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The value of a concept coin is inversely proportional to its radius

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The value of a concept coin is inversely proportional to its radius  [#permalink]

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New post 22 Nov 2017, 11:40
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  55% (hard)

Question Stats:

44% (01:57) correct 56% (01:57) wrong based on 41 sessions

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The value of a concept coin is inversely proportional to its radius. If a coin was melted and smaller coins with radii 1/4th of the original coin and thickness same as that of the original coin were made(using all the metal of the original coin), what will the ove0%^rall percentage increase in value after the operation?

A. 400%
B. 1500%
C. 1600%
D. 6300%
E. 6400%

Source: Experts Global

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The value of a concept coin is inversely proportional to its radius  [#permalink]

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New post 22 Nov 2017, 14:48
Original Coin Radius: r
Thickness: t
Volume of metal: \(\pi\)\(r^2\)t

Melted into smaller coins of radius 1/4 of original: r/4
Volume of each coin: \(\pi\)\((r/4)^2\)t
Since, volume of 16 smaller coins is equal to the larger coin, we now have 16 coins.

Question says that the value of coin is inversely proportional to its radius. So, assume value of original coin = x
Since the new coin has 1/4 radius of original, value of new coin = 4x
We have 16 new coins in total, so total value = 16*4x = 64x

Increase in value = 64x - x = 63x, or 6300%
The value of a concept coin is inversely proportional to its radius &nbs [#permalink] 22 Nov 2017, 14:48
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