Forum Home > GMAT > Quantitative > Problem Solving (PS)
Events & Promotions
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Sep 1111:30 AM EDT
-12:30 PM EDT
Struggling to find the right strategies to score a 99 %ile on GMAT Focus? Riya (GMAT 715) boosted her score by 100-points in just 15 days! Discover how the right mentorship, tailored strategies, and an unwavering mindset can transform your GMAT prep.
Sep 0810:00 AM PDT
-11:00 AM PDT
Paid vs Free GMAT Resources: "What's Best for You?" This concise guide breaks down the pros and cons of both free and paid study materials, helping you make an informed decision for your GMAT journey.
Sep 1211:00 AM EDT
-12:00 PM EDT
Have you ever wondered how to score a PERFECT 805 on the GMAT? Meet Julia, a banking professional who used the Target Test Prep course to achieve this incredible feat. Julia's story is nothing short of an inspiration.
Sep 1310:00 AM EDT
-11:00 AM EDT
More and more TTP students are earning impressive scores on the GMAT. Now is the perfect time to join the many GMAT students who made the switch to TTP and surpassed their wildest expectations on test day.
Sep 1308:00 PM PDT
-09:00 PM PDT
Full-length FE mock with insightful analytics, weakness diagnosis, and video explanations!
Sep 1405:30 AM PDT
-07:30 AM PDT
Unlock GMAT success! Join our webinar for exclusive insights on scoring V85+ in the Verbal section. Proven strategies, expert tips, and essential focus to elevate your GMAT game. Register now for the ultimate Verbal mastery!
Sep 1411:00 AM IST
-01:00 PM IST
Text – Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies, Tackle difficult RC & MSR with confidence, Excel in timed test environment- Sep 15
11:00 AM IST
-01:00 PM IST
Attend this session to evaluate your current skill level, learn process skills, and solve through tough Arithmetic questions.
Region R is defined as the region in the first quadrant satisfying the
[#permalink]
05 May 2020, 03:15
05 May 2020, 03:15
1
Kudos
15
Bookmarks
Expert Reply
Show timer
00:00
A
B
C
D
E
Difficulty:
75%
(hard)
Question Stats:
52% (02:17) correct
48%
(02:29)
wrong
based on 145
sessions
Region R is defined as the region in the first quadrant satisfying the condition 3x + 4y < 12. Given that a point P with coordinates (r, s) lies within the region R, what is the probability that r > 2?
A. 1/6
B. 1/5
C. 1/4
D. 1/3
E. 1/2
Are You Up For the Challenge: 700 Level Questions
A. 1/6
B. 1/5
C. 1/4
D. 1/3
E. 1/2
Are You Up For the Challenge: 700 Level Questions
GMATWhiz Representative
Joined: 07 May 2019
Posts: 3401
Given Kudos: 68
Location: India
GMAT 1: 740 Q50 V41
GMAT 2: 760 Q51 V40
Re: Region R is defined as the region in the first quadrant satisfying the
[#permalink]
05 May 2020, 06:38
05 May 2020, 06:38
4
Kudos
Expert Reply
Bunuel wrote:
Region R is defined as the region in the first quadrant satisfying the condition 3x + 4y < 12. Given that a point P with coordinates (r, s) lies within the region R, what is the probability that r > 2?
A. 1/6
B. 1/5
C. 1/4
D. 1/3
E. 1/2
Are You Up For the Challenge: 700 Level Questions
A. 1/6
B. 1/5
C. 1/4
D. 1/3
E. 1/2
Are You Up For the Challenge: 700 Level Questions
Solution
- • If we draw the line \(3x + 4y = 12\) in co-ordinate plane, we can see that, it passes through Points A(0,3) and B(4,0).
- o So, region R is nothing but triangle, AOB (as shown in the below diagram)
• Now, all the points inside region R whose x co-ordinate is greater than 2 must lies inside the shaded region, as shown in the above diagram. (We can find the co-ordinates of point D by substituting \(x = 2\) in the line \(3x + 4y = 12\)).
• We can observe that the area of triangle AOB represents all the points inside the region R and area of triangle CDB represents the points inside region R whose x- co-ordinate is greater than 2.
• Thus, the required probability = area of triangle CDB / area of the triangle AOB \(= \frac{0.5*CB*DC}{0.5*AO*OB} = \frac{0.5*2*1.5}{0.5*3*4} = \frac{1.5 }{ 6} = \frac{1}{4}\)
GMAT Club Legend
Joined: 03 Oct 2013
Affiliations: CrackVerbal
Posts: 4914
Given Kudos: 221
Location: India
Re: Region R is defined as the region in the first quadrant satisfying the
[#permalink]
02 Oct 2020, 04:43
02 Oct 2020, 04:43
2
Kudos
1
Bookmarks
Top Contributor
This is a pretty decent question combining Co -ordinate geometry and probability.
We are given that 3x + 4y < 12.
The x intercept (when y = 0) is (4, 0) and y intercept (when x = 0) is (0, 3)
The region R is a right angled triangle (Triangle OAB) who's area is 6 units formed by the Origin (0,0), Point A (0,3) and Point B (4,0)
Now to find point (r,s), where r is > 2. The value of s can be found by putting r = 2
6 + 4y = 12
4y = 6
y = 1.5
Point (r, s) as shown by point C is (2,1.5).
This point along with (2,0) shown as Point D and (4,0) forms another right angled triangle (Triangle CDB)
Area = (1/2) * (4 - 2) * 1.5 = 1.5 units
\(Probability = \frac{Favorable \space Outcomes}{Total \space Outcomes}\)
Favorable outcomes = Point lies in the area of 1.5 units
Total Outcomes = Area of R = 6 units.
Therefore the required probability = \(\frac{1.5}{6} = \frac{1}{4}\)
Option C
Arun Kumar
We are given that 3x + 4y < 12.
The x intercept (when y = 0) is (4, 0) and y intercept (when x = 0) is (0, 3)
The region R is a right angled triangle (Triangle OAB) who's area is 6 units formed by the Origin (0,0), Point A (0,3) and Point B (4,0)
Now to find point (r,s), where r is > 2. The value of s can be found by putting r = 2
6 + 4y = 12
4y = 6
y = 1.5
Point (r, s) as shown by point C is (2,1.5).
This point along with (2,0) shown as Point D and (4,0) forms another right angled triangle (Triangle CDB)
Area = (1/2) * (4 - 2) * 1.5 = 1.5 units
\(Probability = \frac{Favorable \space Outcomes}{Total \space Outcomes}\)
Favorable outcomes = Point lies in the area of 1.5 units
Total Outcomes = Area of R = 6 units.
Therefore the required probability = \(\frac{1.5}{6} = \frac{1}{4}\)
Option C
Arun Kumar
Attachments
Probability.jpg [ 569.63 KiB | Viewed 7467 times ]
