Aug 24 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC Aug 25 09:00 AM PDT  12:00 PM PDT Join a FREE 1day verbal workshop and learn how to ace the Verbal section with the best tips and strategies. Limited for the first 99 registrants. Register today! Aug 25 08:00 PM PDT  11:00 PM PDT Exclusive offer! Get 400+ Practice Questions, 25 Video lessons and 6+ Webinars for FREE. Aug 28 08:00 AM PDT  09:00 AM PDT Join a FREE live webinar with examPAL and Admissionado and learn how to master GMAT Critical Reasoning questions and the 6pointed star of MBA application essay glory. Save your spot today! Aug 30 08:00 PM PDT  11:00 PM PDT We'll be posting questions in DS/PS/SC/CR in competition mode. Detailed and quickest solution will get kudos. Will be collecting new links to all questions in this topic. Here you can also check links to fresh questions posted.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 16 Aug 2015
Posts: 20
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.41

If a real number x is chosen at random in the interval [0,3] and a re
[#permalink]
Show Tags
13 Dec 2015, 19:29
Question Stats:
34% (01:53) correct 66% (02:12) wrong based on 91 sessions
HideShow timer Statistics
If a real number x is chosen at random in the interval [0,3] and a real number y is chosen at random in the interval [0,4], what is the probability that x < y? A) 1/2 B) 7/12 C) 5/8 D) 2/3 E) 3/4
Official Answer and Stats are available only to registered users. Register/ Login.



CEO
Joined: 20 Mar 2014
Posts: 2620
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

If a real number x is chosen at random in the interval [0,3] and a re
[#permalink]
Show Tags
Updated on: 14 Dec 2015, 07:57
bablu1234 wrote: If a real number x is chosen at random in the interval [0,3] and a real number y is chosen at random in the interval [0,4], what is the probability that x < y?
A) 1/2 B) 7/12 C) 5/8 D) 2/3 E) 3/4 Refer to the attached picture for the figure. We are given that \(0 \leq x \leq 3\) and \(0 \leq y \leq 4\) Thus the region xy when plotted gives you a rectangle with base = 3 units and height 4 units (as shown in the picture), giving you a total area = 4*3=12 \(units^2\) Now, realize that y=x is a line that passes through (0,0) and (3,3) and divides the above rectangle into a trapezoid (ABCD) and a triangle. The area y>x will belong to the trapezoidal area. Thus, the area of the trapezoid = 0.5*(4+1)*3 = 15/2 Finally, the required probability = trapezoid area / total area = (15/2)/12 = 12/24 = 5/8. C is the correct answer. Hope this helps.
Attachments
121415 95357 AM.jpg [ 26.2 KiB  Viewed 7951 times ]
Originally posted by ENGRTOMBA2018 on 13 Dec 2015, 20:14.
Last edited by ENGRTOMBA2018 on 14 Dec 2015, 07:57, edited 2 times in total.
Updated the solution



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7758
GPA: 3.82

If a real number x is chosen at random in the interval [0,3] and a re
[#permalink]
Show Tags
Updated on: 21 Dec 2015, 01:12
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer. If a real number x is chosen at random in the interval [0,3] and a real number y is chosen at random in the interval [0,4], what is the probability that x < y? A) 1/2 B) 7/12 C) 5/8 D) 2/3 E) 3/4 Following is my approach.... check this out... Since x is in [0,3] and y is in [0,4] we can put them in the coordinate plane. That means in the coordinate plane x and y satisfy 0<= x <=3 and 0<= y <=4. A point (x, y) can be in the rectangle with having (0, 0), (3, 0), (0, 4), (3, 4) as its 4 vertices. Moreover the points with x<y should be in the trapezoid above the line through (0, 0) and (3, 3). The area of the trapezoid above the line(joining (0, 0) and (3, 3)) is 15/2 and the area of the rectangle is 12. So the probability is (15/2)/12 = 15/24=5/8. The answer is, therefore, (C).
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $79 for 1 month Online Course""Free Resources30 day online access & Diagnostic Test""Unlimited Access to over 120 free video lessons  try it yourself"



