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A squirrel climbs a straight wire from point A to point C. If B is the

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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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[Reveal] Spoiler: OA

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New post 30 Mar 2015, 05:29
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


1) Insufficient, no information about the line
2) Insufficient, no information about the highest point
1+2) Information about the line (it's linear, so it's rising equally?) and the highest point is 40. Since you know B is the midpoint, 40/2 = 20. B is 20 feet above the ground.

C.

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Re: A squirrel climbs a straight wire from point A to point C. If B is the [#permalink]

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New post 30 Mar 2015, 05:52
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Option A. Statement 1 alone is sufficient.

1. point C is 40 feet above ground.

Let \(C_1\) by point on ground directly below \(C\)and \(B_1\) be point directly below \(B\).

\(\triangle ABB_1\) is similar to \(\triangle ACC_1\)

\(Therefore \frac{AB}{AC} = \frac{BB_1}{CC_1}\)

Therefore \(BB_1\) = 20


2. x = 60, alone is not sufficient.

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Re: A squirrel climbs a straight wire from point A to point C. If B is the [#permalink]

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New post 06 Apr 2015, 05:27
Bunuel wrote:
Image
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

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:
Attachment:
squirrelonwire_text.PNG
squirrelonwire_text.PNG [ 18.42 KiB | Viewed 1927 times ]

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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: A squirrel climbs a straight wire from point A to point C. If B is the [#permalink]

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New post 12 Apr 2015, 10:49
Hi, Is this a rule? As in; if the squirrel had travelled 1/4 of the distance would he stand 10m above the ground?

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Re: A squirrel climbs a straight wire from point A to point C. If B is the [#permalink]

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tgubbay1 wrote:
Hi, Is this a rule? As in; if the squirrel had travelled 1/4 of the distance would he stand 10m above the ground?

hi tgubbay,
It is called properties of similar triangles i.e if two triangles are similar than their angles are equal and their sides are in proportion suppose c makes a point c1 on ground and b makes a point b1 on ground then ab/bb1= ac/cc1 and the answer to your question is yes b will be 10 just plug in the values in the ratios.

hope it helps

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Re: A squirrel climbs a straight wire from point A to point C. If B is the [#permalink]

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New post 20 Apr 2015, 11:04
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anshul2014 wrote:
tgubbay1 wrote:
Hi, Is this a rule? As in; if the squirrel had travelled 1/4 of the distance would he stand 10m above the ground?

hi tgubbay,
It is called properties of similar triangles i.e if two triangles are similar than their angles are equal and their sides are in proportion suppose c makes a point c1 on ground and b makes a point b1 on ground then ab/bb1= ac/cc1 and the answer to your question is yes b will be 10 just plug in the values in the ratios.

hope it helps


Hi tgubbay1 - let me explain to you how the ratio of the sides was arrived at.

Image

If you look at the figure, you can observe that in triangle ACE which is a right angled triangle, we can write \(Sin x = \frac{CE}{AC}\)

Similarly, in triangle ABD which is also a right angled triangle, we can write \(Sin x = \frac{BD}{AB}\)

From the above two equations, we can write \(\frac{CE}{AC} = \frac{BD}{AB}\). Since we know that \(AB= \frac{AC}{2}\), we can simplify the expression to \(BD = \frac{CE}{2}\). Thus, to find the value of BD, we need to know the value of CE, which is given to us by st-I.

Hence, had AB been equal to \(\frac{AC}{4}\), BD would also have been equal to \(\frac{CE}{4}\).

Hope it helps!

Regards
Harsh
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