Aug 18 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes. Aug 19 08:00 AM PDT  09:00 AM PDT Join a 4day FREE online boot camp to kick off your GMAT preparation and get you into your dream bschool in R1.**Limited for the first 99 registrants. Register today! Aug 20 08:00 PM PDT  09:00 PM PDT EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299) Aug 20 09:00 PM PDT  10:00 PM PDT Take 20% off the plan of your choice, now through midnight on Tuesday, 8/20 Aug 22 09:00 PM PDT  10:00 PM PDT What you'll gain: Strategies and techniques for approaching featured GMAT topics, and much more. Thursday, August 22nd at 9 PM EDT
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 13 Oct 2010
Posts: 20

A circular racetrack is 3 miles in length and has signs post
[#permalink]
Show Tags
13 Dec 2010, 01:26
Question Stats:
59% (02:21) correct 41% (02:29) wrong based on 479 sessions
HideShow timer Statistics
A circular racetrack is 3 miles in length and has signs posted to indicate each 1/10 mile increment. If a race car starts at a random location on the track and travels exactly one half mile, what is the probability that the car ends within a half mile of the sign indicating 2 1/2 miles? A. 1/6 B. 3/10 C. 1/3 D. 1/2 E. 2/3
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 57022

A circular racetrack is 3 miles in length and has signs post
[#permalink]
Show Tags
13 Dec 2010, 04:13
helloanupam wrote: A circular racetrack is 3 miles in length and has signs posted to indicate each 1/10 mile increment. If a race car starts at a random location on the track and travels exactly one half mile, what is the probability that the car ends within a half mile of the sign indicating 2 1/2 miles?
A. 1/6 B. 3/10 C. 1/3 D. 1/2 E. 2/3
Bunuel, Sorry, I could not understand the language of the question and hence probably the answer is not clear to me. If possible , could you reframe the question or explain as to what the question is asking? Look at the diagram: The car ends within a half mile of the sign indicating 2.5 miles means that the car should end in one mile interval, between the signs indicating 2 (2.50.5=2) and 3 miles (2+0.5=3), so within the red segment on the diagram. Now if the car appears somewhere between the blue dots, between 1.5 and 2 miles signs then after traveling 0.5 miles the car will be in the red segment. So in order after traveling 0.5 miles the car to end within the red segment it should appear between 1.5 and 2.5 miles, so within 1 mile interval, as the circumference of the track is 3 miles then the probability of that will be P=favorable/total=1/3. As I mentioned in my previous post actually it doesn't matter where the car appears or what distance it travel, as long as favorable interval in the end is 1 mile and total interval is 3 miles then the probability will be 1/3 miles. Hope it's clear. Attachment:
untitled.PNG [ 5.9 KiB  Viewed 9520 times ]
_________________




Math Expert
Joined: 02 Sep 2009
Posts: 57022

Re: Circular Race Track Probability.
[#permalink]
Show Tags
13 Dec 2010, 02:34
helloanupam wrote: A circular racetrack is 3 miles in length and has signs posted to indicate each 1/10 mile increment. If a race car starts at a random location on the track and travels exactly one half mile,what is the probability that the car ends within a half mile of the sign indicating 2 1/2 miles? (A) 1/6 (B) 3/10 (C) 1/3 (D) 1/2 (E) 2/3
Answer: C
Could somebody explain how to work this out? The car ends within a half mile of the sign indicating 2 1/2 miles means that the car will end in one mile interval, between the signs indicating 2 and 3 miles. Now, it doesn't matter where the car starts or what distance it travels, the probability will be P=(favorable outcome)/(total # of outcomes)=1/3 (as the car starts at random point end travels some distance afterwards we can consider its end point as the point where he randomly appeared, so the probability that the car appeared within 1 mile interval out of total 3 miles will be 1/3). Answer: C. Hope it's clear.
_________________



Intern
Joined: 13 Oct 2010
Posts: 20

Re: Circular Race Track Probability.
[#permalink]
Show Tags
13 Dec 2010, 03:47
Bunuel, Sorry, I could not understand the language of the question and hence probably the answer is not clear to me. If possible , could you reframe the question or explain as to what the question is asking?



