let there be three nos x,y,z in the list
(1) the product of any two is =0 i.e. xy=0, yz=0, zx=0 ... this is possible even if any one element, say y is not equal to zero. so y maybe or may not be zero. therefore stm (1) is insufficient
(2)sum of any two numbers is = 0 i.e. x+y=0, y+z=0, z+x=0
if x+y=0 then x=-y, substituting this in z+x = z-y=0
now we hv two equations z+y=0 & z-y=0 which give us both z&y =0 and so is x=0 .... sufficient
ans (B)
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GMAT Prep / Number Properties
Source: Beat The GMAT — Data Sufficiency |
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earth@work
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earth@work has it down.
here's a possibly more intuitive way to handle statement (2):
your first two numbers are "-x" and "x", since they must be opposites if they sum to zero (remember that any pair sums to zero, so we don't have to pick two "special" numbers for this to happen).
if this is the case, then your third number must be x (so that it adds to -x to give zero), but it must ALSO be -x (so that it adds to x to give zero). the only way that x can equal -x is if x is zero - which means that all three numbers are zero.
therefore, everything must be zero.
so (2) is sufficient.
ans (b)
here's a possibly more intuitive way to handle statement (2):
your first two numbers are "-x" and "x", since they must be opposites if they sum to zero (remember that any pair sums to zero, so we don't have to pick two "special" numbers for this to happen).
if this is the case, then your third number must be x (so that it adds to -x to give zero), but it must ALSO be -x (so that it adds to x to give zero). the only way that x can equal -x is if x is zero - which means that all three numbers are zero.
therefore, everything must be zero.
so (2) is sufficient.
ans (b)
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.
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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
