Data Sufficiency

Hi GMATsid2016,

This question can be solved in a number of different ways. You can use a combination of TESTing VALUES and Number Properties to get to the solution:

We're told that, on a number line, the distance between X and Y is GREATER than the distance between X and Z. We're asked if Z is BETWEEN X and Y on the number line. This is a YES/NO question.

Fact 1: (X)(Y)(Z) < 0

This tells us that the three variables are either all negative OR 1 negative and 2 positives.

IF...
X = 1
Y = -2
Z = 2
Then the answer to the question is NO.

IF...
X = 2
Y = -2
Z = 1
Then the answer to the question is YES.
Fact 1 is INSUFFICIENT

Fact 2: (X)(Y) < 0

This tells us that one variable is positive and the other is negative. Unfortunately it tells us NOTHING about Z. As it stands though, the TESTs that I did in Fact 1 fit Fact 2 as well....

IF...
X = 1
Y = -2
Z = 2
Then the answer to the question is NO.

IF...
X = 2
Y = -2
Z = 1
Then the answer to the question is YES.
Fact 2 is INSUFFICIENT

Combined, we already have two TESTs that fit BOTH Facts and produce different answers (a NO and a YES), so there's no more work needed.
Combined, INSUFFICIENT

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

Hi Sid,

When thinking about 'distance' on a Number Line, you have to think in absolute terms (re: the distance between -1 and 1 is the same distance as between 1 and 3). Mathematically-speaking, that means absolute values are in play. Thus, the distance between X and Y on a Number Line is |X - Y|.

GMAT assassins aren't born, they're made,
Rich

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