Director
Joined: 03 Sep 2006
Posts: 716

Re: Circular Race Track Probability.
[#permalink]
Show Tags
13 Dec 2010, 05:06
Don't we somehow need to use the information 1/10 mile increment signposts in calculating the probability? Approach mentioned above is logical but there must be simple mathematical solution using the increment signposts?



Math Expert
Joined: 02 Sep 2009
Posts: 57022

Re: Circular Race Track Probability.
[#permalink]
Show Tags
13 Dec 2010, 06:14
LM wrote: Don't we somehow need to use the information 1/10 mile increment signposts in calculating the probability? Approach mentioned above is logical but there must be simple mathematical solution using the increment signposts? Stem gives us the information about the signs only to fix the point of 2.5 miles on the track and thus fix the 1 mile interval the car should end within. 1/10 mile increment is totally irrelevant. Consider the following: A circular racetrack is 3 miles in length. If a race car starts at a random location on the track and travels exactly Y miles, what is the probability that the car ends within a half mile of some point X on the track? The answer will be the same: as the interval for the endpoint of the car is 1 mile (from x0.5 to x+0.5) then the probability will be 1/3. Note that a car starts at a random location on the track and travels exactly Y miles means that the endpoint of the car will also be at random location on the track (travel part is also to confuse us: random location plus Y miles=random location). So the question basically ask what is the probability that the car ends within the particular 1 mile interval on the track of 3 miles. Hope it's clear.
_________________



Senior Manager
Status: Bring the Rain
Joined: 17 Aug 2010
Posts: 344
Location: United States (MD)
Concentration: Strategy, Marketing
Schools: Michigan (Ross)  Class of 2014
GPA: 3.13
WE: Corporate Finance (Aerospace and Defense)

Re: Circular Race Track Probability.
[#permalink]
Show Tags
13 Dec 2010, 06:41
+1 for C. Thanks Bunuel
_________________



Intern
Joined: 13 Oct 2010
Posts: 20

Re: Circular Race Track Probability.
[#permalink]
Show Tags
13 Dec 2010, 08:37
Thankyou Bunuel for the extra efforts in explaining. I have now understood your explanation.



Math Expert
Joined: 02 Sep 2009
Posts: 57022

Re: A circular racetrack is 3 miles in length and has signs post
[#permalink]
Show Tags
07 Jun 2013, 07:05
Bumping for review and further discussion*. Get a kudos point for an alternative solution! *New project from GMAT Club!!! Check HERE
_________________



Current Student
Joined: 09 Apr 2013
Posts: 41
Location: United States (DC)
Concentration: Strategy, Social Entrepreneurship
GPA: 3.55
WE: General Management (NonProfit and Government)

Re: A circular racetrack is 3 miles in length and has signs post
[#permalink]
Show Tags
07 Jun 2013, 08:33
Here is a rewording of the original question: What is the probability that the car starts between the 1.5 mile and 2.5 mile mark on a 3 mi racetrack?
2.5  1.5 = 1 that is 1/3 of the racetrack
Answer is C
Everything else in this question is irrelevant. Although, if you really wanted you could rephrase the question to account for the 1/10th mile sign posts: What is the probability that the car stars between the 15th and 25th sign posts if there are 30 sign posts total. But that is unnecessary extra work.



