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

It is currently 17 Oct 2018, 20:08

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

Common Mistakes in Geometry Questions - Exercise Question #1

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

Hide Tags

e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 2065
Common Mistakes in Geometry Questions - Exercise Question #1  [#permalink]

Show Tags

New post Updated on: 07 Aug 2018, 04:09
3
4
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

76% (00:47) correct 24% (01:00) wrong based on 389 sessions

HideShow timer Statistics

Exercise Question #1 Common Mistakes in Geometry Questions


Image

ABCD is a quadrilateral as shown in the figure above. Find the area of the quadrilateral.

    (1) The diagonals bisect each other at \(90^o\) and they are equal.
    (2) The length of each diagonal is 10 cm.



Answer Choices

    A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

    B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. 

    C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. 

    D. EACH statement ALONE is sufficient. 

    E. Statements (1) and (2) TOGETHER are NOT sufficient.


Next Question


Detailed solution will be posted soon.


Image

_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com


Originally posted by EgmatQuantExpert on 22 Nov 2016, 05:32.
Last edited by EgmatQuantExpert on 07 Aug 2018, 04:09, edited 5 times in total.
e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 2065
Re: Common Mistakes in Geometry Questions - Exercise Question #1  [#permalink]

Show Tags

New post Updated on: 01 Dec 2016, 01:47
Note: This questions is related to the article on Common Errors in Geometry

Kindly go through the article once, before solving the question or going through the solution.


Official Solution


Given: ABCD is a quadrilateral.


Analysing statement 1:

The first statements states :

The diagonals bisect each other at \(90^o\) and they are equal.


From the above statement, we can conclude that the quadrilateral is a square.

But to find the area of the quadrilateral we need the length of each side, which is not given.

Hence statement 1 is not sufficient to answer the question.


Analysing statement 2:

The length of each diagonal is 10 cm.

Using only the 2nd statement, we cannot find the area of the quadrilateral, since we don't know what kind of quadrilateral it is.

Hence statement 2 is not sufficient to answer the question.


Combining statement 1 and 2:


Using both the statements, we can conclude that the quadrilateral is a square and the length of it's diagonal is 10cm.

Therefore, AB = BC = CD = AD

AC = BD = 10 (diagonals)

Image

Since ABCD is a square angle ABC = 9\(0^o\), therefore we can infer that the diagonal(AC) is the hypotenuse and the sides AB and BC are the perpendicular and base.

Hence we can write A\(B^2\) + B\(C^2\) = A\(C^2\)

2A\(B^2\) = 1\(0^2\).............(i)

And we know the area of the square = (side\()^2\) = A\(B^2\)

We can find the value of AB from (i) and hence we can find the area of the square!


Hence combining both the statements we can find out the answer.


Correct Option : C



Thanks,
Saquib
Quant Expert
e-GMAT

Image
_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com


Originally posted by EgmatQuantExpert on 22 Nov 2016, 11:13.
Last edited by EgmatQuantExpert on 01 Dec 2016, 01:47, edited 2 times in total.
Manhattan Prep Instructor
User avatar
G
Joined: 04 Dec 2015
Posts: 629
GMAT 1: 790 Q51 V49
GRE 1: Q170 V170
Re: Common Mistakes in Geometry Questions - Exercise Question #1  [#permalink]

Show Tags

New post 22 Nov 2016, 13:15
1
An interesting variant is to figure out what the answer should be if the word 'bisect' is removed from statement (1) :)
_________________

Image

Chelsey Cooley | Manhattan Prep Instructor | Seattle and Online

My upcoming GMAT trial classes | GMAT blog archive

e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 2065
Re: Common Mistakes in Geometry Questions - Exercise Question #1  [#permalink]

Show Tags

New post 27 Nov 2016, 09:23
Hey Everyone,

The official solution has been posted. Kindly go through it and if you have any doubts feel free to post your query. :)


Thanks,
Saquib
Quant Expert
e-GMAT
_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Manager
Manager
avatar
S
Joined: 13 Mar 2013
Posts: 166
Location: United States
Concentration: Leadership, Technology
GPA: 3.5
WE: Engineering (Telecommunications)
Re: Common Mistakes in Geometry Questions - Exercise Question #1  [#permalink]

Show Tags

New post 20 Jun 2017, 17:16
Could you please share the relation between all the polygon .
For Eg . How can a square be a Rhombus .
_________________

Regards ,

Manager
Manager
User avatar
S
Joined: 09 Dec 2015
Posts: 116
Location: India
Concentration: General Management, Operations
Schools: IIMC (A)
GMAT 1: 700 Q49 V36
GPA: 3.5
WE: Engineering (Consumer Products)
Reviews Badge
Re: Common Mistakes in Geometry Questions - Exercise Question #1  [#permalink]

Show Tags

New post 21 Jun 2017, 11:04
abhisheknandy08 wrote:
Could you please share the relation between all the polygon .
For Eg . How can a square be a Rhombus .


