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On a number line distance between x and y is greater than [#permalink]
24 May 2006, 09:52

On a number line 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

_________________

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

St1:
xyz --> negative.
We could have all x, y and z to the left of 0 on the number line and arranged such that z is not between x and y. We could also have all x, y and z to the left of 0 on the number line and arranged such that z is between x and y. Insufficient.

St2:
xy < 0 --> Either x or y is negative.

Same thing. I can arrange x, y or z to be between or to the left of x or y (whichever is negative). Insufficient.

Using St1 and St2:
xy < 0 and xyz < 0

Say x, is negative --> value of -5, y is positive, value of 5. The distance between x and y is 10. This satisfied the inequalitied xy < 0.

We know z must be positive, otherwise the inequality xyz < 0 cannot be satisfied, but we do not know which positive value z takes on the number line.

Case 1 : Any number can be negative or positive. Not conclusive
Case 2.: z can be anywhere. Not conclusive again
Both : lets say x = -ve and y = +ve , z is obviously +ve. Ans distance bt x and y greater than distance bt x and z Hence
__________x______0__z___y_______________

Lets say x=+ve and y = -ve. Hence z can be anywhere.

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."