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Upon melting, ice loses 8% of its volume. Ice cubes, the

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kevincan
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Upon melting, ice loses 8% of its volume. Ice cubes, the [#permalink] New post   26 Jul 2006, 04:32
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Upon melting, ice loses 8% of its volume. Ice cubes, the edges of which all measure 2 cm, are added to a jug containing 5 L, or 5,000 cubic centimetres of hot water. How many ice cubes were added?

(1) When the ice cubes melt, the jug contains between 5.98 L and 6.02 L of cold water.
(2) The number of ice cubes added is an even number.



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Re: Upon melting, ice loses 8% of its volume. Ice cubes, the [#permalink] New post   26 Jul 2006, 08:25
kevincan wrote:
Upon melting, ice loses 8% of its volume. Ice cubes, the edges of which all measure 2 cm, are added to a jug containing 5 L, or 5,000 cubic centimetres of hot water. How many ice cubes were added?

(1) When the ice cubes melt, the jug contains between 5.98 L and 6.02 L of cold water.
(2) The number of ice cubes added is an even number.


Volume of the Cube = 8 cubic cm
Volume of water added if cube melts = 6.8 cubic cm.

5000 + n*6.8 = 5980 n =14
5000+ n*6.8 = 6020 n =15

From St1. & St2 its 14
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Re: Upon melting, ice loses 8% of its volume. Ice cubes, the [#permalink] New post   26 Jul 2006, 13:04
E

Let x = number of ice cubes addded

Volume before ice cubes started meting = B = 8x + 5000
Volume after ice cubes melted = A = 7.36x + 5000

St1: 5980 <A < 6020
i.e 980 < 7.36x < 1020
x coul dbe anything between 134 and 138 (Both inclusive.)

St2: Clearly INSUFF

Combined:

x could be 134, 136 or 138. : INSUFF
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Re: Upon melting, ice loses 8% of its volume. Ice cubes, the [#permalink] New post   26 Jul 2006, 13:28
I know you're a mighty calculator, but how can we conclude that the answer is indeed E without so much calculating?
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Re: Upon melting, ice loses 8% of its volume. Ice cubes, the [#permalink] New post   26 Jul 2006, 13:50
kevincan wrote:
I know you're a mighty calculator, but how can we conclude that the answer is indeed E without so much calculating?


I don't know the trick but I did a division of 98000/736 and 102000/736 and came up with 134 and 138. This is not a big calculation. The whole question took around 3 minutes.
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Re: Upon melting, ice loses 8% of its volume. Ice cubes, the [#permalink] New post   26 Jul 2006, 14:40
kevincan wrote:
Upon melting, ice loses 8% of its volume. Ice cubes, the edges of which all measure 2 cm, are added to a jug containing 5 L, or 5,000 cubic centimetres of hot water. How many ice cubes were added?

(1) When the ice cubes melt, the jug contains between 5.98 L and 6.02 L of cold water.
(2) The number of ice cubes added is an even number.



total volume before the cubes melt = 8n + 5000
total volume after the cubes melt = 8.(0.92)n + 5000 = 7.36n+ 5000

5980<7.36n+5000<6020
=>
980<7.36n<6020
133.something < n < 138.something....

A is insuff

B is insuff

Combining, n could be 134, 136,138....insuff so E
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Re: Upon melting, ice loses 8% of its volume. Ice cubes, the [#permalink] New post   26 Jul 2006, 15:14
Great! E is the OA, but we could do with a better explanation!

Hint: How many cubic centimeters are there between 5.98L and 6.02L?
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Re: Upon melting, ice loses 8% of its volume. Ice cubes, the [#permalink] New post   26 Jul 2006, 17:09
ghantark wrote:
kevincan wrote:
Upon melting, ice loses 8% of its volume. Ice cubes, the edges of which all measure 2 cm, are added to a jug containing 5 L, or 5,000 cubic centimetres of hot water. How many ice cubes were added?

(1) When the ice cubes melt, the jug contains between 5.98 L and 6.02 L of cold water.
(2) The number of ice cubes added is an even number.


Volume of the Cube = 8 cubic cm
Volume of water added if cube melts = 6.8 cubic cm.

5000 + n*6.8 = 5980 n =14
5000+ n*6.8 = 6020 n =15

From St1. & St2 its 14


my bad. stupid calculations....pls ignore my response.
thx
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Re: Upon melting, ice loses 8% of its volume. Ice cubes, the [#permalink] New post   26 Jul 2006, 19:14
kevincan wrote:
Great! E is the OA, but we could do with a better explanation!

Hint: How many cubic centimeters are there between 5.98L and 6.02L?



0.04/0.92 = n*8e-3 => n > 5 which means there will be atleast 5 integer values for the number of cubes in the range specified....

yes we need to keep looking for shortcuts....nice one kevin..
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Re: Upon melting, ice loses 8% of its volume. Ice cubes, the [#permalink] New post   26 Jul 2006, 19:20
Upon melting, ice loses 8% of its volume. Ice cubes, the edges of which all measure 2 cm, are added to a jug containing 5 L, or 5,000 cubic centimetres of hot water. How many ice cubes were added?

(1) When the ice cubes melt, the jug contains between 5.98 L and 6.02 L of cold water.
(2) The number of ice cubes added is an even number.

range of approx = 6.02 - 5.98 = 0.04L = 40 cubic cm..
volume of one cube = approx 7.2 cubic cm.. ( 2^3 * 92%)


statement 1 - not sufficient , range of approximation could vary the results from 1 to 5 additional cubes

statement 2 - not sufficicent - range of approx could vary the results between 2 or 4 additional cubes

together not sufficient

hence E



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Re: Upon melting, ice loses 8% of its volume. Ice cubes, the [#permalink]
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