dave13 wrote:
Bunuel wrote:
SOLUTION
If x and y are different integers and x^2 = xy, which of the following must be true?
I. x = 0
II. y = 0
III. x = -y
(A) l only
(B) II only
(C) III only
(D) I and III only
(E) I, II, and III
\(x^2=xy\) --> \(x(x-y)=0\) --> either \(x=0\) or \(x=y\) but as given that \(x\) and \(y\) are different numbers than the second option is out and we have: \(x=0\). So only I is always true (in fact because of the same reason that \(x\) and \(y\) are different numbers II and III are never true).
Answer: A.
Bunuel why this option is not valid III. x = -y
if y = -2
and x= y ---> x = -2
then \(-2^2 = (-2*)(-2)\) --> \(4 =4\)
can you explain ?
pleaese
This does not make sense.
If y = -2 and x = -y, then x = -(-2) = 2. What x= y has to do with this? x = y is not possible at all because the stem says that x and y are different integers...
Also, the question asks which of the following MUST be true not COULD be true. Even if there would exist x and y, for which x = -y, would satisfy the stem, still this would not be sufficient to say that III MUST be true. MUST be true means true for ALL possible values, not for some specific values only.
Finally, you should be careful with brackets. It's math, they DO matter. -2^2 means -(2^2) = -4, while (-2)^2 = 4.