Author 
Message 
TAGS:

Hide Tags

Director
Joined: 08 Jul 2004
Posts: 596

The figure above shows the dimensions of a semicircular [#permalink]
Show Tags
23 Sep 2004, 15:25
3
This post received KUDOS
11
This post was BOOKMARKED
Question Stats:
51% (02:35) correct
49% (01:32) wrong based on 325 sessions
HideShow timer Statistics
Attachment:
untitled.PNG [ 7.01 KiB  Viewed 17431 times ]
The figure above shows the dimensions of a semicircular cross section of a oneway tunnel. The single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel. If vehicles must clear the top of the tunnel by at least 1/2 foot when they are inside the traffic lane, what should be the limit on the height of vehicles that are allowed to use the tunnel? A. 5½ ft B. 7½ ft C. 8 ½ ft D. 9½ ft E. 10 ft
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by Bunuel on 29 Jan 2012, 08:07, edited 1 time in total.
Edited the question



Senior Manager
Joined: 25 Dec 2003
Posts: 359
Location: India

3
This post received KUDOS
1
This post was BOOKMARKED
See attachement, If unclear, let me know.
Regards
Attachments
q4_870.jpg [ 31.85 KiB  Viewed 10407 times ]
_________________
Giving another SHOT



Math Expert
Joined: 02 Sep 2009
Posts: 39695

Re: Tunnel hight [#permalink]
Show Tags
03 Sep 2010, 09:09
3
This post received KUDOS
Expert's post
3
This post was BOOKMARKED
udaymathapati wrote: The figure attached shows the dimensions of a semicircular cross section of a oneway tunnel. The single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel. If vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane, what should be the limit on the height of vehicles that are allowed to use the tunnel? A. 5½ ft B. 7½ ft C. 8 ½ ft D. 9½ ft E. 10 ft See the diagram attached: Attachment:
untitled.PNG [ 5.25 KiB  Viewed 18439 times ]
Rectangle inscribed has the length of traffic lane 12. So max height of vehicle will be 1/2 foot less than the width of this rectangle. Now, let O be the center of the semicircle, then OA=radius=20/2=10 and OB=12/2=6 > \(AB=\sqrt{OA^2OB^2}=\sqrt{10^26^2}=8\). So max height of the vehicle that are allowed to use the tunnel is 80.5=7.5. Answer: B.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 408
Location: Milky way
Schools: ISB, Tepper  CMU, Chicago Booth, LSB

Re: Tunnel hight [#permalink]
Show Tags
03 Sep 2010, 22:35
udaymathapati wrote: The figure attached shows the dimensions of a semicircular cross section of a oneway tunnel. The single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel. If vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane, what should be the limit on the height of vehicles that are allowed to use the tunnel? A. 5½ ft B. 7½ ft C. 8 ½ ft D. 9½ ft E. 10 ft My approach: Equation of the circle  x^2 + y^2 = a^2 (a is the radius of the circle which is 10 feet.) The diameter of the semicircle is 20 and the traffic lane is 12 feet wide and located at equal distance from the sides of the tunnel. The width of the traffic lane should be 4 feet away from each of the sides. If we position the center of the tunnel (center of the semicircle) to overlap exactly on the origin of the xy coordinate graph then the center of the semicircle would be the origin (0,0) and the end points of the traffic lane would be (6,0) and (6,0). Let us take one of the edges of the traffic lane  (6,0). We need to find distance from the xaxis to the edge of the semicircle ... that is the y coordinate. Making use of the equation of the circle  x^2 + y^2 = 100 .. we already know x coordinate which is 6. Hence y^2 = 100  36. y^2 = 64. Hence y is 8. Hence the height of the tunnel at the edge of the traffic lane is 8 feet high. Minimum clearance should be 1/2 feet hence the maximum height of the vehicles allowed is 7.5 feet.
_________________
Support GMAT Club by putting a GMAT Club badge on your blog



Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 408
Location: Milky way
Schools: ISB, Tepper  CMU, Chicago Booth, LSB

Re: Tunnel hight [#permalink]
Show Tags
04 Sep 2010, 23:40
A little correction to my previous post. The equation of the circle with the given center as (h,k) and radius as r is (xh)^2 + (yk)^2 = r^2. Since the semicircle is centered at origin (0,0) the equation was noted as x^2 + y^2 = r^2.
_________________
Support GMAT Club by putting a GMAT Club badge on your blog



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15978

Re: The figure above shows the dimensions of a semicircular [#permalink]
Show Tags
25 Oct 2013, 23:41
1
This post received KUDOS
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



Manager
Status: Impossible is just an opinion
Joined: 31 Oct 2012
Posts: 52
Location: Ukraine
Concentration: Strategy, Marketing
GMAT 1: 590 Q47 V24 GMAT 2: 650 Q47 V34 GMAT 3: 670 Q49 V31 GMAT 4: 690 Q48 V37
GPA: 3.8
WE: Marketing (Consumer Products)

Re: The figure above shows the dimensions of a semicircular [#permalink]
Show Tags
30 Nov 2013, 14:51
Hi Guys! I was thinking about extreme cases, such a truck with cylidrical tank. In this case you would not take into account the width of the lane. Hence the maximum height of the truck would be R  1/2 = 101/2 = 9 1/2 (where R is the radius of the semicircular cross). Unfortuantely, this answer is wrong, but I still think that it is valid. Can somebody explain why I'm wrong? THX!
Attachments
File comment: example of the truck I was thinking about
fuel_truck_aircraft_3000_gallons_ford_4.jpg [ 22.09 KiB  Viewed 8397 times ]



