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# Brooke uses a paper cutter to cut a 0.004 inch thick piece of paper in

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Math Expert
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Brooke uses a paper cutter to cut a 0.004 inch thick piece of paper in  [#permalink]

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26 Nov 2019, 00:57
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Difficulty:

45% (medium)

Question Stats:

62% (01:52) correct 38% (02:05) wrong based on 34 sessions

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Brooke uses a paper cutter to cut a 0.004 inch thick piece of paper in half. She then stacks the two halves on top of each other and cuts them in half again. She repeats the pattern until the stack becomes too thick for the paper cutter to cut. If the maximum thickness that the paper cutter can cut is 0.12 inches, how many pieces of paper will she have at the end of this process?

A. 16
B. 24
C. 32
D. 48
E. 64

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Re: Brooke uses a paper cutter to cut a 0.004 inch thick piece of paper in  [#permalink]

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26 Nov 2019, 02:57
$$[log_2 (.12/0.004)]+1=5$$

She can cut stack 5 times.

Total number of pieces of paper= 2^5=32

Bunuel wrote:
Brooke uses a paper cutter to cut a 0.004 inch thick piece of paper in half. She then stacks the two halves on top of each other and cuts them in half again. She repeats the pattern until the stack becomes too thick for the paper cutter to cut. If the maximum thickness that the paper cutter can cut is 0.12 inches, how many pieces of paper will she have at the end of this process?

A. 16
B. 24
C. 32
D. 48
E. 64

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Re: Brooke uses a paper cutter to cut a 0.004 inch thick piece of paper in  [#permalink]

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10 Jan 2020, 04:40
Hi nick1816 ,

How do solve from this ---- 0.004 * 2^n = 0.12 or 2 ^ n = 30 , where n is the no of times the cutting has happened.
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Re: Brooke uses a paper cutter to cut a 0.004 inch thick piece of paper in  [#permalink]

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10 Jan 2020, 08:04
16<30<32
$$2^4<2^n<2^5$$

n= 4.xyz

It implies that after 4 cuts the thickness of the stack is less than 0.12inches while after 5 cuts it is greater than 0.12.

As the thickness of stack is less than 0.12 after 4 cuts, you can make 1 more cut. Total number of cuts that can be made is 5.

Total number of pieces at the end of this process= 2^5=32

ShankSouljaBoi wrote:
Hi nick1816 ,

How do solve from this ---- 0.004 * 2^n = 0.12 or 2 ^ n = 30 , where n is the no of times the cutting has happened.
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Re: Brooke uses a paper cutter to cut a 0.004 inch thick piece of paper in  [#permalink]

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14 Jan 2020, 18:29
Bunuel Can you provide your solution? I cannot visualise the solution.
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Re: Brooke uses a paper cutter to cut a 0.004 inch thick piece of paper in  [#permalink]

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15 Jan 2020, 21:18
At each step the thickness will double and the number of sheet will double
So lets see
If the thickness is 0.004 then next step will be 0.008
or 0.004, 0.008, ...upto (0.12+x)
which is a GP hence
.12 = .004 (a^(n-1))
so n = 6 will be .124 and knife wont be able to cut it
hence upto n = 5 or upto 0.064 will be able to cut and total thickness would be 0.064
at each stage sheets doubles
hence again ratio is 2
so after 5 repeats sheets would be
2^5
32
Hence D
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Re: Brooke uses a paper cutter to cut a 0.004 inch thick piece of paper in  [#permalink]

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23 Jan 2020, 01:55
Decent Question. I like nick1816 's solution.
But here's the logical approach.

When the Paper is cut the first time - Two pieces of thickness 0.004 inches will exist. You place one on top of the other, you get a total thickness of 0.008 inches.
Cut #2 - Cutting two papers that lie together will result in 4 pieces of 0.004 inches. Place the two other ones on top and total thickness will be 0.016 inches.
Cut #3 - Cutting 4 pieces -> Total 8 pieces -> Place the 4 newly cut ones on top -> Total Thickness of 0.032
Cut #4 - 8 Pieces -> 16 Pieces -> Place the new ones on top -> Total 0.064 inches
Cut #5 - 16 pieces -> 32 pieces -> Place the new ones -> Total 0.128 inches.

You can't cut any further.
Hence you're left with 32 pieces.
Re: Brooke uses a paper cutter to cut a 0.004 inch thick piece of paper in   [#permalink] 23 Jan 2020, 01:55
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