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

It is currently 10 Dec 2018, 02:58

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 December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Free lesson on number properties

     December 10, 2018

     December 10, 2018

     10:00 PM PST

     11:00 PM PST

    Practice the one most important Quant section - Integer properties, and rapidly improve your skills.
  • Free GMAT Prep Hour

     December 11, 2018

     December 11, 2018

     09:00 PM EST

     10:00 PM EST

    Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.

In the rectangular coordinate system above the area of

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

Hide Tags

Manager
Manager
User avatar
Joined: 06 Feb 2010
Posts: 149
Concentration: Marketing, Leadership
Schools: University of Dhaka - Class of 2010
GPA: 3.63
WE: Business Development (Consumer Products)
In the rectangular coordinate system above the area of  [#permalink]

Show Tags

New post 22 Nov 2010, 05:27
6
15
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

87% (01:20) correct 13% (01:42) wrong based on 829 sessions

HideShow timer Statistics

Attachment:
Coordinate.jpg
Coordinate.jpg [ 25.98 KiB | Viewed 31363 times ]
In the rectangular coordinate system above the area of triangle PQR is what fraction of the area triangle LMN?

A. 1/9
B. 1/8
C. 1/6
D. 1/5
E. 1/3

_________________

Practice Makes a Man Perfect. Practice. Practice. Practice......Perfectly

Critical Reasoning: http://gmatclub.com/forum/best-critical-reasoning-shortcuts-notes-tips-91280.html

Collections of MGMAT CAT: http://gmatclub.com/forum/collections-of-mgmat-cat-math-152750.html

MGMAT SC SUMMARY: http://gmatclub.com/forum/mgmat-sc-summary-of-fourth-edition-152753.html

Sentence Correction: http://gmatclub.com/forum/sentence-correction-strategies-and-notes-91218.html

Arithmatic & Algebra: http://gmatclub.com/forum/arithmatic-algebra-93678.html

Helpful Geometry formula sheet: http://gmatclub.com/forum/best-geometry-93676.html


I hope these will help to understand the basic concepts & strategies. Please Click ON KUDOS Button.

Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51067
In the rectangular coordinate system above the area of  [#permalink]

Show Tags

New post 22 Nov 2010, 06:43
4
8
Image
In the rectangular coordinate system above the area of triangle PQR is what fraction of the area triangle LMN?

A. 1/9
B. 1/8
C. 1/6
D. 1/5
E. 1/3

The area of a triangle equals to \(area=\frac{1}{2}*base*height\).

Now the base of triangle PQR (or simply the length of line segment PR) is 4 units (the difference between x-coordinates of the points P and R), and the height is also 4 units (the altitude from the point Q to the x-axis equals to 4 units). So \(area_{PQR}=\frac{1}{2}*4*4=8\);

Similarly the base of triangle LMN is 12 units (the difference between x-coordinates of the points L and N), and the height is also 12 units (the altitude from the point M to the x-axis equals to 12 units). So \(area_{LMN}=\frac{1}{2}*12*12=72\);

Thus \(\frac{area_{PQR}}{area_{LMN}}=\frac{8}{72}=\frac{1}{9}\).

Answer: A.

As for the difficulty level, I'd say around 600.

Hope it's clear.
_________________

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

General Discussion
Intern
Intern
avatar
Joined: 09 Jun 2012
Posts: 29
Re: In the rectangular coordinate system above the area of  [#permalink]

Show Tags

New post 29 Jul 2013, 02:32
4
monirjewel wrote:
Attachment:
Coordinate.jpg
In the rectangular coordinate system above the area of triangle PQR is what fraction of the area triangle LMN?

A. 1/9
B. 1/8
C. 1/6
D. 1/5
E. 1/3

Understanding the question:
Two triangles are given. They look proportional/similar but this should be confirmed. Also, means are provided to calculate length of base and height.

Facts to refer:
If 2 triangles are similar, then the ratio of their area= (ratio of the sides)^2

What's given in the question and what it implies (noted as =>):
Coordinates for L, P, R, N are given => Base of smaller triangle = 4 and that of larger triangle =12
Coordinate for M and Q are given => Height of smaller triangle = 4 and that of larger triangle =12

What is asked for:
Area of PQR/Area of LMN => Ratio of the areas

Solution:
Since the base and height of the triangles are of the same ratio, the 2 triangles are similar. (Since the base and height are of equal ratio, the other 2 sides will also be of the same ratio.) Hence the fact given in "Facts to refer" can be used.
Ratio of sides = 4/12 =1/3
(Ratio of areas) = (1/3)^2 = 1/9
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51067
Re: In the rectangular coordinate system above the area of  [#permalink]

Show Tags

New post 21 Jul 2014, 09:34
sagnik2422 wrote:
Bunuel wrote:
In the rectangular coordinate system above the area of triangle PQR is what fraction of the area triangle LMN?

A. 1/9
B. 1/8
C. 1/6
D. 1/5
E. 1/3

The area of a triangle equals to \(area=\frac{1}{2}*base*height\).