Intern
Joined: 16 Sep 2014
Posts: 10

Re: The figure above shows the dimensions of a semicircular [#permalink]
Show Tags
19 Nov 2014, 17:33
MDK wrote: Hi Guys! I was thinking about extreme cases, such a truck with cylidrical tank. In this case you would not take into account the width of the lane. Hence the maximum height of the truck would be R  1/2 = 101/2 = 9 1/2 (where R is the radius of the semicircular cross). Unfortuantely, this answer is wrong, but I still think that it is valid. Can somebody explain why I'm wrong? THX! Hi, late response but it might be helpful to someone else. The reason is because any truck can only have a maximum width = width of the lane, that's what the problem is saying. that means, there are parts of the truck, end points on two sides that can only rise to the height limited by the ceiling of the tunnel at those end points, which is the distance we are trying to find out = 8. hope it's clear.



Manager
Status: Kitchener
Joined: 03 Oct 2013
Posts: 98
Location: Canada
Concentration: Finance, Finance
GPA: 2.9
WE: Education (Education)

The figure above shows the dimensions of a semicircular [#permalink]
Show Tags
11 Feb 2015, 08:31
I have question here, if in the above question they sid that If vehicles must clear the top of the tunnel by at least 1/2 foot when they are inside the traffic lane. So, they ask about the max height of the vehicles that allowed to cross the tunnel.We have the radius = 10. So max height of the vehicle that are allowed to use the tunnel is 10 0.5 = 9.5 what is the wrong here?
_________________
Click +1 Kudos if my post helped



Intern
Joined: 31 Dec 2014
Posts: 10
Location: United States
Concentration: Marketing

Re: The figure above shows the dimensions of a semicircular [#permalink]
Show Tags
11 Feb 2015, 12:57
23a2012 wrote: I have question here, if in the above question they sid that If vehicles must clear the top of the
tunnel by at least 1/2 foot when they are inside the traffic lane. So, they ask about the max
height of the vehicles that allowed to cross the tunnel.We have the radius = 10. So max height of
the vehicle that are allowed to use the tunnel is 10 0.5 = 9.5 what is the wrong here? The tunnel is rounded and the lane is 12 feet with 4 feet of space on each side, so the vechicle can't be higher than the edges of the lane. Each half of the lane is 6 feet long, so the max height is 1/2 foot smaller than the height of the tunnel 6 feet from the center. It really helped me to draw it out. As I wrote out the given dimensions, I realized I had a 6810 Pythagorean Triple.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7440
Location: Pune, India

Re: The figure above shows the dimensions of a semicircular [#permalink]
Show Tags
11 Feb 2015, 22:24
23a2012 wrote: I have question here, if in the above question they sid that If vehicles must clear the top of the
tunnel by at least 1/2 foot when they are inside the traffic lane. So, they ask about the max
height of the vehicles that allowed to cross the tunnel.We have the radius = 10. So max height of
the vehicle that are allowed to use the tunnel is 10 0.5 = 9.5 what is the wrong here? The truck has a width. The entire truck must pass through the semi circular tunnel. I did not get the image I had in mind but look here: Attachment:
010MontBlancTunnelTermographiccontrolTruck2011.jpg [ 239.44 KiB  Viewed 6391 times ]
Now imagine that the tunnel is semi circular. If the truck has height of 9.5, its edges will not pass through the sides. Its height needs to be lesser. Since the traffic lane is 12 feet wide and vehicles must stay inside traffic lane, the maximum width of the vehicle will be 12 feet and that will set the limit on the maximum height allowed.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Manager
Status: Kitchener
Joined: 03 Oct 2013
Posts: 98
Location: Canada
Concentration: Finance, Finance
GPA: 2.9
WE: Education (Education)

Re: The figure above shows the dimensions of a semicircular [#permalink]
Show Tags
12 Feb 2015, 06:20
VeritasPrepKarishma wrote: 23a2012 wrote: I have question here, if in the above question they sid that If vehicles must clear the top of the
tunnel by at least 1/2 foot when they are inside the traffic lane. So, they ask about the max
height of the vehicles that allowed to cross the tunnel.We have the radius = 10. So max height of
the vehicle that are allowed to use the tunnel is 10 0.5 = 9.5 what is the wrong here? The truck has a width. The entire truck must pass through the semi circular tunnel. I did not get the image I had in mind but look here: Attachment: 010MontBlancTunnelTermographiccontrolTruck2011.jpg Now imagine that the tunnel is semi circular. If the truck has height of 9.5, its edges will not pass through the sides. Its height needs to be lesser. Since the traffic lane is 12 feet wide and vehicles must stay inside traffic lane, the maximum width of the vehicle will be 12 feet and that will set the limit on the maximum height allowed. Dear Karishma,thank you +1 KUDOS
_________________
Click +1 Kudos if my post helped



Manager
Joined: 03 May 2013
Posts: 75

Re: The figure above shows the dimensions of a semicircular [#permalink]
Show Tags
28 May 2015, 21:09
Alt Solution please refer image
Attachments
20150529_093316.jpg [ 2.95 MiB  Viewed 5756 times ]



Manager
Joined: 08 Jan 2015
Posts: 86

Re: The figure above shows the dimensions of a semicircular [#permalink]
Show Tags
14 Aug 2016, 02:53
Even though this question is from GMATprep, I think it's very ambiguous since the question doesn't mention that the car should/could be as wide as the whole lane.




Re: The figure above shows the dimensions of a semicircular
[#permalink]
14 Aug 2016, 02:53







