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lawn

by grandh01 » Wed Aug 22, 2012 2:07 pm
Raymond took several days to mow a
certain lawn. He mowed
1/3 of the lawn the first day,
1/2 of the remaining unmowed portion the
second day, and 3/4 of the
remaining unmowed portion the third
day. What fraction of the lawn
remained unmowed at the end of the
third day?
(A)1/6
(B)1/8
(C)1/12
(D)1/16
(E)1/24

OA is C
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by theCEO » Wed Aug 22, 2012 3:12 pm
grandh01 wrote:Raymond took several days to mow a
certain lawn. He mowed
1/3 of the lawn the first day,
1/2 of the remaining unmowed portion the
second day, and 3/4 of the
remaining unmowed portion the third
day. What fraction of the lawn
remained unmowed at the end of the
third day?
(A)1/6
(B)1/8
(C)1/12
(D)1/16
(E)1/24

OA is C
day 1 = 1/3
incomplete = 3/3 - 1/3 = 2/3

day 2 = 1/2 * 2/3 = 1/3
incomplete = 2/3 - 1/3 = 1/3

day 3 = 3/4 * 1/3 = 1/4
incomplete = 1/3 - 1/4 = 4/12 - 3/12 = 1/12

ans = c
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by truplayer256 » Wed Aug 22, 2012 6:06 pm
Assume Raymond needs to cut x square feet of lawn.

Amount mowed on first day = x/3, Amount remaining = 2x/3

Amount mowed on second day = (2x/3)(1/2) = x/3, Amount remaining = x/3

Amount mowed on third day = (x/3)(3/4) = x/4, Amount remaining = x/12

Choose C.
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by Ian Stewart » Wed Aug 22, 2012 6:25 pm
The approaches above are perfect, but it's a pure ratio question, so you can start with a number if you prefer. The best number to work with is some multiple of your denominators, so you can start with 12 here. Then we have the following sequence of changes:

12 ----( -1/3 of 12, so -4)----> 8 ----(-1/2 of 8, so -4)----> 4 ----(-3/4 of 4, so -3)----> 1

so 1/12 of the lawn is not mowed.

One advantage of the approach above is that it allows you to answer almost any question quickly, without needing to think about what you would have to do algebraically. If the question asks "what was the ratio of the amount mowed on the first day to the amount mowed on the third" we can see right away that 4 units were mowed on the first day and 3 units were mowed on the third day, so the answer is 4 to 3.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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