A wire that weighs 20 pounds is cut into two pieces so that one of the

Question

A wire that weighs 20 pounds is cut into two pieces so that one of the pieces weighs 16 pounds and is 36 feet long. If the weight of each piece is directly proportional to the square of its length, how many feet long is the other piece of wire?

(A) 9
(B) 12
(C) 18
(D) 24
(E) 27

(A) 9
(B) 12
(C) 18
(D) 24
(E) 27

elegantm · Answer

Weight of 2nd piece = 4 pound

Since the weight is directly proportional to the square of its length., we may write
 \frac{16}{36^2}  =  \frac{4}{x^2}

Solving above, we get x = 18

Hence Answer C

sashiim20 · Answer

20  pounds wire is cut into two pieces =  16  pounds  +   4  pounds

The piece weighs  16  pounds is  36  feet long.

Ratio of weight and length of  16  pounds piece  = \frac{16}{36^2} = \frac{4 * 4}{36 * 36} = \frac{1}{81}

Therefore required ratio of other part would also be  \frac{1}{81}

Ratio  = \frac{4}{x^2} =   \frac{1}{81}

x^2 = 81*4   => x = \sqrt{81*4}

x = 9 * 2 = 18

Hence length of  4  pounds wire  = 18

Answer (C)...

praveen8047 · Answer

IMO (c)
Given, weight proportional to square (length)
=> w1 / w2 = square (l1/l2)
=> 16/4 = square (36/l2)
=> l2 = 18

Sent from my GT-N7100 using  GMAT Club Forum mobile app

ScottTargetTestPrep · Answer

Since the 20-lb wire is cut into two pieces and one of the pieces weighs 16 lbs, the other piece must weigh 4 lbs. Since the 16-lb piece has length of 36 ft and the weight of each piece is directly proportional to the square of its length, we can let x = the length in feet of the 4-lb piece and create the following proportion:
 
16/36^2 = 4/x^2
 
16x^2 = 4 * 36^2
 
4x^2 = 36^2
 
x^2 = 36^2/2^2
 
x^2 = 18^2 
 
x = 18
 
Answer: C

Hal90 · Answer

Per info:

20lb wire cut into 16lbs & 4lbs

16 lbs = 36ft x 36ft

4 = 2 x 2

(16/4)lbs = (36/2)ft x (36/2)ft

4lbs = 18ft x 18ft

Since weight is proportional to the square of the length

4lbs must be 18ft long

Hope this helps

Posted from my mobile device

bumpbot · Answer

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