a correct solution.


I almost concluded D as the answer by confusing similarity for congruency and then realised that strict congruency can only be reached if apart from being isosceles and having BD as the common side BD is also a perpendicular bisector of the AC. But this condition was not found in statement 1.
Then i checked statement 2 and realised that statement 2 gives us exactly what was missing .. the condition for strict congruency and the both statement A and B are needed

Attached here is my wrong answer

THE CORRECT ANSWER IS C


Attached here is my WRONG answer

Image
Attachments

IMG_20160630_213820.jpg
IMG_20160630_213820.jpg [ 550.5 KiB | Viewed 44155 times ]


_________________

Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly.
FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.


Last edited by LogicGuru1 on 02 Sep 2016, 09:57, edited 1 time in total.

Kudos [?]: 410 [0], given: 36

Expert Post
2 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7868

Kudos [?]: 18494 [2], given: 237

Location: Pune, India
Re: For triangle ABC, angle ABC = 90 degrees, and side AC has a length of [#permalink]

Show Tags

New post 04 Jul 2016, 19:54
2
This post received
KUDOS
Expert's post
LogicGuru1 wrote:
Bunuel wrote:
For triangle ABC, angle ABC = 90 degrees, and side AC has a length of 15. If point D lies on side AC, and a line is drawn from point B to point D, what is the length of line segment BD?

(1) Triangle ABC is isosceles.

(2) Line segment BD is perpendicular to side AC.

Kudos for a correct solution.


I almost concluded D as the answer by confusing similarity for congruency and then realised that strict congruency can only be reached if apart from being isosceles and having BD as the common side BD is also a perpendicular bisector of the AC. But this condition was not found in statement 1.
Then i checked statement 2 and realised that statement 2 gives us exactly what was missing .. the condition for strict congruency and the both statement A and B are needed

Attached here is my wrong answer

THE CORRECT ANSWER IS C


Attached here is my WRONG answer

Image


Responding to a pm:

This is where you made a mistake: there is no SSA rule. The rule is SAS (two sides and the INCLUDED angle). If you say AB = BC and BD = BD, the angles which have to be same are DBA and DBC.
A special SSA rule works only in case of a right triangle - It is called the RHS rule. There has to be a right angle in both triangles, the hypotenuses have to be equal and any one set of sides should be equal.

Statement 1 gives you neither SAS nor RHS. So the two triangles may not be congruent.
The other congruency rules are SSS, ASA and AAS.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 18494 [2], given: 237

Director
Director
User avatar
Joined: 04 Jun 2016
Posts: 645

Kudos [?]: 410 [0], given: 36

GMAT 1: 750 Q49 V43
Re: For triangle ABC, angle ABC = 90 degrees, and side AC has a length of [#permalink]

Show Tags

New post 05 Jul 2016, 10:40
VeritasPrepKarishma wrote:
LogicGuru1 wrote:
Bunuel wrote:
For triangle ABC, angle ABC = 90 degrees, and side AC has a length of 15. If point D lies on side AC, and a line is drawn from point B to point D, what is the length of line segment BD?

(1) Triangle ABC is isosceles.

(2) Line segment BD is perpendicular to side AC.

Kudos for a correct solution.


I almost concluded D as the answer by confusing similarity for congruency and then realised that strict congruency can only be reached if apart from being isosceles and having BD as the common side BD is also a perpendicular bisector of the AC. But this condition was not found in statement 1.
Then i checked statement 2 and realised that statement 2 gives us exactly what was missing .. the condition for strict congruency and the both statement A and B are needed

Attached here is my wrong answer

THE CORRECT ANSWER IS C


Attached here is my WRONG answer

Image


Responding to a pm:

This is where you made a mistake: there is no SSA rule. The rule is SAS (two sides and the INCLUDED angle). If you say AB = BC and BD = BD, the angles which have to be same are DBA and DBC.
A special SSA rule works only in case of a right triangle - It is called the RHS rule. There has to be a right angle in both triangles, the hypotenuses have to be equal and any one set of sides should be equal.

Statement 1 gives you neither SAS nor RHS. So the two triangles may not be congruent.
The other congruency rules are SSS, ASA and AAS.


