Explanation
To find the surface area of this rectangular solid, we will
most likely require the height, width, and depth of the shape. We can call the
three dimensions, a, b, and c, so that the surface area would be
. On to the statements, separately first.
Statement (1) tells us about two adjacent faces. They have
one dimension in common, which means they have one variable in common, which we
can take to be a. We can interpret
this as
and
. That gives us a total of two equations and three
variables, so we cannot solve directly. Meanwhile, we don't know
. We can imagine a case in which
. Then
. Case II:
Then
, and since the two cases have different bc's and equal
other areas, they have different surface areas. Insufficient.
Statement (2) tells us that
. That's
, so we could have
. In another case, we could have
. In one case, half the surface area is
In the other, half the surface area is
and we will
just stop there because it is already greater, so we have two possibilities.
Statement (2) alone is insufficient.
When we combine the statements, we now have three
equations and three variables. We will be able to solve completely, and the single
possible case turns out to be Case I above, which is not a complete surprise as
it was allowed by both statements.
The correct answer is (C).
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