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After an ice began to melt out from the freezer, in the first hour los

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MathRevolution
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After an ice began to melt out from the freezer, in the first hour los [#permalink] New post   09 May 2016, 20:50
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After an ice began to melt out from the freezer, in the first hour lost 3/4, in the second hour lost 3/4 of its remaining. If after two hours, the volume is 0.5 cubic inches, what is the original volume of the cubic ice, in cubic inches?

A. 2.5
B. 3.0
C. 4.0
D. 6.5
E. 8.0

* A solution will be posted in two days.
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Re: After an ice began to melt out from the freezer, in the first hour los [#permalink] New post   09 May 2016, 21:30
Let initial volume of ice be = x
Ice Remaining after 1 hour = x - 0.75x = 0.25x
Ice Remaining after 2 hour = (1/4)x - (3/4 * 1/4 * x) = (1/16)x

(1/16)x = 0.5
x = 8

Alternate solution: Try to backsolve.
Initial volume = 8
After one hour --> (1/4)8 = 2
After two hours --> (1/4)2 = 0.5

Answer: E
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Re: After an ice began to melt out from the freezer, in the first hour los [#permalink] New post   09 May 2016, 21:32
Let total volume be x initially.

At the end of 1st hr
Lost: \(\frac{3}{4} x\)
Remaining: \(x - \frac{3}{4} x = \frac{1}{4} x\)

At the end of 2nd hr
Lost: \(\frac{3}{4} * \frac{x}{4} = \frac{3x}{16}\)
Remaining: \(\frac{x}{4} - \frac{3x}{16} = \frac{x}{16}\)

Now, we are givn that remaining after 2 hours is 0.5 cubic inches
Therefore, \(\frac{x}{16} = 0.5\)
=> \(x = 8\) cubic inches

Option E
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Re: After an ice began to melt out from the freezer, in the first hour los [#permalink] New post   09 May 2016, 22:05
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MathRevolution wrote:
After an ice began to melt out from the freezer, in the first hour lost 3/4, in the second hour lost 3/4 of its remaining. If after two hours, the volume is 0.5 cubic inches, what is the original volume of the cubic ice, in cubic inches?

A. 2.5
B. 3.0
C. 4.0
D. 6.5
E. 8.0

* A solution will be posted in two days.



Hi,
another way avoiding a bit of calculations is visualization--
after 2 hrs, it is 0.5 = 1/4 of X, where X is at the beginning of 2nd hour,
So at the beginning of 2nd hour = 0.5 *4=2..
And similarily in the beginning of 1st hour = 2*4 = 8
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Re: After an ice began to melt out from the freezer, in the first hour los [#permalink] New post   11 May 2016, 20:05
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If we consider the original volume of an ice to be x, then we get x(1-3/4)(1-3/4)=0.5. From this, we get x(1/4)(1/4)=0.5. So, x=8. The correct answer is E.
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Re: After an ice began to melt out from the freezer, in the first hour los [#permalink]
11 May 2016, 20:05
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