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In cross section, a tunnel that carries one lane of one-way traffic is a semicircle with radius 4.2 m. Is the tunnel large enough to accommodate the truck that is approaching the entrance to the tunnel?

(1) The maximum width of the truck is 2.4 m
(2) The maximum height of the truck is 4 m

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Bunuel wrote:
In cross section, a tunnel that carries one lane of one-way traffic is a semicircle with radius 4.2 m. Is the tunnel large enough to accommodate the truck that is approaching the entrance to the tunnel?

(1) The maximum width of the truck is 2.4 m
(2) The maximum height of the truck is 4 m

According to the question it is clear that the tunnel's maximum width=diameter=2* radius=2*4.2=8.4 m and maximum height=4.2 m

(1) No information about the height of the truck.Height could exceed 4.2 m(not able to accommodate) or remain below 4.2 m (able to accommodate), Insufficient

(2) No information about the width of the truck.Width could exceed 8.4 m(not able to accommodate) or remain below 8.4 m (able to accommodate), Insufficient

(1)+(2) together provide the height and width of the truck.It is sufficient to tell that the tunnel is large enough to accommodate the truck because both of the height and the width are within the range of the tunnel's

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AbdurRakib wrote:
Bunuel wrote:
In cross section, a tunnel that carries one lane of one-way traffic is a semicircle with radius 4.2 m. Is the tunnel large enough to accommodate the truck that is approaching the entrance to the tunnel?

(1) The maximum width of the truck is 2.4 m
(2) The maximum height of the truck is 4 m

According to the question it is clear that the tunnel's maximum width=diameter=2* radius=2*4.2=8.4 m and maximum height=4.2 m

(1) No information about the height of the truck.Height could exceed 4.2 m(not able to accommodate) or remain below 4.2 m (able to accommodate), Insufficient

(2) No information about the width of the truck.Width could exceed 8.4 m(not able to accommodate) or remain below 8.4 m (able to accommodate), Insufficient

(1)+(2) together provide the height and width of the truck.It is sufficient to tell that the tunnel is large enough to accommodate the truck because both of the height and the width are within the range of the tunnel's

Agreed. At first I thought a truck 2.4 m wide at 4 m height wont be able to pass the tunnel that is 4.2 m high. But quick use of pythagoras theorem shows that at 4 m height a truck 2.56 m wide can pass. Sent from my SM-N910H using Tapatalk
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Bunuel wrote:
In cross section, a tunnel that carries one lane of one-way traffic is a semicircle with radius 4.2 m. Is the tunnel large enough to accommodate the truck that is approaching the entrance to the tunnel?

(1) The maximum width of the truck is 2.4 m
(2) The maximum height of the truck is 4 m

Bunuel, Can u please explain how the tunnel would look like.That is where I am not able to comprehend the question.
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suhasreddy wrote:
Bunuel wrote:
In cross section, a tunnel that carries one lane of one-way traffic is a semicircle with radius 4.2 m. Is the tunnel large enough to accommodate the truck that is approaching the entrance to the tunnel?

(1) The maximum width of the truck is 2.4 m
(2) The maximum height of the truck is 4 m

Bunuel, Can u please explain how the tunnel would look like.That is where I am not able to comprehend the question.

Hi suhasreddy ,

Just draw a semicircle and consider the base of the semi circle as the road.
So for any truck to pass through it, we would require both it's width and height.
Hence C is the ans.
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suhasreddy wrote:
Bunuel wrote:
In cross section, a tunnel that carries one lane of one-way traffic is a semicircle with radius 4.2 m. Is the tunnel large enough to accommodate the truck that is approaching the entrance to the tunnel?

(1) The maximum width of the truck is 2.4 m
(2) The maximum height of the truck is 4 m

Bunuel, Can u please explain how the tunnel would look like.That is where I am not able to comprehend the question.

