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

It is currently 20 Jun 2018, 00:32

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

In the diagram above, ABCD is a square with side M, and EFGH is a squa

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

Hide Tags

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46191
In the diagram above, ABCD is a square with side M, and EFGH is a squa [#permalink]

Show Tags

New post 09 Apr 2015, 07:29
1
7
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

66% (01:55) correct 34% (02:07) wrong based on 206 sessions

HideShow timer Statistics

Image
In the diagram above, ABCD is a square with side M, and EFGH is a square with side K. What is the value of (M + K)?

(1) (M – K) = 9

(2) The area of triangle AEH is 36



Kudos for a correct solution.

Attachment:
gdrtq_img5.png
gdrtq_img5.png [ 8.81 KiB | Viewed 3438 times ]

_________________

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

1 KUDOS received
Director
Director
User avatar
Joined: 07 Aug 2011
Posts: 565
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
GMAT ToolKit User
In the diagram above, ABCD is a square with side M, and EFGH is a squa [#permalink]

Show Tags

New post 09 Apr 2015, 23:03
1
1
Bunuel wrote:
Image
In the diagram above, ABCD is a square with side M, and EFGH is a square with side K. What is the value of (M + K)?

(1) (M – K) = 9

(2) The area of triangle AEH is 36



Kudos for a correct solution.

Attachment:
The attachment gdrtq_img5.png is no longer available


(1) (M – K) = 9
Area of one triangle is \(\frac{M^2 - K^2}{4}\)= \(\frac{(M+K)(M-K)}{4}\) = \(\frac{9*(M+K)}{4}\)
we cannot inference much on \(\frac{9*(M+K)}{4}\)
Insufficient.

(2) The area of triangle AEH is 36
if AH=x
then (M-x)x = 72
again we cannot inference much .
insufficient.


together :

as we know area = \(\frac{9*(M+K)}{4}\) = 36 . we can find (m+k)
answer C
Attachments

gmatclub.jpg
gmatclub.jpg [ 43.79 KiB | Viewed 2964 times ]


_________________

Thanks,
Lucky

_______________________________________________________
Kindly press the Image to appreciate my post !! :-)

1 KUDOS received
Manager
Manager
User avatar
Joined: 21 May 2009
Posts: 107
Re: In the diagram above, ABCD is a square with side M, and EFGH is a squa [#permalink]

Show Tags

New post 11 Apr 2015, 07:26
1
To find M+K

Area of shaded region =\(\frac{M^2 - K^2}{4}\)

We need to find M+K

1) M-K = 9 . Insufficient

2) \(\frac{M^2 - K^2}{4}\) = 36 Not sufficent

From 1 and 2 we can get M+K. sufficient

Answer : C
Manager
Manager
avatar
Joined: 05 Feb 2015
Posts: 63
Concentration: Finance, Entrepreneurship
Schools: ISB '16, IIMA , IIMB, IIMC
WE: Information Technology (Health Care)
Re: In the diagram above, ABCD is a square with side M, and EFGH is a squa [#permalink]

Show Tags

New post 11 Apr 2015, 11:51
Hi Lucky2783

Could you please explain why the 4 triangles are congruent?
Expert Post
1 KUDOS received
EMPOWERgmat Instructor
User avatar
D
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11803
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: In the diagram above, ABCD is a square with side M, and EFGH is a squa [#permalink]

Show Tags

New post 11 Apr 2015, 16:10
1
Hi Naina1,

The reason why the 4 triangles are congruent involves a few geometry rules:

1) The angles on a line sum to 180 degrees
2) The angles in a triangle sum to 180 degrees
3) The corners of squares are 90 degree angles.

To prove the point, I'm going to have you do a little work....

1) Start with the purple triangle in the drawing and select two values (you get to choose) for the two non-90 degree angles. Remember that you're dealing with a triangle, so the sum of the angles has to be 180 degrees.
2) Next, working clockwise or counter-clockwise, figure out the next angle (remember, the corners of squares are 90 degrees and lines must sum to 180 degrees).

As you keep working, you'll find that each of the other triangles has the exact same angles (and side lengths) as the purple one.

