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Does z lies between x and y on the number line?

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Source: — Data Sufficiency |

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by [email protected] » Mon Dec 05, 2016 10:16 am
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

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by GMATsid2016 » Mon Dec 05, 2016 11:03 pm
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.
Hi Rich ,

Thanks for your explanation. Just a quick question.

Its give that distance between x and y, so it means x-y right?

Can we also assume y-x?

Please advise.

Thanks,

Sid
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by Mo2men » Tue Dec 06, 2016 10:06 am
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

OAE
Another way is visual representation:

https://gmatclub.com/forum/on-the-number ... 37747.html

Hope it helps
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by [email protected] » Tue Dec 06, 2016 10:16 am
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|.

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by Matt@VeritasPrep » Thu Dec 08, 2016 9:25 pm
Here's an algebraic approach.

Statement 1 tells us that either all three values are negative OR exactly one of them is negative. But which one? We don't know ... insufficient.

Statement 2 tells us that exactly one of x and y is negative and the other is positive. We don't know anything about z, however ... insufficient.

Taking the two together, we know exactly one of the numbers (either x or y) is negative. This tells us z is positive. But z could be on either side of the other positive number! (This is where GMATGuru's approach of trying numbers is helpful.) Hence the two statements together are insufficient.
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by Jeff@TargetTestPrep » Sat Dec 10, 2016 4:58 am
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

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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