Many thanks Karishma

I realised I am arriving at that wrong answer if I am choosing D.
Just got confused about congruency.
You are a tremendous help..
_________________

Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly.
FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.

Kudos [?]: 410 [0], given: 36

Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7868

Kudos [?]: 18494 [1], given: 237

Location: Pune, India
Re: For triangle ABC, angle ABC = 90 degrees, and side AC has a length of [#permalink]

Show Tags

New post 05 Sep 2016, 02:15
1
This post received
KUDOS
Expert's post
Bunuel wrote:
For triangle ABC, angle ABC = 90 degrees, and side AC has a length of 15. If point D lies on side AC, and a line is drawn from point B to point D, what is the length of line segment BD?

(1) Triangle ABC is isosceles.

(2) Line segment BD is perpendicular to side AC.

Kudos for a correct solution.


Responding to a pm:
Quote:
How come if angles ABC and ADB are equal at 90, and angle A is shared between triangles ABC and ADB, and these triangles also share AB as one of their sides...why aren't they similar making B sufficient?


Triangles ABC and ADB are similar using AA rule (two equal angles) - no problem there.
The point is - how do you get the length of the line segment BD?
All you know is that AC is 15. You don't know the ratio of the corresponding sides of the two triangles. You don't know AB/BC/AD. How will you find BD?
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 18494 [1], given: 237

Expert Post
Top Contributor
2 KUDOS received
SVP
SVP
User avatar
P
Joined: 11 Sep 2015
Posts: 1999

Kudos [?]: 2873 [2], given: 364

Location: Canada
Re: For triangle ABC, angle ABC = 90 degrees, and side AC has a length of [#permalink]

Show Tags

New post 09 Sep 2016, 13:20
2
This post received
KUDOS
Expert's post
Top Contributor
Bunuel wrote:
For triangle ABC, angle ABC = 90 degrees, and side AC has a length of 15. If point D lies on side AC, and a line is drawn from point B to point D, what is the length of line segment BD?

(1) Triangle ABC is isosceles.

(2) Line segment BD is perpendicular to side AC.

Kudos for a correct solution.


IMPORTANT: For geometry DS questions, we are typically checking to see whether the statements "lock" a particular angle or length into having just one value. This concept is discussed in much greater detail in our video at the bottom of this post.

This technique can save a lot of time.

Target question: What is the length of line segment BD?

Given: For triangle ABC, angle ABC = 90 degrees, and side AC has a length of 15.

So, we have a shape that looks something like this . . .
Image
. . . where the legs of the triangle can vary AND the location of point D can vary.

Statement 1: Triangle ABC is isosceles.
Since there is ONLY ONE isosceles right triangle with hypotenuse 15, this statement LOCKS triangle ABC into having one and only one shape.
Image

However, statement 1 does NOT lock in the location of point D.
Since this statement does not lock in the location of point D, the length of BD is NOT LOCKED IN.
Consider these two examples.
Image
Image
Notice the different lengths of line segment BD
Since statement 1 does not lock in the length of line segment BD, it is NOT SUFFICIENT

Statement 2: Line segment BD is perpendicular to side AC.
This statement locks in the location of point D (in relation to the triangle's hypotenuse), but it does NOT lock in the shape of the triangle.
Consider these two examples:
Image
Image
Notice the different lengths of line segment BD
Since statement 2 does not lock in the length of line segment BD, it is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 locks in the shape of triangle ABC.
Statement 2 then locks in the location of point D as follows:
Image
Since there's only one diagram that can be drawn with the given information, there can be ONLY ONE length of line segment BD
Are we required to find this length? No. We need only recognize that there can be only one length.
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer =
[Reveal] Spoiler:
C


RELATED VIDEOS



_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Kudos [?]: 2873 [2], given: 364

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 14213

Kudos [?]: 291 [0], given: 0

Premium Member
Re: For triangle ABC, angle ABC = 90 degrees, and side AC has a length of [#permalink]

Show Tags

New post 20 Dec 2017, 10:40
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 291 [0], given: 0

Re: For triangle ABC, angle ABC = 90 degrees, and side AC has a length of   [#permalink] 20 Dec 2017, 10:40
Display posts from previous: Sort by

For triangle ABC, angle ABC = 90 degrees, and side AC has a length of

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


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.