Author 
Message 
TAGS:

Hide Tags

VP
Joined: 22 Nov 2007
Posts: 1080

The figure above shows the dimensions of a semicircular [#permalink]
Show Tags
08 Jan 2008, 06:10
5
This post was BOOKMARKED
Question Stats:
48% (02:52) correct
52% (01:33) wrong based on 118 sessions
HideShow timer Statistics
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 OPEN DISCUSSION OF THIS QUESTION IS HERE: thefigureaboveshowsthedimensionsofasemicircular100337.html
Official Answer and Stats are available only to registered users. Register/ Login.
Attachments
semi.doc [23.5 KiB]
Downloaded 113 times



CEO
Joined: 17 Nov 2007
Posts: 3584
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth)  Class of 2011

Re: semicircle [#permalink]
Show Tags
08 Jan 2008, 12:27
3
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
Attachments
t58167.gif [ 5.39 KiB  Viewed 2859 times ]
_________________
HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android)  The OFFICIAL GMAT CLUB PREP APP, a musthave app especially if you aim at 700+  PrepGame



Director
Joined: 12 Jul 2007
Posts: 858

Re: semicircle [#permalink]
Show Tags
08 Jan 2008, 08:07
1
This post received KUDOS
That does make more sense (since automobiles aren't 2D ). In that case: Answer BCreate a right triangle using the radius of 10 as a hypotenuse. The legs of the triangle will be 6 (1/2 of the travel lane) and X (the height at the edge of the road). 345 right triangle gives us a height of 8' at the side of the road. 8.5 = 7.5' max



Director
Joined: 12 Jul 2007
Posts: 858

Re: semicircle [#permalink]
Show Tags
08 Jan 2008, 12:06
1
This post received KUDOS
Hypotenuse is 10, not 9.5.
You take the 1/2 off of the height when you find it (8.5 =7.5), not off the hypotenuse.



Math Expert
Joined: 02 Sep 2009
Posts: 39751

Re: The figure above shows the dimensions of a semicircular [#permalink]
Show Tags
01 Dec 2013, 07:06
marcodonzelli 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: 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. OPEN DISCUSSION OF THIS QUESTION IS HERE: thefigureaboveshowsthedimensionsofasemicircular100337.html
_________________
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



Director
Joined: 12 Jul 2007
Posts: 858

Re: semicircle [#permalink]
Show Tags
08 Jan 2008, 07:15
Are they asking for the height of the tunnel at the EDGE of the 12 foot lane? or the height of the tunnel in the center? It's kind of vague, but I would assume they want the height of the tunnel at it's highest point (even though this isn't entirely practical, but perhaps that's where the 1/2 foot of tolerance comes in).
10 feet because the radius is 10 feet then subtract 1/2 foot of clearance 101/2 = 9.5 feet Answer D



Manager
Joined: 01 Jan 2008
Posts: 223
Schools: Booth, Stern, Haas

Re: semicircle [#permalink]
Show Tags
08 Jan 2008, 07:48
eschn3am wrote: Are they asking for the height of the tunnel at the EDGE of the 12 foot lane? or the height of the tunnel in the center? It's kind of vague, but I would assume they want the height of the tunnel at it's highest point (even though this isn't entirely practical, but perhaps that's where the 1/2 foot of tolerance comes in).
10 feet because the radius is 10 feet then subtract 1/2 foot of clearance 101/2 = 9.5 feet Answer D I think it is better to find height at the 12 foot lane, because shape of car not triangle, rather it is rectangle... so I would have picked A, since height will be 6 and 61/2=5.5



Manager
Joined: 01 Jan 2008
Posts: 223
Schools: Booth, Stern, Haas

Re: semicircle [#permalink]
Show Tags
08 Jan 2008, 09:12
eschn3am wrote: That does make more sense (since automobiles aren't 2D ). In that case: Answer BCreate a right triangle using the radius of 10 as a hypotenuse. The legs of the triangle will be 6 (1/2 of the travel lane) and X (the height at the edge of the road). 345 right triangle gives us a height of 8' at the side of the road. 8.5 = 7.5' max great, I agree with you) tellingly I never hit the right answer I am always close to it but it doesn't make me happy because real GMAT exam makes sever punishments for wrong answers whether it is close to right answer or not. what would you suggest me to do in order to decrease errors and increase precision? not to rush?



Director
Joined: 12 Jul 2007
Posts: 858

Re: semicircle [#permalink]
Show Tags
08 Jan 2008, 09:20
kazakhb wrote: eschn3am wrote: That does make more sense (since automobiles aren't 2D ). In that case: Answer BCreate a right triangle using the radius of 10 as a hypotenuse. The legs of the triangle will be 6 (1/2 of the travel lane) and X (the height at the edge of the road). 345 right triangle gives us a height of 8' at the side of the road. 8.5 = 7.5' max great, I agree with you) tellingly I never hit the right answer I am always close to it but it doesn't make me happy because real GMAT exam makes sever punishments for wrong answers whether it is close to right answer or not. what would you suggest me to do in order to decrease errors and increase precision? [b]not to rush[b/]? that's it in a nutshell. Slow down, double check your work and draw out a diagram when doing geometry problems. I find I do much better on the Club Challenges when I slow down a bit. After awhile you'll know all the math you need, it's just eliminating stupid mistakes.



Intern
Joined: 13 Dec 2007
Posts: 28

Re: semicircle [#permalink]
Show Tags
08 Jan 2008, 09:37
eschn3am wrote: That does make more sense (since automobiles aren't 2D ). In that case: Answer BCreate a right triangle using the radius of 10 as a hypotenuse. The legs of the triangle will be 6 (1/2 of the travel lane) and X (the height at the edge of the road). 345 right triangle gives us a height of 8' at the side of the road. 8.5 = 7.5' max correct! ...7.5' for me too..



VP
Joined: 22 Nov 2007
Posts: 1080

Re: semicircle [#permalink]
Show Tags
08 Jan 2008, 10:44
akhi wrote: eschn3am wrote: That does make more sense (since automobiles aren't 2D ). In that case: Answer BCreate a right triangle using the radius of 10 as a hypotenuse. The legs of the triangle will be 6 (1/2 of the travel lane) and X (the height at the edge of the road). 345 right triangle gives us a height of 8' at the side of the road. 8.5 = 7.5' max correct! ...7.5' for me too.. OA is B. This kind of questions are easy to solve reading the text well because the are written in a tricky way! I answered D too...



Manager
Joined: 04 Jan 2008
Posts: 83

Re: semicircle [#permalink]
Show Tags
08 Jan 2008, 12:04
B is the answer=7.5. think of a right triangle with base 6 (12/2) and hypotnuse 9.5 (101/2) and find out the height=answer



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16024

Re: The figure above shows the dimensions of a semicircular [#permalink]
Show Tags
30 Nov 2013, 13:50
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




Re: The figure above shows the dimensions of a semicircular
[#permalink]
30 Nov 2013, 13:50







