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
GMAT Prep / Arithmetic
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lunarpower
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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
