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# QOTD#16 The interior dimensions of a rectangular tank are as

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CEO
Joined: 07 Jun 2014
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QOTD#16 The interior dimensions of a rectangular tank are as [#permalink]  12 Sep 2016, 11:52
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The interior dimensions of a rectangular tank are as follows: length 110 centimeters, width 90 centimeters, and height 270 centimeters. The tank rests on level ground. Based on the assumption that the volume of water increases by 10 percent when it freezes, which of the following is closest to the maximum height, in centimeters, to which the tank can be filled with water so that when the water freezes, the ice would not rise above the top of the tank?

A. 230
B. 235
C. 240
D. 245
E. 250

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Question: 17
Page: 206-207
[Reveal] Spoiler: OA

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CEO
Joined: 07 Jun 2014
Posts: 2547
GRE 1: 323 Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 41

Kudos [?]: 733 [0], given: 125

Re: QOTD#16 The interior dimensions of a rectangular tank are as [#permalink]  12 Sep 2016, 11:55
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Explanation

Let x be the maximum height, in centimeters, to which the tank can be filled with water, so that when the water freezes, the ice will not rise above the top of the tank. Based on the assumption that the volume of water increases by 10 percent when it freezes and the fact that the length and width of the tank will not change, the maximum height of the ice is 1.1x centimeters. Since the height of the tank is 270 centimeters, it follows that 1.1x = 270, or, to the nearest whole number, x = 245. The correct answer is Choice D.
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Re: QOTD#16 The interior dimensions of a rectangular tank are as [#permalink]  06 Jun 2017, 23:02
The solution makes sense, but I'm wondering, why doesn't the following solution work?

The height of the tank is 270, and 10% of 270 is 27. Therefore, if we fill up water to the height of 270-27=243, we will have 10% of the height left when the water freezes.
CEO
Joined: 07 Jun 2014
Posts: 2547
GRE 1: 323 Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 41

Kudos [?]: 733 [0], given: 125

Re: QOTD#16 The interior dimensions of a rectangular tank are as [#permalink]  07 Jun 2017, 01:10
Expert's post
preppingGRE6758 wrote:
The solution makes sense, but I'm wondering, why doesn't the following solution work?

The height of the tank is 270, and 10% of 270 is 27. Therefore, if we fill up water to the height of 270-27=243, we will have 10% of the height left when the water freezes.

You can test ypur soultion.

We know volume increases by 10% when frozen so if the water level was 243 then frozen water level would be 243 + 10% of 243 = 267.3. This is less than 270.

The reason for this is you need to look at the base for percentage. For example

10% of 100 is 10. So if we add we get 110.
But 10% of 110 is 11. So if we substract we get 99. Not 100.
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Re: QOTD#16 The interior dimensions of a rectangular tank are as   [#permalink] 07 Jun 2017, 01:10
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