rommysingh wrote:On the number line, the distance between x and y is greater than the distance between x and z. Does z lie between x and y on the number line?
(1) xyz<0
(2) xy<0
Neither statement is sufficient alone, as we'll see when we combine them. Using both, we know xy < 0, and (xy)(z) < 0, so z must be positive. We also know that x is closer to z than it is to y, and that x and y have opposite signs (because xy < 0). But that still leaves us with possible number lines like this one:
-----y-----0-------z--x-------
where the answer to the question is 'yes', and this one:
-----y------0--------x---z-----
where the answer to the question is 'no', so the two statements together are not sufficient and the answer is E.
