Problem Solving

The figure above[see attached figure] 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

IMO B

whats the OA

Oa is B. Can you explain

Let O be the center and draw perpendicular from the edges of rectangle 12feet wide.

then create 2 right triangles whic will the radius 10 feet.

Hence the length is 8ft = sqrt(100-36)

subtract 1/2 feet and hence the answer

cn u explain it a bit...its not clear

attached is the diagram.

I hope this will help. The radius is 10ft and the breadth of highway is 12 ft which is divided into 6ft each.

schumi_gmat wrote:attached is the diagram.

I hope this will help. The radius is 10ft and the breadth of highway is 12 ft which is divided into 6ft each.

I marked A

Thanks a lot for your invaluable contribution.

thanks, the diagram certainly helped

Thanks. The diagram has really helped a lot.

Why are we considering only the line perperndicular to X? Why not another line can be 3 feet away from both sides of the traffic lane?

What am I doing wrong?

Refer attached diagram.

Since each lane is 6 feet wide, we need to consider the shortest possible distance, imagine if a vehicle were to pass at the extreme left end of the lane for the figure you have drawn, it obviously violates the height clearance, if it asked for the maximum possible height we could just take the radius and subtract 1 feet for clearance getting 9. But then thats not what they ask.

gmatIntent wrote:Why are we considering only the line perperndicular to X? Why not another line can be 3 feet away from both sides of the traffic lane?

What am I doing wrong?

Refer attached diagram.

shankar.ashwin wrote:Since each lane is 6 feet wide, we need to consider the shortest possible distance, imagine if a vehicle were to pass at the extreme left end of the lane for the figure you have drawn, it obviously violates the height clearance, if it asked for the maximum possible height we could just take the radius and subtract 1 feet for clearance getting 9. But then thats not what they ask.

gmatIntent wrote:Why are we considering only the line perperndicular to X? Why not another line can be 3 feet away from both sides of the traffic lane?

What am I doing wrong?

Refer attached diagram.

I'm sorry. I don't understand your explanation. Can you elaborate further please?

The question says 'what should be the limit on the height of vehicles that are allowed to use the tunnel'. So it should be maximum possible height. right?

Since you have drawn 2 cases here, let us use Case 2 as an example,

If you said height permitted can be 9.5-1 = 8.5.

Imagine a vehicle with height 8.5 travelled at the left extreme of the road (as drawn in Case 1), the height permitted would be only 8, if a vehicle with height 8.5 travels, it violates the design.

To avoid that, we calculate the distance at the left extreme (as in Case 1) and that would be considering vehicles travel along the full width of the road. Makes sense?

gmatIntent wrote: I'm sorry. I don't understand your explanation. Can you elaborate further please?

The question says 'what should be the limit on the height of vehicles that are allowed to use the tunnel'. So it should be maximum possible height. right?

shankar.ashwin wrote:Since you have drawn 2 cases here, let us use Case 2 as an example,

If you said height permitted can be 9.5-1 = 8.5.

Imagine a vehicle with height 8.5 travelled at the left extreme of the road (as drawn in Case 1), the height permitted would be only 8, if a vehicle with height 8.5 travels, it violates the design.

To avoid that, we calculate the distance at the left extreme (as in Case 1) and that would be considering vehicles travel along the full width of the road. Makes sense?

gmatIntent wrote: I'm sorry. I don't understand your explanation. Can you elaborate further please?

The question says 'what should be the limit on the height of vehicles that are allowed to use the tunnel'. So it should be maximum possible height. right?

Thanks. I get your point.
But the vehicle not necessarily has to travel at the left & right edge of the lane. It can leave space of 3 feet at both the end of the lanes to cover more height. Isn't it?

Don't get confused by the wording, just consider the vehicle itself to be 12 feet wide, and find the height in that case (basically inscribing a rectangle inside the semi-circle)

gmatIntent wrote:
Thanks. I get your point.
But the vehicle not necessarily has to travel at the left & right edge of the lane. It can leave space of 3 feet at both the end of the lanes to cover more height. Isn't it?