There you go bud!
Attachments truck.png [ 11.6 KiB | Viewed 13618 times ]

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i THINK the answer should be E.
Reason:
Option 2. says MAXIMUM height of the truck is 4.
If we assume the truck is conical in shape and having only one point of 4 Meter height then yes it can pass through a tunnel of radius 4.2 M
WHat if the truck is rectangular in shape?.Then it will have a 2 point of height 4 M separated by distance of 2.4 M (its width )
.In that case its both edges will not pass through the semicircular tunnel of max heigh 4.2 M

Makes sense guys?
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Bunuel wrote:
In cross section, a tunnel that carries one lane of one-way traffic is a semicircle with radius 4.2 m. Is the tunnel large enough to accommodate the truck that is approaching the entrance to the tunnel?

(1) The maximum width of the truck is 2.4 m
(2) The maximum height of the truck is 4 m

We are given that a tunnel in the shape of a semicircle has a radius of 4.2 meters. Since it has a radius of 4.2 meters and hence a diameter of 8.4 meters, its maximum height is 4.2 meters and its maximum width is 8.4 meters. We need to determine whether the tunnel is large enough to fit a particular truck.

Statement One Alone:

The maximum width of the truck is 2.4 m.

Using the information in statement one, we can determine that the width of the truck (2.4 m) can fit within the tunnel that has a diameter 8.4 m. However, since we do not know the maximum height of the truck, we cannot determine whether it can fit in the tunnel. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The maximum height of the truck is 4 m.

Although we know the maximum height of the truck, without knowing the maximum width of the truck, we cannot determine whether the truck can fit through the tunnel. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

From the given information and the statements, we know that the width of the tunnel is 8.4 m, the maximum height of the tunnel is 4.2 m, the maximum width of the truck is 2.4 m, and the maximum height of the truck is 4 m. Since we have all of the necessary dimensions of the truck and the tunnel, we have the information to determine whether the truck would fit through the tunnel. Note that it is not necessary to perform the calculations, but the answer is yes, the truck can pass through the tunnel.

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JeffTargetTestPrep wrote:
Bunuel wrote:
In cross section, a tunnel that carries one lane of one-way traffic is a semicircle with radius 4.2 m. Is the tunnel large enough to accommodate the truck that is approaching the entrance to the tunnel?

(1) The maximum width of the truck is 2.4 m
(2) The maximum height of the truck is 4 m

We are given that a tunnel in the shape of a semicircle has a radius of 4.2 meters. Since it has a radius of 4.2 meters and hence a diameter of 8.4 meters, its maximum height is 4.2 meters and its maximum width is 8.4 meters. We need to determine whether the tunnel is large enough to fit a particular truck.

Statement One Alone:

The maximum width of the truck is 2.4 m.

Using the information in statement one, we can determine that the width of the truck (2.4 m) can fit within the tunnel that has a diameter 8.4 m. However, since we do not know the maximum height of the truck, we cannot determine whether it can fit in the tunnel. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The maximum height of the truck is 4 m.

Although we know the maximum height of the truck, without knowing the maximum width of the truck, we cannot determine whether the truck can fit through the tunnel. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

From the given information and the statements, we know that the width of the tunnel is 8.4 m, the maximum height of the tunnel is 4.2 m, the maximum width of the truck is 2.4 m, and the maximum height of the truck is 4 m. Since we have all of the necessary dimensions of the truck and the tunnel, we have the information to determine whether the truck would fit through the tunnel. Note that it is not necessary to perform the calculations, but the answer is yes, the truck can pass through the tunnel.

Why is it not necessary to perform a calculation?

I would think you would need to know the height of the tunnel, 1.2m away from the center of the tunnel (semi circle).

(1.2)^2 + 4^2 is less than (4.2)^2
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Bunuel: Can you please suggest similar problems
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fearose wrote:
i THINK the answer should be E.
Reason:
Option 2. says MAXIMUM height of the truck is 4.
If we assume the truck is conical in shape and having only one point of 4 Meter height then yes it can pass through a tunnel of radius 4.2 M
WHat if the truck is rectangular in shape?.Then it will have a 2 point of height 4 M separated by distance of 2.4 M (its width )
.In that case its both edges will not pass through the semicircular tunnel of max heigh 4.2 M

Makes sense guys?

Good point made buddy! EVen in the case of rectangular truck with 4m height & 2.4m width, the truck can pass through the tunnel. Lets consider the truck is in the middle of the semicircle tunnel. we can form a right angle triangle with half of the width 2.4/2=1.2 m as base and 4m as height. The hypotenuse will be approximately 4.17, which is less than 4.2m. So the truck can pass through easily.