Manager
Joined: 14 Nov 2011
Posts: 116
Location: United States
Concentration: General Management, Entrepreneurship
GPA: 3.61
WE: Consulting (Manufacturing)

Re: Circular Race Track Probability.
[#permalink]
Show Tags
09 Jun 2013, 05:44
Bunuel wrote: helloanupam wrote: Bunuel, Sorry, I could not understand the language of the question and hence probably the answer is not clear to me. If possible , could you reframe the question or explain as to what the question is asking? Look at the diagram: Attachment: untitled.PNG The car ends within a half mile of the sign indicating 2.5 miles means that the car should end in one mile interval, between the signs indicating 2 (2.50.5=2) and 3 miles (2+0.5=3), so within the red segment on the diagram. Now if the cars appears somewhere between the blue dots, between 1.5 and 2 miles signs then after traveling 0.5 miles the car will be in the red segment. So in order after traveling 0.5 miles the car to end within the red segment it should appear between 1.5 and 2.5 miles, so within 1 mile interval, as the circumference of the track is 3 miles then the probability of that will be P=favorable/total=1/3. As I mentioned in my previous post actually it doesn't matter where the car appears or what distance it travel, as long as favorable interval in the end is 1 mile and total interval is 3 miles then the probability will be 1/3 miles. Hope it's clear. Hi Bunnel, What about if car starts between 0.5 and 2.5 miles? So this will make probability = 2*1/3 ?



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 7367
Location: United States (CA)

Re: A circular racetrack is 3 miles in length and has signs post
[#permalink]
Show Tags
14 Feb 2017, 16:55
helloanupam wrote: A circular racetrack is 3 miles in length and has signs posted to indicate each 1/10 mile increment. If a race car starts at a random location on the track and travels exactly one half mile, what is the probability that the car ends within a half mile of the sign indicating 2 1/2 miles?
A. 1/6 B. 3/10 C. 1/3 D. 1/2 E. 2/3 We are given that a circular racetrack is 3 miles in length and has signs posted to indicate each 1/10 mile increment. We are also given that a race car starts at a random location on the track and travels exactly one half mile, and we need to determine the probability that the car ends within a half mile of the sign indicating 2 1/2 (or 2.5) miles. If the car ends within a half mile of the 2.5mile sign, that means the car can end as far as the 2.0mile sign or the 3.0mile sign. However, since the car travels exactly one half mile, the starting point of the car can be anywhere from the 1.5 mile sign to the 2.5mile sign. In other words, the car can be anywhere in this 2.5  1.5 = 1 mile stretch. Since the racetrack is 3 miles long, the probability that the car is in this 1 mile stretch is ⅓. Answer: C
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Senior Manager
Joined: 03 Apr 2013
Posts: 268
Location: India
Concentration: Marketing, Finance
GPA: 3

Re: A circular racetrack is 3 miles in length and has signs post
[#permalink]
Show Tags
11 Jul 2017, 06:42
Bunuel wrote: helloanupam wrote: A circular racetrack is 3 miles in length and has signs posted to indicate each 1/10 mile increment. If a race car starts at a random location on the track and travels exactly one half mile,what is the probability that the car ends within a half mile of the sign indicating 2 1/2 miles? (A) 1/6 (B) 3/10 (C) 1/3 (D) 1/2 (E) 2/3
Answer: C
Could somebody explain how to work this out? The car ends within a half mile of the sign indicating 2 1/2 miles means that the car will end in one mile interval, between the signs indicating 2 and 3 miles. Now, it doesn't matter where the car starts or what distance it travels, the probability will be P=(favorable outcome)/(total # of outcomes)=1/3 (as the car starts at random point end travels some distance afterwards we can consider its end point as the point where he randomly appeared, so the probability that the car appeared within 1 mile interval out of total 3 miles will be 1/3). Answer: C. Hope it's clear. BunuelShouldn't the answer be 2/3? The question doesn't specify in which direction the car has to travel, so it could be in either direction. Or may be I'm overthinking
_________________
Spread some love..Like = +1 Kudos



