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# A cube of cheese is 3-inches high. The cheese is sliced twic

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A cube of cheese is 3-inches high. The cheese is sliced twic [#permalink]  29 Oct 2017, 02:12
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51% (00:18) correct 48% (00:46) wrong based on 27 sessions
A cube of cheese is 3-inches high. The cheese is sliced twice.

 Quantity A Quantity B Resulting surface area of all the slices of cheese 90 square inches

A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

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[Reveal] Spoiler: OA
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Re: A cube of cheese is 3-inches high. The cheese is sliced twic [#permalink]  08 Apr 2018, 20:45
@Bunuel Can you please explain this one?
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Re: A cube of cheese is 3-inches high. The cheese is sliced twic [#permalink]  09 Apr 2018, 08:01
Same! I also would like for an explanation please. I said B but it's wrong.
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Re: A cube of cheese is 3-inches high. The cheese is sliced twic [#permalink]  09 Apr 2018, 14:34
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Let me try this one out - If the cube is sliced twice it will result in 3 cuboids -
Scenario 1: The cheese is sliced twice along length at 1 inches, the 3 cuboids formed will have length (l) = 1 inch, width(w) = 3 inches, height(h) = 3inches.
The area of surface Area of one of these cuboids = 2*(w*h) + 2*(h*l) + 2*(w*l) = 2*(3*3) + 2*(3*1) + 2*(3*1) = 30
Surface area of all 3 cuboids = 3 * 30 = 90

Scenario 2: The cheese is sliced first along length at 1.5 inches giving 2 equal cuboids now cut one of cuboids from width giving 2 more cuboids w = 1.5 inch, h = 3inches, l = 1.5 inch. In total 3 cuboids formed.
First cuboid will have length (l) =2 inch, width(w) = 3 inches, height(h) = 3inches. Second and Third Cuboid cuboid will have length (l) =0.5 inch, width(w) = 3 inches, height(h) = 3inches.
The area of surface Area of First cuboid = 2*(w*h) + 2*(h*l) + 2*(w*l) = 2*(3*3) + 2*(3*1.5) + 2*(3*1.5) = 26 inches
Surface area of second and third cuboids = 2*(1.5*3) + 2*(3*1.5) + 2*(1.5*1.5) = 22.5 inches
Total Surface Area of 3 cuboids 26 + 2*(22.5) = 71inches

However, this took a bit of time in trying out different scenarios.
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Re: A cube of cheese is 3-inches high. The cheese is sliced twic [#permalink]  09 Apr 2018, 15:54
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Expert's post
You do not need to solve this question at all.

A cube of cheese is 3-inches high. The cheese is sliced twice. Nothing has been mentioned about how the cheese is sliced.

Attachment:

Inkedimages_LI.jpg [ 591.29 KiB | Viewed 936 times ]

Take a look at the picture above. both cases satisfy the questions requirement however the area of the resultant solids are vastlz varying .

Imagine if you cut two really thin slices and rest of the bolck is intact then the area would be different from when the block is sliced from the middle.

This kind of question needs a bit of vizualization.
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Re: A cube of cheese is 3-inches high. The cheese is sliced twic [#permalink]  10 Apr 2018, 00:27
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One way is to not slice straight down, using, instead, a circular cut. By giving the cheese a circular cut, the area will involve $$pi$$ so ans will not equal $$90$$.

To make the total surface area equal to $$90$$ a combination of $$3$$ blocks with length=$$1$$; breadth=$$3$$; height=$$3$$ (this shape can be obtained by cutting so that the length reduces but other dimension are intact)
Option D
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This is my response to the question and may be incorrect. Feel free to rectify any mistakes

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Re: A cube of cheese is 3-inches high. The cheese is sliced twic [#permalink]  10 Apr 2018, 02:10
Thanks for the explanations!
Re: A cube of cheese is 3-inches high. The cheese is sliced twic   [#permalink] 10 Apr 2018, 02:10
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