grantcke wrote:
What is the value of x - y ?
(1) 3x - z = 42 and y - z = 5.
(2) x^2 - xy - xz + yz = 84 and x - z = 12.
This is that kind of question which seems full of variables(algebra) and thus scares us away, but a slight thinking-on-feet ability and re-arranging the given data often makes the question simple.
(1) 3x - z = 42 and y - z = 5.
Clearly, z can be eliminated if we subtract any equation from the other. If we subtract second equation from first, we get:
3x - y = 42-5 = 37. But this gives us 3x-y, while we need x-y. Nothing else is given. So
Insufficient.
(2) x^2 - xy - xz + yz = 84 and x - z = 12.
Can we somehow use x-z = 12 here. Lets factorise the first equation:
x(x-y) - z(x-y) = 84 OR (x-z)(x-y) = 84. We can now substitute x-z = 12 and that will give us a single value of x-y. That's what we need.
Sufficient.
Hence
B answer