The comparison cannot be simplified any further. Although you are given that
you still
don't know how
w
compares to or 1.8. For example, if
then
but
if
then
In
other words, the relationship between
w
and cannot be
determined. Note that each of these simplification steps is reversible, so
in reverse order,
each simplification step implies that the
relationship cannot be determined
in the preceding
comparison. Thus, the relationship between Quantities A and B cannot be determined.
The
correct answer is Choice D
,
the relationship cannot be determined from the
information given
.
The strategy of simplifying the comparison works most efficiently when you note that a
simplification step is reversible while actually taking the step. Here are some
common steps
that are always reversible:
•
Adding any number or expression to both sides of a comparison
•
Subtracting any number or expression from both sides
•
Multiplying both sides by any nonzero number or
expression
•
Dividing both sides by any nonzero number or expression
Remember that if the relationship is an
inequality
, multiplying or dividing both sides by
any
negative
number or expression
will yield the
opposite
inequality. Be aware that some
common operations like squaring both sides are generally not reversible and may require
further analysis using other information given in the question in order to justify reversing
such steps.
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