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JeffTargetTestPrep wrote:

Statements One and Two Together:

From the given information and the statements, we know that the width of the tunnel is 8.4 m, the maximum height of the tunnel is 4.2 m, the maximum width of the truck is 2.4 m, and the maximum height of the truck is 4 m. Since we have all of the necessary dimensions of the truck and the tunnel, we have the information to determine whether the truck would fit through the tunnel. Note that it is not necessary to perform the calculations, but the answer is yes, the truck can pass through the tunnel.

Why is it not necessary to perform a calculation?

I would think you would need to know the height of the tunnel, 1.2m away from the center of the tunnel (semi circle).

(1.2)^2 + 4^2 is less than (4.2)^2

Because Data Sufficiency is awesome!

If this was a Problem Solving question, you'd be 100% correct. But because this is DS, it actually doesn't matter whether the truck can or can't fit through the tunnel. It just matters whether we have enough info to figure it out, if we wanted to. If we knew all of the dimensions of the truck and the tunnel, we could figure out whether it would fit just by doing some math, so having that information is sufficient.

This is a tough thing to get your head around, because you're used to solving math problems where the question is 'can it fit?'. But in DS, that's not really the question you're being asked. You're being asked "have we provided enough information that a smart person would be able to determine whether it could fit?". If someone could figure it out, it's sufficient. You don't have to do the actual 'figuring out' part.
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ccooley wrote:
JeffTargetTestPrep wrote:

Statements One and Two Together:

From the given information and the statements, we know that the width of the tunnel is 8.4 m, the maximum height of the tunnel is 4.2 m, the maximum width of the truck is 2.4 m, and the maximum height of the truck is 4 m. Since we have all of the necessary dimensions of the truck and the tunnel, we have the information to determine whether the truck would fit through the tunnel. Note that it is not necessary to perform the calculations, but the answer is yes, the truck can pass through the tunnel.

Why is it not necessary to perform a calculation?

I would think you would need to know the height of the tunnel, 1.2m away from the center of the tunnel (semi circle).

(1.2)^2 + 4^2 is less than (4.2)^2

Because Data Sufficiency is awesome!

If this was a Problem Solving question, you'd be 100% correct. But because this is DS, it actually doesn't matter whether the truck can or can't fit through the tunnel. It just matters whether we have enough info to figure it out, if we wanted to. If we knew all of the dimensions of the truck and the tunnel, we could figure out whether it would fit just by doing some math, so having that information is sufficient.

This is a tough thing to get your head around, because you're used to solving math problems where the question is 'can it fit?'. But in DS, that's not really the question you're being asked. You're being asked "have we provided enough information that a smart person would be able to determine whether it could fit?". If someone could figure it out, it's sufficient. You don't have to do the actual 'figuring out' part.

On the contrary, IT IS necessary to perform the calculations to know the answer to that question.

Using Pythagore, the height of the tunnel 1.2m (4.2m/2) from its center can be found to be 4.05m. Because, the truck's maximum height is 4m (< 4.05m), the tunnel will be able to accomodate the truck. However, if while looking for the height of the tunnel 1.2m from its center we found ANY number lower than 4m -- say 3.90m --, because we are given only maximum height and not actual height, it would have been impossible to know if the truck would have been able to go through the tunnel or not.

In that particular case of height = 3.9m, if the truck is 3.95m high, it will be able to go through the tunnel. If it is only 3.85m high, it will not be able to go through the tunnel. The answer would have been E

Given the length of calculations to arrive at the tunnel's height at 1.2m form the center, I think the stated difficulty level of this problem should be readjusted. Bunuel
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ccooley wrote:
JeffTargetTestPrep wrote:

Statements One and Two Together:

From the given information and the statements, we know that the width of the tunnel is 8.4 m, the maximum height of the tunnel is 4.2 m, the maximum width of the truck is 2.4 m, and the maximum height of the truck is 4 m. Since we have all of the necessary dimensions of the truck and the tunnel, we have the information to determine whether the truck would fit through the tunnel. Note that it is not necessary to perform the calculations, but the answer is yes, the truck can pass through the tunnel.

