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09 Apr 2017, 05:42
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
69% (02:02) correct
31%
(01:45)
wrong
based on 604
sessions
History
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Not Attempted Yet
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
A. 64/125
B. 4/5
C. 21/25
D. 24/25
E. 124/125
18 Apr 2017, 16:06
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Bunuel
Since 4/5 of the dust is removed with each cycle, after cycle 1, we see that 4/5 is removed and 1 - 4/5 = 1/5 is left. After cycle 2, (4/5)(1/5) = 4/25 is removed and 1/5 - 4/25 = 1/25 is left. Finally, after cycle 3, (4/5)(1/25) = 4/125 is removed and 1/25 - 4/125 = 1/125 is left. Therefore, after 3 cycles, 4/5 + 4/25 + 4/125 = 124/125 (i.e., 1 - 1/125 = 124/125) of the dust is removed.
Answer: E
10 Apr 2017, 11:26
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Bunuel
Let the total dust in the room be 125 units...
In the first run \(\frac{4}{5}*125 = 100\) units are removed and \(25\) units are left
In the second run \(\frac{4}{5}*25 = 20\) units are removed and \(5\) units are left
In the third run \(\frac{4}{5}*5 = 4\) units are removed and \(1\) units is left
Thus, we find that only \(1\) unit is left out of \(125\) units, so \frac{[fraction]124}{125}[/fraction] fraction of the dust in the home is removed.
Thus, answer must be (E) \(\frac{124}{125}\)
