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by hansoo » Sat Sep 12, 2009 3:27 pm
A squirrel climbs a straight wire from point A to point C. If B is the midpoint of AC, how far above the ground is point B?

(1) Point C is 40 feet above the ground.

(2) x = 60

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Last edited by hansoo on Sun Sep 13, 2009 5:47 pm, edited 1 time in total.
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by Nermal » Sun Sep 13, 2009 2:16 am
Is statement 2 saying x=6 or x=60?

Then it would be a 30-60-90-triangle and with the information of statement 1 you could solve for the distance from B to the ground.

IMO C
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by ronaldo780 » Sun Sep 13, 2009 5:08 am
It's actually A.
Regardless of what angle x is, B is always the midpoint on AC and hence also the mid point in terms of height, so its height is 20.

To prove it I drew two lines from B to D and E. Now, CEB and BDA are identical because they have two equal angles (<DAB=<EBC=x, <ECB=<DBA=90-x) and an equal side (AB=BC).
Hence, DB=EC, and since all angles are 90 DBFE is a rectangle, DB=EF, so FC=40 and DB=1/2FC=20.

(i) is sufficient and (ii) isn't.

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by hansoo » Sun Sep 13, 2009 5:49 pm
Great diagram ronaldo780! The offical answer is A.

Here's another explanation to add to the great ones we already have:

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