If x and y are non-zero integers and |x| + |y| = 32, what is xy?
(1) -4x – 12y = 0
(2) |x| – |y| = 16
..The Answer is A. However, I am confused by the explanation below:
(1) SUFFICIENT: Statement (1) can be rephrased as follows:
-4x – 12y = 0
-4x = 12y
x = -3y
If x and y are non-zero integers, we can deduce that they must have opposite signs: one positive, and the other negative. Therefore, this last equation could be rephrased as
|x| = 3|y| {WHY DO THIS STEP? WHY DOES THIS MAKE SENSE?}
We don’t know whether x or y is negative, but we do know that they have the opposite signs. Converting both variables to absolute value cancels the negative sign in the expression x = -3y.
We are left with two equations and two unknowns, where the unknowns are |x| and |y|:
|x| + |y| = 32
|x| – 3|y| = 0
Subtracting the second equation from the first yields
4|y| = 32
|y| = 8
Substituting 8 for |y| in the original equation, we can easily determine that |x| = 24. Because we know that one of either x or y is negative and the other positive, xy must be the negative product of |x| and |y|, or -8(24) = -192.
(1) -4x – 12y = 0
(2) |x| – |y| = 16
..The Answer is A. However, I am confused by the explanation below:
(1) SUFFICIENT: Statement (1) can be rephrased as follows:
-4x – 12y = 0
-4x = 12y
x = -3y
If x and y are non-zero integers, we can deduce that they must have opposite signs: one positive, and the other negative. Therefore, this last equation could be rephrased as
|x| = 3|y| {WHY DO THIS STEP? WHY DOES THIS MAKE SENSE?}
We don’t know whether x or y is negative, but we do know that they have the opposite signs. Converting both variables to absolute value cancels the negative sign in the expression x = -3y.
We are left with two equations and two unknowns, where the unknowns are |x| and |y|:
|x| + |y| = 32
|x| – 3|y| = 0
Subtracting the second equation from the first yields
4|y| = 32
|y| = 8
Substituting 8 for |y| in the original equation, we can easily determine that |x| = 24. Because we know that one of either x or y is negative and the other positive, xy must be the negative product of |x| and |y|, or -8(24) = -192.
under-dog
