courtesy of a student:

from GMAT PREP

What is the value of xy?

1. y = x + 1

2. y = x^2 + 1

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it shouldn't take you too long to figure out that each of the statements, taken individually, is insufficient.
if you have good enough algebraic intuition, you can figure this out by just looking at the expressions and realizing that they aren't going to give you xy. otherwise, you can look at some numbers:

STATEMENT (1) if x = 1 and y = 2, then xy = 2; if x = 2 and y = 3, then xy = 6.
insufficient.

STATEMENT (2) if x = 1 and y = 2, then xy = 2; if x = 2 and y = 5, then xy = 10.
insufficient.

at this point, this becomes a standard SIMULTANEOUS EQUATIONS problem.
remember that there are two ways to solve SIMULTANEOUS EQUATIONS problems:
1) LINE THEM UP AND DO ARITHMETIC
2) SUBSTITUTION

this one will go either way.

line them up:
y = x^2 + 1
y = x + 1
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0 = x^2 - x <-- subtract

substitution:
since both expressions are equal to y, just set them equal to each other:
x + 1 = x^2 + 1
x = x^2
0 = x^2 - x

so, either way, you have x^2 - x = 0.
factor --> x(x - 1) = 0
x = 0 or 1

notice that this does NOT YET mean that the data are insufficient. you must ascertain that THE DESIRED QUANTITY has two or more different values to say "insufficient".

if x = 0, then y = 1 (from either of the statements) --> xy = 0.
if x = 1, then y = 2 (from either of the statements) --> xy = 2.
so this really is INSUFFICIENT.

answer = (e)

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two notes:

* if the question had instead been "What is |x - 1| + |y - 1| ?" -- with EXACTLY the same statements -- then the answer would be (c) rather than (e). make sure you know why.

* you might actually discover the answer to this problem really quickly, by pure chance. when you're "plugging in" to the individual statements, it's entirely possible that you'll discover (x = 0, y = 1) and (x = 1, y = 2) -- for both statements. if you realize that these same numbers work for both statements -- and that they give two different answers to the prompt question -- then you'll immediately know that the answer is (e).