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One-third of a barrel's contents is emptied with each turn

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by BTGmoderatorDC » Tue Jul 31, 2018 4:48 pm

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One-third of a barrel's contents is emptied with each turn of the wheel. If the barrel begins full, what fraction of the barrel remains after 2 turns of the wheel?

A. 1/9

B. 4/7

C. 4/9

D. 2/3

E. 8/9
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by [email protected] » Tue Jul 31, 2018 6:00 pm
Hi All,

We're told that one-third of a barrel's contents is emptied with each turn of the wheel. We're asked, if the barrel begins full, what fraction of the barrel remains after 2 turns of the wheel. This question can be solved in a couple of different ways, including by TESTing VALUES.

IF.... a full barrel contains 90 gallons
then after the first turn, (1/3)(90) = 30 gallons is emptied, leaving 90 - 30 = 60 gallons
and after the second turn, (1/3)(60) = 20 gallons is emptied, leaving 60 - 20 = 40 gallons

Thus, 40/90 = 4/9 of the barrel's contents remain.

Final Answer: C

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by Jeff@TargetTestPrep » Sat Aug 18, 2018 7:01 pm
BTGmoderatorDC wrote:One-third of a barrel's contents is emptied with each turn of the wheel. If the barrel begins full, what fraction of the barrel remains after 2 turns of the wheel?

A. 1/9

B. 4/7

C. 4/9

D. 2/3

E. 8/9
After the 1st turn, 1 - 1/3 = 2/3 of the barrel's contents remains.

After the 2nd turn, 2/3 - (1/3)(2/3) = 2/3 - 2/9 = 4/9 of the barrel's contents remains.

Answer: C

Jeffrey Miller
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