Problem Solving

gmatIntent wrote:

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?

Your paraphrase of the question isn't quite right. The given condition is that vehicles MUST clear the top of the tunnel by at least 1/2 foot when they are inside the traffic lane. To GUARANTEE that ANY vehicle inside the 12 foot lane will clear the tunnel by 1/2 foot, we must consider the WORST-CASE SCENARIO: the WIDEST possible vehicle (12 feet) traveling down the 12 foot lane.

GMATGuruNY wrote:

gmatIntent wrote:

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?

Your paraphrase of the question isn't quite right. The given condition is that vehicles MUST clear the top of the tunnel by at least 1/2 foot when they are inside the traffic lane. To GUARANTEE that ANY vehicle inside the 12 foot lane will clear the tunnel by 1/2 foot, we must consider the WORST-CASE SCENARIO: the WIDEST possible vehicle (12 feet) traveling down the 12 foot lane.

Thanks. Got it.
I keep making these kind of mistakes in word problems.
How can I improve on this? Can you provide some strategy / tip please?

Thanks

where are we getting 10 as the radius?

Thanks!!

gmatpup wrote:where are we getting 10 as the radius?

Thanks!!

Check the attachment of the original post by gmat009. It shows the diameter as 20.

Thanks

GMATGuruNY wrote:

gmatIntent wrote:

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?

Your paraphrase of the question isn't quite right. The given condition is that vehicles MUST clear the top of the tunnel by at least 1/2 foot when they are inside the traffic lane. To GUARANTEE that ANY vehicle inside the 12 foot lane will clear the tunnel by 1/2 foot, we must consider the WORST-CASE SCENARIO: the WIDEST possible vehicle (12 feet) traveling down the 12 foot lane.

I have question here, if in the above question they said 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 Unfortuantely, this answer is wrong,

but I still think that it is valid. Can somebody explain why I'm wrong

GMATGuruNY wrote:

gmatIntent wrote:

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?

Your paraphrase of the question isn't quite right. The given condition is that vehicles MUST clear the top of the tunnel by at least 1/2 foot when they are inside the traffic lane. To GUARANTEE that ANY vehicle inside the 12 foot lane will clear the tunnel by 1/2 foot, we must consider the WORST-CASE SCENARIO: the WIDEST possible vehicle (12 feet) traveling down the 12 foot lane.

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

Asma77 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

As the figure above illustrates, a truck with a width of 12 feet and a height of 9.5 feet will not clear the sides of the tunnel.

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

To GUARANTEE that ANY vehicle inside the 12 foot lane will clear the tunnel by 1/2 foot, we must consider the WORST-CASE SCENARIO:
The WIDEST possible vehicle -- a truck that is 12-feet wide -- traveling down the 12 foot lane.



In the figure above, O is the center of the circle and rectangle ABCD represents a 12-foot wide truck.
CD is the height of a truck that would TOUCH the top of the tunnel.
Since AD = 12, OD = 6.
Since the diameter of the semi-circle is 20, radius OC = 10.
Thus, ∆OCD is a 6-8-10 triangle, implying that CD=8.
Since a truck with a height of 8 feet would touch the top of the tunnel, the maximum height that guarantees CLEARING the tunnel by 1/2 foot = 8 - 1/2 = 7.5 feet.

The correct answer is B.