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# A computer can solve a particular type of problem in an amount of time

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Intern
Joined: 05 Mar 2017
Posts: 6
A computer can solve a particular type of problem in an amount of time [#permalink]

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26 Aug 2017, 12:41
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95% (hard)

Question Stats:

39% (01:44) correct 61% (02:02) wrong based on 56 sessions

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A computer can solve a particular type of problem in an amount of time proportional to the cube of the number of elements in the problem. Problems whose data are compressed must first be run through a decompression algorithm, which takes time directly proportional to the number of elements in the problem. If the computer can solve a compressed 100-element problem in 1 minute 40 seconds, 20 percent of which is spent on decompression, how much time will the computer take to solve a compressed 200-element problem?

A.) 3 minutes
B.) 3 minutes 20 seconds
C.) 10 minutes 40 seconds
D.) 11 minutes 20 seconds
E.) 13 minutes 20 seconds
[Reveal] Spoiler: OA
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Joined: 02 Aug 2009
Posts: 5660
Re: A computer can solve a particular type of problem in an amount of time [#permalink]

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27 Aug 2017, 01:09
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brettbrettbrettcom wrote:
A computer can solve a particular type of problem in an amount of time proportional to the cube of the number of elements in the problem. Problems whose data are compressed must first be run through a decompression algorithm, which takes time directly proportional to the number of elements in the problem. If the computer can solve a compressed 100-element problem in 1 minute 40 seconds, 20 percent of which is spent on decompression, how much time will the computer take to solve a compressed 200-element problem?

A.) 3 minutes
B.) 3 minutes 20 seconds
C.) 10 minutes 40 seconds
D.) 11 minutes 20 seconds
E.) 13 minutes 20 seconds

hi..
it may seem to be complicated because of the length of Q and the data involved but break it down in pieces..

Quote:
A computer can solve a particular type of problem in an amount of time proportional to the cube of the number of elements in the problem.

$$T_1=k_1*n^3$$ where T is time, k is constant and n is number of element

Quote:
Problems whose data are compressed must first be run through a decompression algorithm, which takes time directly proportional to the number of elements in the problem.

$$T_2=k_2*n$$ where T is time, k is constant and n is number of element

and $$T=T_1+T_2$$

(1) 100 elements..
T = 1 min 40 sec=100 sec, $$T_1=100*0.8=80......T_2=20$$
$$T_1=k_1*n^3......80=k_1*100^3........k_1=\frac{80}{100^3}$$
$$T_2=k_2*n........20=k_2*100......k_2=\frac{1}{5}$$

now find for 200 elements after finding values of CONSTANT

(2) 200 elements
$$k_1=\frac{80}{100^3}......k_2=\frac{1}{5}$$
$$T_1=k_1*n^3=\frac{80}{100^3}*200^3=\frac{80}{100^3}*2^3*100^3=80*8=640$$
$$T_2=k_2*n=\frac{1}{5}*200=40$$
T=640+40=680 secs = 11 min 20secs

D
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Re: A computer can solve a particular type of problem in an amount of time   [#permalink] 27 Aug 2017, 01:09
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