RTQ - Read the Question!

In the GMAT, it is essential to RTQ (read the question) very carefully.
Today, in considering two data sufficiency questions, we'll come across an extremely sneaky problem that demands you must do exactly that.

Question 1.
Is X^2 equal to XY?
(1) X^2 - Y^2 = (X+5)(Y-5)
(2) X = Y

Solution:
Consider the given info.
If X^2 = XY, then X=Y as long as X is not equal to 0.

Consider (1).
Expanding right side, we obtain:
X^2 - Y^2 = XY -5X +5Y -25.
Rearranging, X^2 -XY = Y^2 -5X +5Y -25
X^2 = XY iff and only if X^2 - XY = 0,
that is, if Y^2 -5X +5Y -25 = 0.
But there are no constraints on what values X and Y can take, so we cannot determine what Y^2 -5X +5Y -25 is equal to.
Not sufficient info.
Eliminate A and D.

Consider (2)
X=Y implies that XY = X^2.
Sufficient.
Answer is B.


Question 2.
A jewelry dealer initially offered a bracelet for sale at an asking price that would give a profit to the dealer of 40% of the original cost. What was the original cost of the bracelet?
(1) After reducing this asking price by 10%, the jewelry dealer sold the bracelet at a profit of $403.
(2) The jeweler sold the bracelet for $1953.

Consider question stem.
Let original cost = C.
Therefore, profit = 0.4C, and price = 1.4C.
These will be critical when considering (1) and (2).

Consider (1)
Price is reduced by 10%.
10% of 1.4C is 0.14C.
So new price is 1.26C.
Profir is now 0.26C.
0.26C= 403, so C = 403/0.26, which you don’t need to calculate.
(1) is sufficient

Consider (2)
We do not know if the actual selling price is the same as the initial offer price. So we do not know if it is valid to say that 1.4C = 1953.
(2) is not sufficient.
This is a very sneaky question, which demonstrates that you have to RTQ very carefully.
Answer is A.