Why is it not necessary to perform a calculation?

I would think you would need to know the height of the tunnel, 1.2m away from the center of the tunnel (semi circle).

(1.2)^2 + 4^2 is less than (4.2)^2

Because Data Sufficiency is awesome!

If this was a Problem Solving question, you'd be 100% correct. But because this is DS, it actually doesn't matter whether the truck can or can't fit through the tunnel. It just matters whether we have enough info to figure it out, if we wanted to. If we knew all of the dimensions of the truck and the tunnel, we could figure out whether it would fit just by doing some math, so having that information is sufficient.

This is a tough thing to get your head around, because you're used to solving math problems where the question is 'can it fit?'. But in DS, that's not really the question you're being asked. You're being asked "have we provided enough information that a smart person would be able to determine whether it could fit?". If someone could figure it out, it's sufficient. You don't have to do the actual 'figuring out' part.

I agree with Aardwolf. It is absolutely necessary to calculate in order to solve this Q since the statements in question refer to maximum height and width. So a given rectangle is the maximum possible area of the truck, but the truck could be any other shape to that more easily fits within the tunnel. If the Q specifically said the truck is in the shape of a rectangle, you could avoid calc. but this is not the case either.

Preferred Approach:

Taking both statements together, the maximum possible area of the truck is a rectangle with height of 4m and width of 2.4m. Since it's a one-lane road, the best possible way to fit the truck is if it drives perfectly midway of the tunnel such that that bottom-centre of the truck is equidistant from the walls.

We then need to split this rectangle into two halves (each with width=2.4/2=1.2, height=4) and identify if the diagonal of that rectangle (referred to below as x) is greater than the radius (r) of the tunnel.

Attachment:
File comment: Flowchart Gmat_quant_DS.jpg [ 122.39 KiB | Viewed 6102 times ]

Since it is a right-angled triangle with base of 1.2 and height of 4, x is calculated by pythag: $$x=\sqrt{1.2^2+4^2}\approx{4.18}$$. As per the Question, $$r=4.2$$.

The tunnel will always accommodate the truck, regardless of the truck's actual shape if $$r>x$$. So the question effectively becomes is $$4.2>\sqrt{1.2^2+4^2}\approx{4.18}$$? The answer to this Q is YES hence C is correct.

HOWEVER if the answer to this Q is NO then, it does not mean the truck will not fit (see above diagram). It merely means the truck MAY not fit, depending on the shape of the truck. There are shapes other than a rectangle that would could have a $$maximum$$ width of 2.4m and height of 4m. Hence there would be insufficient information to answer the question and the answer would be E in these circumstances.

Would really appreciate if someone could shed light on how to more efficiently approximate that 4.2 is indeed greater than $$\sqrt{1.2^2+4^2}$$. This part of the question caused me the most difficulty given time constraints. Bunuel
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If you have \sqrt{2} memorized than you know it is equal to 1.4. Using this information I estimated up and made 1.2 -->1.4.

We originally have \sqrt{(1.2)^2+(4)^2} --estimating up for 1.2--> \sqrt{(1.4)^2+(4)^2} =\sqrt{2+16/square_root]

=[square_root]18} = 3\sqrt{2} = (3)*(1.4) = 4.2 ---> since I estimated up. The actual number must be smaller than 4.2

It would be good to have \sqrt{2} & \sqrt{3} memorized.
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I agree with ngmat12 about the fact that we should do the necessary calculations to evaluate the two statements together.

ngmat12 wrote:
Would really appreciate if someone could shed light on how to more efficiently approximate that 4.2 is indeed greater than $$\sqrt{1.2^2+4^2}$$. This part of the question caused me the most difficulty given time constraints.

Instead of comparing $$\sqrt{1.2^2+4^2}$$ to 4.2, we can compare the squares of these two positive terms.

$$\left(\sqrt{1.2^2+4^2}\right)^2=1.2^2+4^2=1.44+16=17.44$$

$$4.2^2=17.64$$

$$17.44<17.64 \implies \sqrt{1.2^2+4^2}<4.2$$
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