Manager
Joined: 26 Dec 2017
Posts: 153

Re: A circular racetrack is 3 miles in length and has signs post
[#permalink]
Show Tags
15 Jul 2018, 11:47
Bunuel wrote: helloanupam wrote: Bunuel, Sorry, I could not understand the language of the question and hence probably the answer is not clear to me. If possible , could you reframe the question or explain as to what the question is asking? Look at the diagram: Attachment: untitled.PNG The car ends within a half mile of the sign indicating 2.5 miles means that the car should end in one mile interval, between the signs indicating 2 (2.50.5=2) and 3 miles (2+0.5=3), so within the red segment on the diagram. Now if the car appears somewhere between the blue dots, between 1.5 and 2 miles signs then after traveling 0.5 miles the car will be in the red segment. So in order after traveling 0.5 miles the car to end within the red segment it should appear between 1.5 and 2.5 miles, so within 1 mile interval, as the circumference of the track is 3 miles then the probability of that will be P=favorable/total=1/3. As I mentioned in my previous post actually it doesn't matter where the car appears or what distance it travel, as long as favorable interval in the end is 1 mile and total interval is 3 miles then the probability will be 1/3 miles. Hope it's clear. BunuelA small doubt here to be precise the correct ranges would be 2.1,2.2,2.3,2.4,2.5,2.6,2.7,2.8,2.9 as 2.5 miles /+ 0.4 miles (within 0.5 miles i.e, <=0.5> <0.4) is between 2.1 and 2.9 probability would be 9/31. (31 0,0.1,....3.0) I know the above is wrong but I am having confusion with distance vs exact point transition.(In other words I am calculating exact point like 2.1,2.2,... as in question given 2.5 (within half mile) but unable to know how 23> as OS is capturing the exact condition of question) Pls help me to figure out where I faltered.
_________________
If you like my post pls give kudos



Intern
Joined: 10 Jul 2018
Posts: 4
GMAT 1: 600 Q47 V26 GMAT 2: 630 Q48 V28

Re: A circular racetrack is 3 miles in length and has signs post
[#permalink]
Show Tags
31 Jul 2018, 14:42
Shouldn't the question say "one half miles" instead of "one half mile"? Because "one half mile" can be read as one of 1/2 mile.
_________________
Official GMAT 1  600 v26 q47 Official GMAT 2  630 v27 q48 MCAT 1  610 v28 q47 MCAT 2  630 v29 q48 MCAT 3  680 v35 q48 MCAT 4  640 v33 q45 MCAT 5  660 v34 q46 MCAT 6  640 v31 q47 Veritas CAT 1  690 v34 q51 Official CAT 2  720 v37 q50 Official CAT 4  690 v32 q50 Official CAT 6  700 v34 q50 Veritas CAT 2  680 v34 q49



Senior Manager
Joined: 29 Dec 2017
Posts: 382
Location: United States
Concentration: Marketing, Technology
GMAT 1: 630 Q44 V33 GMAT 2: 690 Q47 V37 GMAT 3: 710 Q50 V37
GPA: 3.25
WE: Marketing (Telecommunications)

Re: A circular racetrack is 3 miles in length and has signs post
[#permalink]
Show Tags
22 Aug 2018, 13:27
outofpocket wrote: Shouldn't the question say "one half miles" instead of "one half mile"? Because "one half mile" can be read as one of 1/2 mile. The question exactly says: 1/2 miles.



Intern
Joined: 22 Jan 2018
Posts: 1

A circular racetrack is 3 miles in length and has signs post
[#permalink]
Show Tags
28 Jul 2019, 10:25
So, I solved it like this, How many half miles (0.50) miles in in 3 miles, 6 so the probability that car ends within a half mile is 1/6, but, the car could have moved in any direction; clockwise or counterclockwise so multiply the probability of 1/6 by 2 hence, 1/3.



