NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 13:38 It is currently 25 Apr 2024, 13:38
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

In the rectangular coordinate plane, a rectangular region has vertices

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619010 [17]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
In the rectangular coordinate plane, a rectangular region has vertices [#permalink] New post   12 Nov 2019, 03:56
17
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

71% (02:52) correct 29% (03:05) wrong based on 272 sessions
Hide Show timer Statistics
In the rectangular coordinate plane, a rectangular region has vertices (2.5, 4.5), (2.5, −1.5), (−7.5, -1.5), and (−7.5, 4.5). If a point from within the rectangle is to be randomly selected such that both the x- and y-coordinates are integers, what is the probability that both coordinates of the selected point are negative?

A. 1/11
B. 7/60
C. 2/15
D. 16/77
E. 4/15


Are You Up For the Challenge: 700 Level Questions
ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
S
TheGuyDangerous
Current Student
Joined: 10 Sep 2019
Posts: 137
Own Kudos [?]: 33 [11]
Given Kudos: 59
Location: India
Concentration: Social Entrepreneurship, Healthcare
Schools: Fuqua '24 (D) ISB '23 (A) Darden '24 (D) Johnson '24 (D) Kenan-Flagler '24 (I) McDonough '24 (S) Tepper '24 (S)
GMAT 1: 680 Q49 V33
GMAT 2: 720 Q50 V37
GRE 1: Q167 V159
GPA: 2.59
WE:Project Management (Non-Profit and Government)
Send PM
Reviews Badge
In the rectangular coordinate plane, a rectangular region has vertices [#permalink] New post   12 Nov 2019, 09:52
6
Kudos
4
Bookmarks
Given that the randomly chosen point should have X- & Y- coordinates as negative, the point should lie in the III Quadrant. => The point has to lie between X - (0 to -7.5) & Y - (0 to -1.5).
Also given that the coordinates for the randomly selected points are 'Negative integers'.
=>X can be any one of (-7,-6,-5,-4,-3,-2,-1) => 7C1
=> Y can be any one of (-1) => 1C1
=> Total combinations = 7C1*1C1 = 7

Total combinations for a point to lie anywhere in the rectangle =
X- (-7,-6,-5,-4,-3,-2,-1,0,1,2) & Y- (-1,0,1,2,3,4)
=> 10C1*6C1 = 10*6 = 60

=> Probability = 7/60

IMO B
General Discussion
User avatar
B
TumharaFaizal
Current Student
Joined: 07 Jul 2019
Posts: 35
Own Kudos [?]: 19 [2]
Given Kudos: 105
Location: India
Concentration: Strategy, Technology
Schools: Desautels '23 (A$) Rice Jones '23 (A$) Tepper '23 (WL)
GMAT 1: 710 Q50 V35
GPA: 4
WE:Analyst (Computer Software)
Send PM
Re: In the rectangular coordinate plane, a rectangular region has vertices [#permalink] New post   19 May 2020, 14:10
2
Bookmarks
Integers in length of rect. ( -7 to 2) = 10
Integers in breadth of rect. ( -1 to 4) = 6
total integer cordinates = 10* 6 = 60

negative cordinate X (-1 to -7) =7
negative cordinate Y (-1 to -1) = 1
Total negative cordinates possible= 7*1 = 7

required probability = 7/60

IMO (B).

Thanks
User avatar
S
LucienH
Manager
Manager
Joined: 14 Sep 2023
Posts: 95
Own Kudos [?]: 33 [0]
Given Kudos: 25
Send PM
Re: In the rectangular coordinate plane, a rectangular region has vertices [#permalink] New post   14 Oct 2023, 08:31
-7.5 < x < 2.5
-1.5 < y < 4.5

x and y will be integers, so:
-7 < x < 2
-1 < y < 4

the cases where x can be negative are {-7, -6, -5, -4, -3, -2, -1} which is 7/10 cases
the only case where y can be negative is{-1} which is 1/6 cases

probability = 7/10 * 1/6 = 7/60

Answer B
GMAT Club Bot
gmatclubot
Re: In the rectangular coordinate plane, a rectangular region has vertices [#permalink]
14 Oct 2023, 08:31
Moderators:
Bunuel
Math Expert
92915 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions