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
Number Line
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- rommysingh
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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: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
-----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.
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Hi rommysingh,
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
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