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Re: AcmeCorp claims that its new robotic vacuum, RoboVac, will remove 4/5 [#permalink]
what is the answer for this.
I get it we have to find 4/5 of the dust left over after every consecutive run.
1st run-> 4/5
2nd run->4/5(1-4/5)
3rd run->4/5(4/5(1-4/5))
so the final answer should be = > 1st run + 2nd run+ 3rd run
It should be 124/125
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Re: AcmeCorp claims that its new robotic vacuum, RoboVac, will remove 4/5 [#permalink]
divyamurali wrote:
what is the answer for this.
I get it we have to find 4/5 of the dust left over after every consecutive run.
1st run-> 4/5
2nd run->4/5(1-4/5)
3rd run->4/5(4/5(1-4/5))
so the final answer should be = > 1st run + 2nd run+ 3rd run
It should be 124/125


ARE YOU SURE OF YOUR ANSWER? IT SAYS "what fraction of the dust in her home will be removed?" I GOT 64/125
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Re: AcmeCorp claims that its new robotic vacuum, RoboVac, will remove 4/5 [#permalink]
If we take 100 as an example:

(100/5)*4= 80
(80/5)*4= 64
(64/5*4)=51.2

So after 3 cycles: 51.2/100= 0.512
There is no such answer like that but if you divide 64/125 you get 0.512

Therefore answer A is the correct one.
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Re: AcmeCorp claims that its new robotic vacuum, RoboVac, will remove 4/5 [#permalink]
Bunuel wrote:
AcmeCorp claims that its new robotic vacuum, RoboVac, will remove 4/5 of the dust in a home or apartment in every cycle it runs. If Shay runs her new RoboVac three cycles in a row, what fraction of the dust in her home will be removed?

A. 64/125
B. 4/5
C. 21/25
D. 24/25
E. 124/125



Each time 1/5 dust will remain or a 5th of a 5th of a 5th.

This is the same as 5^-3.

\(\frac{1}{125}\) will remain, \(\frac{124}{125}\) removed.
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Re: AcmeCorp claims that its new robotic vacuum, RoboVac, will remove 4/5 [#permalink]
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Bunuel wrote:
AcmeCorp claims that its new robotic vacuum, RoboVac, will remove 4/5 of the dust in a home or apartment in every cycle it runs. If Shay runs her new RoboVac three cycles in a row, what fraction of the dust in her home will be removed?

A. 64/125
B. 4/5
C. 21/25
D. 24/25
E. 124/125


First cycle Removes 4/5 dust so remaining dust after 1 cycle = 1-4/5 = 1/5

Second cycle Removes 4/5 of remaining dust so remaining dust after 2 cycles = (1/5)*(1/5) = 1/25

Third cycle Removes 4/5 of remaining dust so remaining dust after 3 cycles = (1/5)*(1/25) = 1/125

Hence, Dust removed = 1-1/125 = 124/125

Answer: Option E
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Re: AcmeCorp claims that its new robotic vacuum, RoboVac, will remove 4/5 [#permalink]
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Re: AcmeCorp claims that its new robotic vacuum, RoboVac, will remove 4/5 [#permalink]
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