Now the base of triangle PQR (or simply the length of line segment PQ) is 4 units (the difference between x-coordinates of the points P and Q), and the height is also 4 units (the altitude from the point Q to the x-axis equals to 4 units). So \(area_{PQR}=\frac{1}{2}*4*4=8\);

Similarly the base of triangle LMN is 12 units (the difference between x-coordinates of the points L and N), and the height is also 12 units (the altitude from the point M to the x-axis equals to 12 units). So \(area_{LMN}=\frac{1}{2}*12*12=72\);

Thus \(\frac{area_{PQR}}{area_{LMN}}=\frac{8}{72}=\frac{1}{9}\).

Answer: A.

As for the difficulty level, I'd say around 600.

Hope it's clear.



also for altitude are we subtracting the y coordinate of R from y coordiante of Q? (4 - 0) ?


No. The coordinates of Q are (8, 4). So, Q is 4 units above 0.
_________________

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
User avatar
Joined: 26 Nov 2014
Posts: 93
Reviews Badge
Re: In the rectangular coordinate system above the area of  [#permalink]

Show Tags

New post 09 Aug 2015, 00:21
For Area PQR,

Base = 10-6 = 4 (x axis points P & R)
Height = 4 (y axis point Q)

Area of PQR = 1/2 * b * h =1/2 * 4 * 4 = 8

Also for Area LMN, Same procedure as above

Base = 14-2 = 12
Height = 12-0 = 12

Area of LMN = 1/2 * b * h =1/2 * 12 * 12 = 72

Area PQR/ Area LMN = 8/72 = 1/9
Current Student
User avatar
Joined: 12 Aug 2015
Posts: 286
Concentration: General Management, Operations
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
GMAT 3: 600 Q47 V27
GPA: 3.3
WE: Management Consulting (Consulting)
Re: In the rectangular coordinate system above the area of  [#permalink]

Show Tags

New post 14 Apr 2016, 22:10
Jaisri wrote:
monirjewel wrote:
Attachment:
Coordinate.jpg
In the rectangular coordinate system above the area of triangle PQR is what fraction of the area triangle LMN?

A. 1/9
B. 1/8
C. 1/6
D. 1/5
E. 1/3

Understanding the question:
Two triangles are given. They look proportional/similar but this should be confirmed. Also, means are provided to calculate length of base and height.

Facts to refer:
If 2 triangles are similar, then the ratio of their area= (ratio of the sides)^2

What's given in the question and what it implies (noted as =>):
Coordinates for L, P, R, N are given => Base of smaller triangle = 4 and that of larger triangle =12
Coordinate for M and Q are given => Height of smaller triangle = 4 and that of larger triangle =12

What is asked for:
Area of PQR/Area of LMN => Ratio of the areas

Solution:
Since the base and height of the triangles are of the same ratio, the 2 triangles are similar. (Since the base and height are of equal ratio, the other 2 sides will also be of the same ratio.) Hence the fact given in "Facts to refer" can be used.
Ratio of sides = 4/12 =1/3
(Ratio of areas) = (1/3)^2 = 1/9


do we really need to confirm the similarity of the 2 triangles for PS question? if I am not mistaken in PS questions the figures are drawn to scale if not stated otherwise (in DS questions figures are NOT drawn to scale if not stated otherwise). Given that the base of the larger triangle relates to the base of the smaller one as 12/4 => 1/3 we can conclude that the areas should follow the ratio (1/3)^2 = 1/9
_________________

KUDO me plenty

Retired Moderator
User avatar
P
Joined: 19 Mar 2014
Posts: 942
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
GMAT ToolKit User Premium Member
Re: In the rectangular coordinate system above the area of  [#permalink]

Show Tags

New post 30 Jun 2017, 13:40
Coordinate.jpg[/attachment]In the rectangular coordinate system above the area of triangle PQR is what fraction of the area triangle LMN?

\(Area of Triangle = \frac{1}{2} * Base * Height\)

\(Area PQR = \frac{1}{2} * 4 * 4\)

\(Area PQR = 8\)

\(Area LMN = \frac{1}{2} * 12 * 12\)

\(Area LMN = 72\)

Ratio:

\(\frac{Area PQR}{Area LMN} = \frac{8}{72}\)

\(\frac{Area PQR}{Area LMN} = \frac{1}{9}\)

Hence, Answer is A
_________________

"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475

Manager
Manager
User avatar
B
Status: IF YOU CAN DREAM IT, YOU CAN DO IT
Joined: 03 Jul 2017
Posts: 203
Location: India
Concentration: Finance, International Business
Re: In the rectangular coordinate system above the area of  [#permalink]

Show Tags

New post 15 Jul 2017, 23:12
while calculating the base i found that triangles are isosceles and so the sides are equal .then i used the Pythagorean therm theorem found the height of the triangle. Is that the correct method??
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9088
Premium Member
Re: In the rectangular coordinate system above the area of  [#permalink]

Show Tags

New post 21 Jul 2018, 18:12
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

GMAT Club Bot
Re: In the rectangular coordinate system above the area of &nbs [#permalink] 21 Jul 2018, 18:12
Display posts from previous: Sort by

In the rectangular coordinate system above the area of

  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®.