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Director
Director
User avatar
Joined: 07 Aug 2011
Posts: 565
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
GMAT ToolKit User
Re: In the diagram above, ABCD is a square with side M, and EFGH is a squa [#permalink]

Show Tags

New post 11 Apr 2015, 20:36
Naina1 wrote:
Hi Lucky2783

Could you please explain why the 4 triangles are congruent?



Please see attached.
one right angle.
one side of triangle i.e. Hypotnuse
and the highlighted angle are equal
Attachments

Sketch120113358.png
Sketch120113358.png [ 117.01 KiB | Viewed 2849 times ]


_________________

Thanks,
Lucky

_______________________________________________________
Kindly press the Image to appreciate my post !! :-)

Manager
Manager
avatar
Joined: 05 Feb 2015
Posts: 63
Concentration: Finance, Entrepreneurship
Schools: ISB '16, IIMA , IIMB, IIMC
WE: Information Technology (Health Care)
Re: In the diagram above, ABCD is a square with side M, and EFGH is a squa [#permalink]

Show Tags

New post 11 Apr 2015, 20:54
got it..thanks :)
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46191
Re: In the diagram above, ABCD is a square with side M, and EFGH is a squa [#permalink]

Show Tags

New post 13 Apr 2015, 05:33
Bunuel wrote:
Image
In the diagram above, ABCD is a square with side M, and EFGH is a square with side K. What is the value of (M + K)?

(1) (M – K) = 9

(2) The area of triangle AEH is 36



Kudos for a correct solution.

Attachment:
gdrtq_img5.png


VERITAS PREP OFFICIAL SOLUTION:

In the diagram, we literally have two squares, M squared and K squared. The four right triangle are what we get if we subtract one square from the other: they are literally the difference of two squares, so we can use the Difference of Two Squares formula:

M^2 - K^2 = (M + K)(M - K)

We could find (M + K) if we knew (M – K) and the difference of the squares.

Statement #1: this gives us (M – K), but we don’t know the difference of the two squares. This statement, alone and by itself, is not sufficient.

Statement #2: this gives us the area of one triangle, and if we multiply by 4, we have the difference of the two squares. But, now we don’t know (M – K), so we can solve. This statement, alone and by itself, is not sufficient.

Combined statements. With the two statements, we know both (M – K) and the difference of the squares, so we can solve for (M + K). Together, the statements are sufficient.

Answer = (C)
_________________

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

Manager
Manager
avatar
Joined: 07 Apr 2015
Posts: 177
In the diagram above, ABCD is a square with side M, and EFGH is a squa [#permalink]

Show Tags

New post 03 May 2015, 05:17
What are the correct values for M and K? Solved it in a different way and would like to know if my calculation was correct or if i just correctly guessed C. Much appreciated!
Board of Directors
User avatar
P
Joined: 17 Jul 2014
Posts: 2730
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Premium Member Reviews Badge
In the diagram above, ABCD is a square with side M, and EFGH is a squa [#permalink]

Show Tags

New post 20 Sep 2016, 06:39
1. we can't get any info from here
2. we can find AE, AH, and side of the inner square - K. but we don't know for M.

1+2 - we know K, we can find M. sufficient.
Intern
Intern
avatar
Joined: 23 Jun 2016
Posts: 42
Re: In the diagram above, ABCD is a square with side M, and EFGH is a squa [#permalink]

Show Tags

New post 20 Sep 2016, 16:17
Statement 1 is insufficient because it does not give us anything relevant m-k = 9

Statement 2 is insufficient but is helpful in the following way:
We know the area of bigger square = m^2
Area of smaller square is K^2
We can infer that M^2 = K^2 + (4*36) {area of smaller square plus area of 4 triangles}

This gives us M^2 - K^2 = 144
(M-K)(M+K) = 144

To solve we can get M-K from first statement so C is sufficient
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 7006
Premium Member
Re: In the diagram above, ABCD is a square with side M, and EFGH is a squa [#permalink]

Show Tags

New post 13 Jan 2018, 17:08
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

Re: In the diagram above, ABCD is a square with side M, and EFGH is a squa   [#permalink] 13 Jan 2018, 17:08
Display posts from previous: Sort by

In the diagram above, ABCD is a square with side M, and EFGH is a squa

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


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.