We have:
x=lightest box
y=median box
z=3rd box
y=9
x+y+z/3=7 => x+y+z=21 => x+z=12
We replace z with the lowest possible weight (in order to find the maximum possible wight for x), so z=9 (they CAN be equal with y, 9 is still the median value). So x=3.
hence, C
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GMAT Prep / Arithmetic
Source: Beat The GMAT — Problem Solving |
a good, and surprisingly simple, way to impose structure on problems involving the median of a set is to write a series of BLANKS that represent the numbers in the set IN ORDER, and then fill them in as appropriate.
start with 3 blanks:
_ _ _
in this set, we're given that the median is 9. this means that the middle one of the 3 blanks is 9:
_ 9 _
we want to maximize the left hand blank.
general takeaway: to MAXIMIZE a quantity, MINIMIZE all OTHER QUANTITIES over which you have discretion.
in this problem, that just means minimize the right-hand blank.
the right-hand blank must be > 9; otherwise it wouldn't be the right-hand blank anymore (remember, the blanks are in increasing order).
so, to minimize it, put a 9 in it.
_ 9 9
finally, the average is 7, meaning that the sum is 7 x 3 = 21.
21 - 9 - 9 = 3.
3 9 9
done.
start with 3 blanks:
_ _ _
in this set, we're given that the median is 9. this means that the middle one of the 3 blanks is 9:
_ 9 _
we want to maximize the left hand blank.
general takeaway: to MAXIMIZE a quantity, MINIMIZE all OTHER QUANTITIES over which you have discretion.
in this problem, that just means minimize the right-hand blank.
the right-hand blank must be > 9; otherwise it wouldn't be the right-hand blank anymore (remember, the blanks are in increasing order).
so, to minimize it, put a 9 in it.
_ 9 9
finally, the average is 7, meaning that the sum is 7 x 3 = 21.
21 - 9 - 9 = 3.
3 9 9
done.
Ron has been teaching various standardized tests for 20 years.
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Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
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Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
--
Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
--
Learn more about ron
never mind... my biggest mistake is in not reading the question thoroughly.
thanks very much for the explanation
thanks very much for the explanation
Last edited by mayuran23 on Tue Apr 14, 2009 7:18 pm, edited 1 time in total.
