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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8781
GMAT 1: 760 Q51 V42
GPA: 3.82
After an ice began to melt out from the freezer, in the first hour los  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 79% (01:49) correct 21% (02:40) wrong based on 49 sessions

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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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Marshall & McDonough Moderator D
Joined: 13 Apr 2015
Posts: 1680
Location: India
Re: After an ice began to melt out from the freezer, in the first hour los  [#permalink]

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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

Manager  B
Status: One Last Shot !!!
Joined: 04 May 2014
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Location: India
Concentration: Marketing, Social Entrepreneurship
GMAT 1: 630 Q44 V32
GMAT 2: 680 Q47 V35
Re: After an ice began to melt out from the freezer, in the first hour los  [#permalink]

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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
Math Expert V
Joined: 02 Aug 2009
Posts: 8314
Re: After an ice began to melt out from the freezer, in the first hour los  [#permalink]

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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
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8781
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: After an ice began to melt out from the freezer, in the first hour los  [#permalink]

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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.
_________________ Re: After an ice began to melt out from the freezer, in the first hour los   [#permalink] 11 May 2016, 19:05
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# After an ice began to melt out from the freezer, in the first hour los  