Intern
Joined: 09 Apr 2017
Posts: 45
Location: Nepal
Concentration: Finance, Entrepreneurship
WE: Information Technology (Computer Software)

Re: A circular racetrack is 3 miles in length and has signs post
[#permalink]
Show Tags
04 Aug 2019, 20:49
Bunuel wrote: helloanupam wrote: A circular racetrack is 3 miles in length and has signs posted to indicate each 1/10 mile increment. If a race car starts at a random location on the track and travels exactly one half mile, what is the probability that the car ends within a half mile of the sign indicating 2 1/2 miles?
A. 1/6 B. 3/10 C. 1/3 D. 1/2 E. 2/3
Bunuel, Sorry, I could not understand the language of the question and hence probably the answer is not clear to me. If possible , could you reframe the question or explain as to what the question is asking? Look at the diagram: The car ends within a half mile of the sign indicating 2.5 miles means that the car should end in one mile interval, between the signs indicating 2 (2.50.5=2) and 3 miles (2+0.5=3), so within the red segment on the diagram. Now if the car appears somewhere between the blue dots, between 1.5 and 2 miles signs then after traveling 0.5 miles the car will be in the red segment. So in order after traveling 0.5 miles the car to end within the red segment it should appear between 1.5 and 2.5 miles, so within 1 mile interval, as the circumference of the track is 3 miles then the probability of that will be P=favorable/total=1/3. As I mentioned in my previous post actually it doesn't matter where the car appears or what distance it travel, as long as favorable interval in the end is 1 mile and total interval is 3 miles then the probability will be 1/3 miles. Hope it's clear. One doubt about the question. It is only given that a car starts in the circular race track. Doesnt direction come into play in such scenarios? Shouldn't it be mentioned that what direction the car is travelling in. If we imagine it can be either way the answer changes to the question. Just a thought. Looking at the question, I wasnt sure if we are supposed to take into consideration that the car could have travelled both ways.



Manager
Joined: 29 Jun 2018
Posts: 56
Location: India
GPA: 4

Re: A circular racetrack is 3 miles in length and has signs post
[#permalink]
Show Tags
11 Aug 2019, 23:42
helloanupam wrote: A circular racetrack is 3 miles in length and has signs posted to indicate each 1/10 mile increment. If a race car starts at a random location on the track and travels exactly one half mile, what is the probability that the car ends within a half mile of the sign indicating 2 1/2 miles?
A. 1/6 B. 3/10 C. 1/3 D. 1/2 E. 2/3 Ihave solved it this way. If the vehicle starts at a random location and travels 1/2 mile, it is still at some arbit location. Hence , I would try to find out the range of desired outcomes. If the vehicle is between the mileposts indicating 2 miles and 3 miles, it is within a halfmile of the 2 and a half milepost. That's the desired range of 1 mile, out of a possible range of 3 miles length of the track. The probability, then, is 1 / 3. The answer is C
_________________



Intern
Joined: 16 Apr 2019
Posts: 3

Re: A circular racetrack is 3 miles in length and has signs post
[#permalink]
Show Tags
12 Aug 2019, 21:18
Bunuel wrote: helloanupam wrote: A circular racetrack is 3 miles in length and has signs posted to indicate each 1/10 mile increment. If a race car starts at a random location on the track and travels exactly one half mile,what is the probability that the car ends within a half mile of the sign indicating 2 1/2 miles? (A) 1/6 (B) 3/10 (C) 1/3 (D) 1/2 (E) 2/3
Answer: C
Could somebody explain how to work this out? The car ends within a half mile of the sign indicating 2 1/2 miles means that the car will end in one mile interval, between the signs indicating 2 and 3 miles. Now, it doesn't matter where the car starts or what distance it travels, the probability will be P=(favorable outcome)/(total # of outcomes)=1/3 (as the car starts at random point end travels some distance afterwards we can consider its end point as the point where he randomly appeared, so the probability that the car appeared within 1 mile interval out of total 3 miles will be 1/3). Answer: C. Hope it's clear. I got a little mixed up on the wording of question. I interpreted "Within" a half mile to mean "less than a half a mile" not "A half mile or less." Could you rephrase the question.




Re: A circular racetrack is 3 miles in length and has signs post
[#permalink]
12 Aug 2019, 21:18






