Explanation
On the GMAT, the radical sign denotes the positive square
root of something (even though, when we solve for a variable squared, there are
positive and negative possibilities), so both sides of this inequality are
positive. We can therefore square it and obtain:
This is the question we are being asked. On to the
statements, separately first.
Statement (1) tells us exactly what we want to know. It
says that
is a fact, so
the answer to the question of whether
will be
definitively "yes." Sufficient.
Statement (2) looks similar. It simplifies to
. We'll analyze by cases. Say
. In that case, the statement demands that
. So the
statement would allow, among other possibilities,
and
. These two x-y possibilities yield opposite answers
to the question posed, so this statement is insufficient.
The correct answer is (A).
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