ccooley
dadoprso
JeffTargetTestPrep
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.
Answer: C
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 31624 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