These questions show you several (usually 3) views of a
3-dimensional cube with unique symbols or markings on each face
and then asks you a question about it. For example, which symbol
is on the opposite face?
Example Question
1) Three views of the same cube are shown above. Which symbol is
opposite the X?
Answers
1) D
Some people seem to have a natural talent for imagining objects
in 3 dimensions and find these questions straightforward. However,
if you’re not one of them and you find thinking in three
dimensions difficult, there are other ways to get the answer. In
the question above for example, you can simply use a process of
elimination. If you can see a symbol on the same illustration as
the ‘X’ then it cannot be opposite. The second and third cubes
eliminate A, B and C. This leaves only D and ‘other’ as
possibilities. D has edges shared with A and B which would be
consistent with the third cube illustrated. Therefore D is
correct.
Although it is not usually specified in the instructions, it is
almost always true that in these questions each symbol is used
only once. This means that even in cases where elimination is not
possible, it is sometimes quite easy to see the solution without
mentally manipulating the cube too much. In the example above, you
can simply compare the first and third illustrations. The third
illustration shows a 90 degree clockwise rotation (looking at the
cube from above) of the first illustration. Therefore D must be
opposite the ‘X’.
Cubes in 2 and 3 Dimensions
These questions show a flat (2-dimensional) pattern which can
be folded to make a cube and a number of 3-dimensional cubes
(usually 4). The pattern and the cubes have symbols or marking on
each face. You need to look at the pattern and decide which of the
cubes, if any could be made from it.
Example Questions
2) Which of the cubes shown could be made from the pattern?
Answer
2) A - The key to these questions is to remember that only
three faces of the cube can be shown in the illustration, this
means that you need only to consider the relationship between the
three visible elements on each cube and see if the same
relationship exists in the pattern.
The best strategy for this type of question is to call one face of
the cube the ‘front’ and then to name the other faces of the cube
in relation to it. For example:
This is obviously an arbitrary decision as you could look at a
cube from any side. However, thinking of the problem this way
makes it much easier to ‘see’ the relationship between the faces
of the cube. You can then: look at the front of the cube, find
that face on the pattern, use the pattern to identify the ‘top’
and eliminate any options that do not match, use the pattern to
identify the other face that touches the ‘front’ (in this example
LHS) and eliminate any options that do not match.
Another type of question poses the problem the other way around.
Here you have a single 3-dimensional cube and a number of
2-dimensional patterns, only one of which when folded, will make
the cube.
3) Which of the patterns when folded will make the cube shown?
Answer
3) B - The same strategy can be used to solve these questions,
remember don’t be intimidated by these problems even if imagining
things in 3 dimensions does not come easily to you. The problem
can always be reduced to the relationship between three elements,
which you can then try to locate in the answer figures.
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