Find all School-related info fast with the new School-Specific MBA Forum

It is currently 19 Sep 2014, 07:48

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

An (x, y) coordinate pair is to be chosen at random from the

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
User avatar
Joined: 12 Dec 2012
Posts: 163
Location: Poland
Followers: 4

Kudos [?]: 92 [0], given: 67

An (x, y) coordinate pair is to be chosen at random from the [#permalink] New post 18 Jan 2013, 15:38
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

79% (01:50) correct 21% (01:24) wrong based on 106 sessions
An (x, y) coordinate pair is to be chosen at random from the xy-plane. What is the probability that y\geq|x|?

(A) 1/10
(B) 1/8
(C) 1/6
(D) 1/5
(E) 1/4


Here's how I bumped on the answer - very quickly, but I am not 100% sure if logic I used was correct. Someone could proof please?
[Reveal] Spoiler:
The |x| is always positive.

The y is positive in two quadrants - so P[y\geq0]=\frac{1}{2}.

(I am deliberately ignoring here y=0, because theoretically the axes lie inbetween the quadrants, so 0 isn't part of any quadrant equally.)

So, when P[y\geq0=\frac{1}{2}], we need to figure out P[y>x].

Since there is infinite number of possibilities for positive values of x and y, I concluded that there's a 50% chance of picking (x, y) at random, such that y>x.

(Here's another apparent leave-out: the possibility that x=y. However, this is only one possibility among infinity, so as for me it's acceptable. Please correct me if I am wrong.)

This way we've got P[y\geq0]=\frac{1}{2} and P[y>x]=\frac{1}{2}.

Therefore P[y\geq|x|]=(\frac{1}{2})(\frac{1}{2})=\frac{1}{4}.

The answer is E.

The answer is correct and I hope it's not pure luck :).
[Reveal] Spoiler: OA

_________________

If I answered your question with this post, use the motivating power of kudos!

Expert Post
4 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23483
Followers: 3500

Kudos [?]: 26433 [4] , given: 2712

Re: An (x, y) coordinate pair is to be chosen at random from the [#permalink] New post 18 Jan 2013, 16:04
4
This post received
KUDOS
Expert's post
HumptyDumpty wrote:
An (x, y) coordinate pair is to be chosen at random from the xy-plane. What is the probability that y\geq|x|?

(A) 1/10
(B) 1/8
(C) 1/6
(D) 1/5
(E) 1/4


Here's how I bumped on the answer - very quickly, but I am not 100% sure if logic I used was correct. Someone could proof please?
[Reveal] Spoiler:
The |x| is always positive.

The y is positive in two quadrants - so P[y\geq0]=\frac{1}{2}.

(I am deliberately ignoring here y=0, because theoretically the axes lie inbetween the quadrants, so 0 isn't part of any quadrant equally.)

So, when P[y\geq0=\frac{1}{2}], we need to figure out P[y>x].

Since there is infinite number of possibilities for positive values of x and y, I concluded that there's a 50% chance of picking (x, y) at random, such that y>x.

(Here's another apparent leave-out: the possibility that x=y. However, this is only one possibility among infinity, so as for me it's acceptable. Please correct me if I am wrong.)

This way we've got P[y\geq0]=\frac{1}{2} and P[y>x]=\frac{1}{2}.

Therefore P[y\geq|x|]=(\frac{1}{2})(\frac{1}{2})=\frac{1}{4}.

The answer is E.

The answer is correct and I hope it's not pure luck :).


Below is given graph of y=|x|:
Attachment:
Graph.png
Graph.png [ 11.52 KiB | Viewed 1506 times ]
All points which satisfy y\geq|x| condition lie above that graph. You can see that portion of the plane which is above the graph is 1/4.

Answer: E.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

2 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 27 Jun 2012
Posts: 417
Concentration: Strategy, Finance
Followers: 40

Kudos [?]: 357 [2] , given: 182

Re: An (x, y) coordinate pair is to be chosen at random from the [#permalink] New post 18 Jan 2013, 16:12
2
This post received
KUDOS
Attachment:
XY Plane probability.jpg
XY Plane probability.jpg [ 171.15 KiB | Viewed 1506 times ]


Just plot the y>|x| on your paper and you will see it takes 1/4 of the space i.e. Probability = 1/4

Hence choice(E) is the answer.
_________________

Thanks,
PraPon

Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7
Reading Comprehension notes: Click here
VOTE: vote-best-gmat-practice-tests-excluding-gmatprep-144859.html
PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here

SVP
SVP
User avatar
Joined: 09 Sep 2013
Posts: 2425
Followers: 197

Kudos [?]: 38 [0], given: 0

Premium Member
Re: An (x, y) coordinate pair is to be chosen at random from the [#permalink] New post 09 Jun 2014, 07:05
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: An (x, y) coordinate pair is to be chosen at random from the   [#permalink] 09 Jun 2014, 07:05
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic If x and y are both integers chosen at random between 1 and Galiya 1 07 Apr 2012, 03:04
Experts publish their posts in the topic If x is to be chosen at random from the set {1,2,3,4} and y Madelaine88 3 01 Mar 2011, 08:32
Set X = Set Y = If a number is chosen at random from Set X bmwhype2 2 02 Nov 2007, 11:39
If the variables w,x,y and z are chosen at random so that kevincan 7 20 Apr 2007, 06:12
If X is to be chosen at random from the set {1,2,3,4} and Y empanado 4 17 Mar 2007, 14:26
Display posts from previous: Sort by

An (x, y) coordinate pair is to be chosen at random from the

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.