whoa whoa
wait
hold on
Stuart Kovinsky wrote:
Excellent analysis (including the part about the question not making sense).
most of the analysis is good, but the treatment of statement (2) is fatally flawed. see below.
Stuart Kovinsky wrote:One additional point: cubes, like squares and circles (and equilateral triangles), really only have 1 measurement (side for cubes and squares, radius for circles). For these shapes, if you have ANY concrete measurement, you can figure out everything about them.
***
excellent point, and, indeed,
this is all you need to solve the problem.
Stuart Kovinsky wrote:So, ignoring the "this question would never appear as written" issue,
and ignore it we should, because the 'issue' is nonexistent. see below for details.
Stuart Kovinsky wrote: we see that each statement gives us a measurement of the cube, so each one will be sufficient on its own.
yes.
Stuart Kovinsky wrote:Remember, DS isn't about actually getting the answer, DS is about determining if it's possible to get the answer.
yes again.
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simplyjat wrote:Volume of cube is s*s*s. Surface Area of cube = 6*s*s. where s is the side of the cube.
right.
so this means s^2 = 18 / 6 = 3, so side length = √3.
so far so good.
here's where things take a turn southward:
simplyjat wrote: The furthest points on the cube are the points on diagonals of a single face = S*sqrt(2).
nope.
the longest such distance is between the two points at
opposite corners of the cube - i.e., the points at either end of a
main diagonal of the cube. that distance is actually (side)*√3, so
side*√3 = 3
side = √3
and note that this is perfectly consistent with the first statement.
nb: if you drew the distance between these two points, the distance would go diagonally through the cube itself; in other words, the
distance segment itself is not on the surface of the cube. but make sure you notice that this does not in any way violate the question, which stipulates only that the
points must be on the surface of the cube.
simplyjat wrote:But there is a problem. if you take the first statement, S = sqrt(3) and if you take second statement S = 3/sqrt(2)... both do not match. Where did you get the question, official GMAT DS questions will result in the same answer through both statements....
both values are side = √3, so there's no problem.
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here are the two most important things you should learn from this topic:
(1) stuart's point above about the unidimensionality of cubes, etc. (see above, marked 'excellent point' with 3 asterisks)
(2) if you want 'longest distance', 'farthest apart', etc., with a cube, it's a fairly safe bet that they're talking about the main diagonal.
