GMATsid2016 wrote:On the number line, the distance between x and y is greater that the distance between x and z. Does z lies between x and y on the number line?
1) xyz<0
2) xy<0
We are given that on the number line, the distance between x and y is greater than the distance between x and z. We need to determine whether z lies between x and y on the number line.
Statement One Alone:
xyz < 0
Using the information in statement one, we have two possible cases:
Case 1: Exactly one variable (either x, y, or z) is negative
Case 2: All three variables are negative.
Even with this information, we cannot determine whether z lies between x and y.
For example, for Case 1, if x = -1, y = 2, and z = 1, then z falls between x and y. However, for Case 2, if x = 1, y = 4, and z = -1, then z does not fall between x and y. Statement one alone is not sufficient. We can eliminate answer choices A and D.
Statement Two Alone:
xy < 0
Using the information from statement two, we know that exactly one of the values x or y is negative and the other is positive. However, without knowing anything about z, we cannot determine whether z falls between x and y. Statement two alone is not sufficient. We can eliminate answer choice B.
Statements One and Two Together:
From the information in statements one and two, we know that z must be positive and exactly one of the values x or y is negative. However, we still we cannot determine whether z falls between x and y or outside x and y.
For example, if x = -1, y = 2, and z = 1, then z falls between x and y. However, if x = 1, y = -2, and z = 2, then z does not fall between x and y. The two statements together are still not sufficient.
Answer: E
