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

It is currently 19 Nov 2018, 14:24

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 in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • How to QUICKLY Solve GMAT Questions - GMAT Club Chat

     November 20, 2018

     November 20, 2018

     09:00 AM PST

     10:00 AM PST

    The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
  • The winning strategy for 700+ on the GMAT

     November 20, 2018

     November 20, 2018

     06:00 PM EST

     07:00 PM EST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

What is the area of the shaded quadrilateral in the figure above?

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

Hide Tags

Intern
Intern
avatar
B
Joined: 02 Mar 2016
Posts: 5
GMAT ToolKit User
What is the area of the shaded quadrilateral in the figure above?  [#permalink]

Show Tags

New post 27 Feb 2017, 13:13
2
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

84% (01:10) correct 16% (01:32) wrong based on 110 sessions

HideShow timer Statistics

What is the area of the shaded quadrilateral in the figure above?

(1) a^2 − b^2 = 40

(2) a^2 + b^2 = 58

Attachments

shadedQuad.png
shadedQuad.png [ 28.03 KiB | Viewed 2531 times ]

Intern
Intern
avatar
B
Joined: 07 Jul 2016
Posts: 12
Location: Canada
GMAT 1: 700 Q47 V39
GPA: 3.38
What is the area of the shaded quadrilateral in the figure above?  [#permalink]

Show Tags

New post 27 Feb 2017, 16:20
Would appreciate other people's feedback on Statement 1, but came about it as follows:

1) X^2 - Y^2 = 40

Even after breaking down into (x+y) * (x-y) = 40, didn't seem to help much. Left it as insufficient.

2) X^2 + Y^2 = 58

Using the pythagorean theorem, broke it down into a^2 + b^2 = c^2. Therefore, c^2 = 58, which is the area of the quadrilateral. Accordingly, B is sufficient.
Senior CR Moderator
User avatar
V
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1378
Location: Viet Nam
GMAT ToolKit User Premium Member
Re: What is the area of the shaded quadrilateral in the figure above?  [#permalink]

Show Tags

New post 28 Feb 2017, 06:54
2
Matruco wrote:
What is the area of the shaded quadrilateral in the figure above?

(1) a^2 − b^2 = 40

(2) a^2 + b^2 = 58


The area of the big square is \((a+b)^2\)

The area of each triangle is \(\frac{ab}{2}\)

Hence, the area of the shaded quadrilateral is
\((a+b)^2-4 \times \frac{ab}{2}=a^2+b^2\)

(1) \(a^2-b^2=40\). We can't know what the value of \(a^2+b^2\) is. Insufficient.

(2) It's clear that \(a^2 + b^2 = 58\) is the area of the shaded quadrilateral . Sufficient.

The answer is B
_________________

Actual LSAT CR bank by Broall

How to solve quadratic equations - Factor quadratic equations
Factor table with sign: The useful tool to solve polynomial inequalities
Applying AM-GM inequality into finding extreme/absolute value

New Error Log with Timer

Director
Director
avatar
S
Joined: 12 Nov 2016
Posts: 743
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Re: What is the area of the shaded quadrilateral in the figure above?  [#permalink]

Show Tags

New post 13 Mar 2017, 14:15
In order to solve this question, we need to know the lengths of the hypotenuses of the triangles. I think.


What is the area of the shaded quadrilateral in the figure above?

(1) a^2 − b^2 = 40

(2) a^2 + b^2 = 58

Statement (1) gives us two variables, meaning we cannot solve the equation. We cannot extrapolate a hypotenuse length from this equation either. Insufficient.

Statement (2) allows us to determine what the length of side C is by squaring 58. Sufficient.
Senior Manager
Senior Manager
User avatar
S
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 496
Location: India
Premium Member
Re: What is the area of the shaded quadrilateral in the figure above?  [#permalink]

Show Tags

New post 15 Mar 2017, 05:24
St 1: a^2-b^2 = 40
or (a+b)(a-b) = 40
number of cases possible. INSUFFICIENT

St 2: a^2 +b^2 = 58.
for each side if the shaded quadrilateral, we can say that a^2 +b^2 = c^2
therefore the shaded region is a square with side c and the area c^2 = 58. ANSWER

Option B
_________________

GMAT Mentors
Image

Manager
Manager
User avatar
S
Joined: 22 Nov 2016
Posts: 213
Location: United States
Concentration: Leadership, Strategy
GPA: 3.4
Reviews Badge
Re: What is the area of the shaded quadrilateral in the figure above?  [#permalink]

Show Tags

New post 07 Nov 2017, 09:49
Area of the shaded region = Area of square - (sum of all areas of triangles)
\(= (a+b)^2 - 4* [ \frac{1}{2} * a * b]\) ; if you notice area of each triangle is the same \(= \frac{1}{2} *a * b\)
\(= (a+b)^2 - 2ab\)
\(= a^2 + b^2 + 2ab - 2ab\)
\(= a^2 + b^2\)

Statement 1 : Not sufficient.

Statement 2: gives us the direct value of \(a^2 + b^2\)
_________________

Kudosity killed the cat but your kudos can save it.

GMAT Club Bot
Re: What is the area of the shaded quadrilateral in the figure above? &nbs [#permalink] 07 Nov 2017, 09:49
Display posts from previous: Sort by

What is the area of the shaded quadrilateral in the figure above?

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


Copyright

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®.