Juggernaut_86 wrote:If x and y are non-zero integers and |x| + |y| = 32, what is xy?
(1) -4x - 12y = 0
(2) |x| - |y| = 16
OA after some discussion..
Thanks!
Cool question. The answer is
A.
Stat. (1) tells us that x=-3y. Plug this into the equation in the stem:
|-3y| + |y| = 32.
Look at two things separately: sign and value.
Value-wise, y must equal to 8, as 32 = 4*8.
Sign wise, either y=8 or y=-8 will satisfy this equation:
y=8 --> |-24|+|8| = 24+8 = 32
y=-8 --> |-3*-8| + |-8| = |24| + |-8| = 24+8 = 32.
x also has two possible corresponding values from x=-3y:
if y=8, x=-24
if y=-8, x=24
So we haven't limited x and y to a single individual value (actually to two sets of values), but the value of xy will remain the same at -8*24. This is because x and y have opposite signs, so the product will remain negative regardless of which set of value we choose. Stat. (1) - sufficient.
Stat. (2): |x| = |y|+16. Plug this into the equation in the stem:
|x| + |y| = |y|+16 + |y| = 2|y| + 16 = 32.
2|y| = 16
|y| = 8.
Again, this allows y to equal 8 or -8. What about x?
If y=8, then |x| = |8|+16 = 24
If y=-8, then |x| = |-8|+16 = 24
So we get that |x| is equal to 24 - which could still mean that x is equal to +/- 24.
And that's the main difference between (1) and (2): both indicate that y and x are +/- 8 and +/- 24 respectively, but stat. (1) add the additional information for opposite signs, while stat. (2) allows x and y to have opposite signs (e.g. 8 and -24) OR the same sign (e.g. 8 and 24). Thus, the product xy could equal -8*24 or + 8*24 - two possible values. Insufficient.