Hi abhisheknandy08,

There can be many types of polygons based on number of sides.
Now, there are regular polygons and non-regular polygons.
Regular polygons have all sides equal but non-regular polygons can have any shape.

For the purpose of understanding this question, I'll stick with regular and non regular 4 sided polygon which have opposites sides parellel.

So, any polygon which has 2 of its opposite sides parallel and equal will be a parallelogram (so rectangle, rhombus and square are all parallelogram)
If in a parallelogram we make 2 sides equal (not all 4) and all angles 90 degree, we get a rectangle.
If we make all sides equal but the angles are not equal to 90 degree, we get a rhombus
Now if we make all angles 90 degree and all sides equal, we get a square (all squares are rhombus with 90 degree angles or all squares are rectangle with equal sides and all rhombus are parallelogram).

Hope it helps.
Senior DS Moderator
User avatar
D
Joined: 27 Oct 2017
Posts: 875
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
Re: Common Mistakes in Geometry Questions - Exercise Question #1  [#permalink]

Show Tags

New post 11 May 2018, 11:49
in that case, Answer would have been E.

ccooley wrote:
An interesting variant is to figure out what the answer should be if the word 'bisect' is removed from statement (1) :)

_________________

Win Tests/ Prep Courses- Weekly Quant Quiz Contest
SC: Confusable words

All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

Intern
Intern
avatar
B
Joined: 31 Oct 2017
Posts: 2
GMAT 1: 690 Q49 V34
Reviews Badge
Re: Common Mistakes in Geometry Questions - Exercise Question #1  [#permalink]

Show Tags

New post 14 Aug 2018, 22:30
Dear Experts,

Statement 1 says that the diagonals bisect each other at 90 degrees and that they are equal. This is could mean that the given quadrilateral could just be a rectangle instead of a square. If this is the case, then combining statement 1 and 2, we still cannot find the area since two adjacent sides of a rectangle can be different.

Please clarify.
e-GMAT Representative
User avatar
P
Joined: 04 Jan 2015
Posts: 2065
Re: Common Mistakes in Geometry Questions - Exercise Question #1  [#permalink]

Show Tags

New post 14 Aug 2018, 22:58
1
kckartick wrote:
Dear Experts,

Statement 1 says that the diagonals bisect each other at 90 degrees and that they are equal. This is could mean that the given quadrilateral could just be a rectangle instead of a square. If this is the case, then combining statement 1 and 2, we still cannot find the area since two adjacent sides of a rectangle can be different.

Please clarify.


Hey kckartick,

Not in each and every rectangle the diagonals bisect each other at 90 degrees. It happens only when the rectangle is a square - in that case, the lengths of the adjacent sides remain same.
_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Senior Manager
Senior Manager
User avatar
P
Joined: 08 Jun 2013
Posts: 445
Location: India
Schools: INSEAD Jan '19
GMAT 1: 200 Q1 V1
GPA: 3.82
WE: Engineering (Other)
GMAT ToolKit User Premium Member
Re: Common Mistakes in Geometry Questions - Exercise Question #1  [#permalink]

Show Tags

New post 24 Aug 2018, 20:34
ccooley wrote:
An interesting variant is to figure out what the answer should be if the word 'bisect' is removed from statement (1) :)


ccooley -

Answer - C

Diagonals are still equal and perpendicular - So Square.
_________________

It seems Kudos button not working correctly with all my posts...

Please check if it is working with this post......

is it?....

Anyways...Thanks for trying :cool:

GMAT Club Bot
Re: Common Mistakes in Geometry Questions - Exercise Question #1 &nbs [#permalink] 24 Aug 2018, 20:34
Display posts from previous: Sort by

Common Mistakes in Geometry Questions - Exercise Question #1

  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®.