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

It is currently 16 Nov 2018, 08:06

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 November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • Free GMAT Strategy Webinar

     November 17, 2018

     November 17, 2018

     07:00 AM PST

     09:00 AM PST

    Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
  • GMATbuster's Weekly GMAT Quant Quiz # 9

     November 17, 2018

     November 17, 2018

     09:00 AM PST

     11:00 AM PST

    Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage.

If a real number x is chosen at random in the interval [0,3] and a re

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

Hide Tags

Intern
Intern
avatar
Joined: 16 Aug 2015
Posts: 22
Location: India
Concentration: General Management, Entrepreneurship
GMAT 1: 510 Q22 V19
GPA: 3.41
GMAT ToolKit User
If a real number x is chosen at random in the interval [0,3] and a re  [#permalink]

Show Tags

New post 13 Dec 2015, 18:29
2
12
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

34% (01:45) correct 66% (02:11) wrong based on 82 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
CEO
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2635
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
If a real number x is chosen at random in the interval [0,3] and a re  [#permalink]

Show Tags

New post Updated on: 14 Dec 2015, 06:57
1
2
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 x-y 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

12-14-15 9-53-57 AM.jpg
12-14-15 9-53-57 AM.jpg [ 26.2 KiB | Viewed 6019 times ]


Originally posted by ENGRTOMBA2018 on 13 Dec 2015, 19:14.
Last edited by ENGRTOMBA2018 on 14 Dec 2015, 06:57, edited 2 times in total.
Updated the solution
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6517
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
If a real number x is chosen at random in the interval [0,3] and a re  [#permalink]

Show Tags

New post Updated on: 21 Dec 2015, 00:12
3
1
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 spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"


Originally posted by MathRevolution on 14 Dec 2015, 00:17.
Last edited by MathRevolution on 21 Dec 2015, 00:12, edited 2 times in total.
CEO
CEO
avatar
S
Joined: 20 Mar 2014
Posts: 2635
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
Re: If a real number x is chosen at random in the interval [0,3] and a re  [#permalink]

Show Tags

New post 14 Dec 2015, 06:46
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
Intern
avatar
Joined: 16 Aug 2015
Posts: 22
Location: India
Concentration: General Management, Entrepreneurship
GMAT 1: 510 Q22 V19
GPA: 3.41
GMAT ToolKit User
Re: If a real number x is chosen at random in the interval [0,3] and a re  [#permalink]

Show Tags

New post 14 Dec 2015, 10:54
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
Manager
avatar
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

New post 17 Dec 2015, 11:53
1
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
User avatar
V
Joined: 16 Aug 2015
Posts: 6517
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: If a real number x is chosen at random in the interval [0,3] and a re  [#permalink]

Show Tags

New post 21 Dec 2015, 00:20
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 spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8786
Premium Member
Re: If a real number x is chosen at random in the interval [0,3] and a re  [#permalink]

Show Tags

New post 27 Jul 2018, 18:55
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: If a real number x is chosen at random in the interval [0,3] and a re &nbs [#permalink] 27 Jul 2018, 18:55
Display posts from previous: Sort by

If a real number x is chosen at random in the interval [0,3] and a re

  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®.