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the shortest piece of wood

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by sanju09 » Wed Mar 23, 2011 2:06 am
Five pieces of wood have an average (arithmetic mean) length of 124 centimeter and a median length of 140 centimeter. What is the maximum possible length, in centimeter, of the shortest piece of wood?
(A) 90
(B) 100
(C) 110
(D) 130
(E) 140



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by srcc25anu » Wed Mar 23, 2011 2:32 am
_ / _ / 140 / _ / _ are 5 wood pieces
avg of 5 pieces =124 therefore total of 5 pieces = 124 * 5 = 620
to make the shortest peice, maximum length, we must minimize the length of larger 2 pieces. make them equal to median length .. that's the shortest they can be
so the 3 larger pieces length total 140*3 = 420
remaining = 620 - 420 = 200 (this is total length of 2 smaller pieces)
for smallest peice to have maximum length, make the 2 pieces equal to 100 each
hence 100 is the greatest length for the smallest wood piece.
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by HSPA » Wed Mar 23, 2011 2:36 am
5 objects with avg = 124 so total = 620

median is 140.. remove this out of total = 620-140 = 480

Now we have 4 values 2 > 140 and 2 less than 140

The items in bold are inversly proportional in theory
we need two above 140 ...
Consider 141, 142
So 620-(140+141+142) = 620- 423 = 197

Here answer is 100 because elements in set are not distinct and the set is { 100, 100, 140,140, 140}

IMO B
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