CEO
Joined: 20 Mar 2014
Posts: 2620
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: If a real number x is chosen at random in the interval [0,3] and a re
[#permalink]
Show Tags
14 Dec 2015, 07:46
MathRevolution wrote: Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.
If a real number x is chosen at random in the interval [0,3] and a real number y is chosen at random in the interval [0,4], what is the probability that x < y?
A) 1/2 B) 7/12 C) 5/8 D) 2/3 E) 3/4
Hi! Engr I'm afraid that you made a mistake to understand the problem because x and y are not integers but real numbers. So we cannot count the all the cases of (x, y) satisfying x<y.
The following is my approach.... check this out...
Since x is in [0,3] and y is in [0,4] we can put them in the coordinate plane. That means in the coordinate plane x and y satisfy 0<= x <=3 and 0<= y <=4. A point (x, y) can be in the rectangle with having (0, 0), (3, 0), (0, 4), (3, 4) as its 4 vertices. Moreover the points with x<y should be in the trapezoid above the line through (0, 0) and (3, 4).
The area of the trapezoid above the line(joining (0, 0) and (3, 4)) is 15/2 and the area of the rectangle is 12.
So the probability is (15/2)/12 = 15/24=5/8.
The answer is, therefore, (C). MathRevolution, thank you. That is indeed an incorrect assumption on my end. Also, I think the text in red above is not correct. I believe you wanted to write the line joining (0,0) and (3,3) and NOT (3,4). The line joining (0,0) and (3,4) will not leave a trapezoid at the top.



Intern
Joined: 16 Aug 2015
Posts: 20
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.41

Re: If a real number x is chosen at random in the interval [0,3] and a re
[#permalink]
Show Tags
14 Dec 2015, 11:54
MathRevolution wrote: Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.
If a real number x is chosen at random in the interval [0,3] and a real number y is chosen at random in the interval [0,4], what is the probability that x < y?
A) 1/2 B) 7/12 C) 5/8 D) 2/3 E) 3/4
Hi! Engr I'm afraid that you made a mistake to understand the problem because x and y are not integers but real numbers. So we cannot count the all the cases of (x, y) satisfying x<y.
The following is my approach.... check this out...
Since x is in [0,3] and y is in [0,4] we can put them in the coordinate plane. That means in the coordinate plane x and y satisfy 0<= x <=3 and 0<= y <=4. A point (x, y) can be in the rectangle with having (0, 0), (3, 0), (0, 4), (3, 4) as its 4 vertices. Moreover the points with x<y should be in the trapezoid above the line through (0, 0) and (3, 4).
The area of the trapezoid above the line(joining (0, 0) and (3, 4)) is 15/2 and the area of the rectangle is 12.
So the probability is (15/2)/12 = 15/24=5/8.
The answer is, therefore, (C). Thanks MathRevolution. It was tough one and I couldn't crack it.



Manager
Joined: 09 Jul 2013
Posts: 109

If a real number x is chosen at random in the interval [0,3] and a re
[#permalink]
Show Tags
17 Dec 2015, 12:53
Another way to look at the problem: Break up the range of y into two parts. 1. \(y>3\) 2. \(0\leq{y}\leq{3}\) We can consider the probability of \(y>x\) for each part, then add them up. For part 1, if \(y>3\), then it will always be greater than x no matter what x is. y will be in this range 1/4 of the time. Probability = 1*1/4 = 1/4. For part 2, both x and y are in the range of [0,3], so we can logically conclude that \(y>x\) half the time (similarly \(x>y\) half the time). y will be in this range 3/4 of the time. 1/2*3/4 = 3/8 Add up both parts: 1/4 + 3/8 = 5/8 Answer C
_________________
Dave de Koos GMAT aficionado



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7758
GPA: 3.82

Re: If a real number x is chosen at random in the interval [0,3] and a re
[#permalink]
Show Tags
21 Dec 2015, 01:20
That is indeed an incorrect assumption on my end. Also, I think the text in red above is not correct. I believe you wanted to write the line joining (0,0) and (3,3) and NOT (3,4). The line joining (0,0) and (3,4) will not leave a trapezoid at the top. Hi! Engr Thank you for pointing out my error. As you pointed out the line is joining (0,0) and (3,3) and NOT (3,4). That makes the diagram a trapezoid.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $79 for 1 month Online Course""Free Resources30 day online access & Diagnostic Test""Unlimited Access to over 120 free video lessons  try it yourself"



NonHuman User
Joined: 09 Sep 2013
Posts: 12075

Re: If a real number x is chosen at random in the interval [0,3] and a re
[#permalink]
Show Tags
27 Jul 2018, 19:55
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.
_________________




Re: If a real number x is chosen at random in the interval [0,3] and a re
[#permalink]
27 Jul 2018, 19:55






