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

 It is currently 09 Dec 2019, 05:19

### 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

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

# The figure above shows the dimensions of a semicircular cross section

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 08 Jul 2004
Posts: 448
The figure above shows the dimensions of a semicircular cross section  [#permalink]

### Show Tags

Updated on: 26 Nov 2018, 04:30
5
53
00:00

Difficulty:

75% (hard)

Question Stats:

55% (02:11) correct 45% (02:12) wrong based on 758 sessions

### HideShow timer Statistics

The figure above shows the dimensions of a semicircular cross section of a one-way 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. 5 ½ ft
B. 7 ½ ft
C. 8 ½ ft
D. 9 ½ ft
E. 10 ft

Attachment:

untitled.PNG [ 7.01 KiB | Viewed 45515 times ]

Originally posted by saurya_s on 23 Sep 2004, 15:25.
Last edited by Bunuel on 26 Nov 2018, 04:30, edited 2 times in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 59624
The figure above shows the dimensions of a semicircular cross section  [#permalink]

### Show Tags

23 Jul 2014, 02:24
29
17
Nihit wrote:

The figure above shows the dimensions of a semicircular cross section of a one-way 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

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 semi-circle, then OA=radius=20/2=10 and OB=12/2=6 --> $$AB=\sqrt{OA^2-OB^2}=\sqrt{10^2-6^2}=8$$.

So max height of the vehicle that are allowed to use the tunnel is 8-0.5=7.5.

Attachment:

untitled.PNG [ 2.53 KiB | Viewed 17488 times ]

_________________
VP
Joined: 07 Nov 2007
Posts: 1137
Location: New York
Re: The figure above shows the dimensions of a semicircular cros  [#permalink]

### Show Tags

04 Sep 2008, 07:49
8
3
Nihit wrote:
Attachment:
IMAGE.JPG

The figure above shows the dimensions of a semicircular cross section of a one-way tunnel(dia= 20 ft). 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

Say AOB is base of the semi circle.
points X and Y are on edges of the traffic lane (XY=12)
OX=6

Find the height perpendicular to X and touches the semi circle.
= sqrt (6^2+10^2) =8

we need 1/2 ft clearance.

so height must be (8-1/2) =71/2 ft

B.
##### General Discussion
Senior Manager
Joined: 25 Dec 2003
Posts: 282
Location: India
Re: The figure above shows the dimensions of a semicircular cross section  [#permalink]

### Show Tags

23 Sep 2004, 21:44
5
2
See attachement, If unclear, let me know.

Regards
Attachments

q4_870.jpg [ 31.85 KiB | Viewed 30631 times ]

Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 327
Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB
Re: The figure above shows the dimensions of a semicircular cross section  [#permalink]

### Show Tags

03 Sep 2010, 22:35
udaymathapati wrote:
The figure attached shows the dimensions of a semicircular cross section of a one-way 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 x-y 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 x-axis to the edge of the semi-circle ... 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.
Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 327
Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB
Re: The figure above shows the dimensions of a semicircular cross section  [#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

(x-h)^2 + (y-k)^2 = r^2.

Since the semicircle is centered at origin (0,0) the equation was noted as x^2 + y^2 = r^2.
Intern
Status: Impossible is just an opinion
Joined: 31 Oct 2012
Posts: 43
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 cross section  [#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 = 10-1/2 = 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 28608 times ]

Intern
Joined: 16 Sep 2014
Posts: 9
Re: The figure above shows the dimensions of a semicircular cross section  [#permalink]

### Show Tags

19 Nov 2014, 17:33
1
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 = 10-1/2 = 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: 87
Concentration: Finance, Finance
GPA: 2.9
WE: Education (Education)
Re: The figure above shows the dimensions of a semicircular cross section  [#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?
Intern
Joined: 31 Dec 2014
Posts: 8
Location: United States
Concentration: Marketing
GMAT 1: 700 Q44 V41
Re: The figure above shows the dimensions of a semicircular cross section  [#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 6-8-10 Pythagorean Triple.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9859
Location: Pune, India
Re: The figure above shows the dimensions of a semicircular cross section  [#permalink]

### Show Tags

11 Feb 2015, 22:24
5
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:

010-Mont-Blanc-Tunnel-Termographic-control-Truck-2011.jpg [ 239.44 KiB | Viewed 26596 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

Manager
Status: Kitchener
Joined: 03 Oct 2013
Posts: 87
Concentration: Finance, Finance
GPA: 2.9
WE: Education (Education)
Re: The figure above shows the dimensions of a semicircular cross section  [#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:
010-Mont-Blanc-Tunnel-Termographic-control-Truck-2011.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
Manager
Joined: 03 May 2013
Posts: 68
Re: The figure above shows the dimensions of a semicircular cross section  [#permalink]

### Show Tags

28 May 2015, 21:09
Alt Solution

Attachments

20150529_093316.jpg [ 2.95 MiB | Viewed 26026 times ]

Current Student
Joined: 08 Jan 2015
Posts: 73
Re: The figure above shows the dimensions of a semicircular cross section  [#permalink]

### Show Tags

14 Aug 2016, 02:53
1
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.
Manager
Joined: 22 Sep 2014
Posts: 104
GMAT 1: 720 Q50 V37
Re: The figure above shows the dimensions of a semicircular cross section  [#permalink]

### Show Tags

07 Sep 2018, 17:11
maths is easy ...to understand the problem is really hard for a non-native speaker
Intern
Joined: 21 Nov 2018
Posts: 4
Re: The figure above shows the dimensions of a semicircular cross section  [#permalink]

### Show Tags

23 Dec 2018, 19:10
How are we certain that the shape of the traffic lane is rectangular? Can't it have a curved head?
Re: The figure above shows the dimensions of a semicircular cross section   [#permalink] 23 Dec 2018, 19:10
Display posts from previous: Sort by