NEW HERE? LEARN MORE
closeclose
Last visit was: 28 Apr 2024, 17:20 It is currently 28 Apr 2024, 17:20
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

The distance between Urbania and Metropolis is 30 miles, with numbered

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
S
filipembribeiro
Intern
Intern
Joined: 20 Jul 2020
Posts: 36
Own Kudos [?]: 125 [2]
Given Kudos: 48
Location: Brazil
WE:Consulting (Consulting)
Send PM
The distance between Urbania and Metropolis is 30 miles, with numbered [#permalink] New post   25 Jul 2021, 11:04
2
Bookmarks
00:00
A
B
C
D
E

Difficulty:

95% (hard)

Question Stats:

27% (02:22) correct 73% (02:05) wrong based on 62 sessions
Hide Show timer Statistics
The distance between Urbania and Metropolis is 30 miles, with numbered markers indicating each mile out of Urbania. If a person starts at a random location on the road between the two cities and drives exactly five miles in the direction of Metropolis—without passing the city—what is the probability that this person ends within five miles of the sign indicating 25 miles from Urbania?

(A) \(16 \frac{1}{6}%\)
(B) \(20%\)
(C) \(33 \frac{1}{3}%\)
(D) \(40%\)
(E) \(80%\)
ShowHide Answer
Official Answer
D
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11183
Own Kudos [?]: 32023 [2]
Given Kudos: 291
Send PM
Reviews Badge
Re: The distance between Urbania and Metropolis is 30 miles, with numbered [#permalink] New post   26 Jul 2021, 09:52
1
Kudos
Expert Reply
filipembribeiro wrote:
The distance between Urbania and Metropolis is 30 miles, with numbered markers indicating each mile out of Urbania. If a person starts at a random location on the road between the two cities and drives exactly five miles in the direction of Metropolis—without passing the city—what is the probability that this person ends within five miles of the sign indicating 25 miles from Urbania?

(A) \(16 \frac{1}{6}%\)
(B) \(20%\)
(C) \(33 \frac{1}{3}%\)
(D) \(40%\)
(E) \(80%\)



Probability is almost always between 0 and 1, both inclusive. So I believe we are looking for likelihood in %.

If the person travels 5 miles towards M, he can never be within 5 miles from U.

So total event = 5 to 30 = 25
Event of being within 5 miles from 25 mile marker = 20 to 30 = 10

P = \(\frac{10}{25}=\frac{2}{5}\).

As a % = \(100*\frac{2}{5}=40\)%


D
User avatar
L
IanStewart
GMAT Tutor
Joined: 24 Jun 2008
Posts: 4128
Own Kudos [?]: 9248 [0]
Given Kudos: 91
 Q51  V47
Send PM
Re: The distance between Urbania and Metropolis is 30 miles, with numbered [#permalink] New post   26 Jul 2021, 10:23
Expert Reply
chetan2u wrote:
So total event = 5 to 30 = 25


It's only correct to calculate probability in this way if each event is equally likely, and as I would read the question, some final locations are more likely than others for the person. When I read the question:

filipembribeiro wrote:
The distance between Urbania and Metropolis is 30 miles, with numbered markers indicating each mile out of Urbania. If a person starts at a random location on the road between the two cities and drives exactly five miles in the direction of Metropolis—without passing the city—what is the probability that this person ends within five miles of the sign indicating 25 miles from Urbania?


if the person truly starts in a random location between M and U, then there's a 30 mile stretch where he could start, so that must be the denominator of the probability. Now, it's not clear what the person does when they start within 5 miles of M, but since the person travels towards M "without passing the city", I'd just assume they stop there. If that interpretation is correct, then as long as the person starts within 15 miles of M, the person will end up within 10 miles of M, and will thus be within 5 miles of the "25 miles from U/5 miles from M" sign. Under that interpretation, the answer is 15/30 = 1/2.

If the question designer wants the answer to be 2/5, then the question isn't properly worded, because in that case, the person does not "start at a random location on the road", but that's what the question tells us is happening. What is the source?
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11183
Own Kudos [?]: 32023 [0]
Given Kudos: 291
Send PM
Reviews Badge
Re: The distance between Urbania and Metropolis is 30 miles, with numbered [#permalink] New post   26 Jul 2021, 11:08
Expert Reply
IanStewart wrote:
chetan2u wrote:
So total event = 5 to 30 = 25


It's only correct to calculate probability in this way if each event is equally likely, and as I would read the question, some final locations are more likely than others for the person. When I read the question:

filipembribeiro wrote:
The distance between Urbania and Metropolis is 30 miles, with numbered markers indicating each mile out of Urbania. If a person starts at a random location on the road between the two cities and drives exactly five miles in the direction of Metropolis—without passing the city—what is the probability that this person ends within five miles of the sign indicating 25 miles from Urbania?


if the person truly starts in a random location between M and U, then there's a 30 mile stretch where he could start, so that must be the denominator of the probability. Now, it's not clear what the person does when they start within 5 miles of M, but since the person travels towards M "without passing the city", I'd just assume they stop there. If that interpretation is correct, then as long as the person starts within 15 miles of M, the person will end up within 10 miles of M, and will thus be within 5 miles of the "25 miles from U/5 miles from M" sign. Under that interpretation, the answer is 15/30 = 1/2.

If the question designer wants the answer to be 2/5, then the question isn't properly worded, because in that case, the person does not "start at a random location on the road", but that's what the question tells us is happening. What is the source?


I would agree it is not worded properly and that is why ‘without passing the city’ could easily mean that he picks a random location but does not pass the city even after travelling 5 miles towards M. That would mean he does not start between 25 and 30. The answer would again be 2/5 here.

For the answer to be 1/2, the question should have been that ‘he travels 5 miles in direction of M or the distance till M if the distance is less than 5.’

The question could have been better worded either way.
GMAT Club Bot
gmatclubot
Re: The distance between Urbania and Metropolis is 30 miles, with numbered [#permalink]
26 Jul 2021, 11:08
Moderators:
Bunuel
Math Expert
92977 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