We are give the radius =10
Let the base of the semicircle is AOB.
Let points X and Y be on edges of the traffic lane (XY=12)
OX=6
Now we have a right triangle with one side as 6 and the hypotenuse as 10, we can easily calculate the height using the Pythagorus theorem
= sqrt (6^2+10^2) =8
we need 1/2 ft clearance.
so height must be (8-1/2) =71/2 ft
B.
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perwinsharma
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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 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
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.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
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j_shreyans
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HI j_shreyans,
You can get the 2 free practice CATs and practice questions at www.mba.com
GMAT assassins aren't born, they're made,
Rich
You can get the 2 free practice CATs and practice questions at www.mba.com
GMAT assassins aren't born, they're made,
Rich
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j_shreyans
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Hi j_shreyans,
If you're asking about free Official material, then that's all that I think there really is. If you're talking about free material in general, then most GMAT Companies offer some type of free resources (practice questions, CATs, Trial Accounts, etc.), so you can visit the various Company websites and see what they have to offer.
GMAT assassins aren't born, they're made,
Rich
If you're asking about free Official material, then that's all that I think there really is. If you're talking about free material in general, then most GMAT Companies offer some type of free resources (practice questions, CATs, Trial Accounts, etc.), so you can visit the various Company websites and see what they have to offer.
GMAT assassins aren't born, they're made,
Rich
