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On the number line, the distance between x and y is greater

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Senior Manager
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On the number line, the distance between x and y is greater [#permalink]

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New post 01 Nov 2006, 23:09
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

67% (01:25) correct 33% (01:33) wrong based on 545 sessions

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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
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 [#permalink]

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New post 01 Nov 2006, 23:25
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I get E.

Statement 1:

xyz < 0. All this tells us that either one or three of the numbers is negative and none of them are zero.

So, you can have x = 1, y = 8, z = -3, where the distance between XY is greater than the distance between XZ. Here, z does not lie between x and y.

But you can also have x = -1, y = -8, z = -3, where the distance between XY is greater than the distance between XZ, but where z lies between the two on the number line. Insufficient.

Statement 2:

xy < 0

All this tells us is that either x or y is negative and neither is zero. Taking x = -1, y = 8, z = -3, where the distance between XY is greater than the distance between XZ. Here, z does not lie between them on the number line.

But, taking x = 1, y = -8, z = -3, you fulfill the distance requirement and z falls between x and y on the number line. Insufficient.

Both Statements:

Taking both statements together, we learn that either x or y is negative and everything else is positive. Taking x = -1, y = 8, z = 2, we find that z lies between the points on the number line and fulfills the distance requirement. However, taking x = 8, y = -1, z = 10, z no longer lies between the two points but XY is still greater than XZ. Still insufficient.

So, answer E.
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 [#permalink]

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New post 01 Nov 2006, 23:59
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yes. it is E.

draw the number line. place the 3 numbers in different relative positions and u'll see the answer.
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Re: DS-Number line [#permalink]

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New post 18 Jun 2010, 07:24
Bunuel, the expert, is there a better way to solve this problem. I just took the Prep test and took me a long time to test each number. Is theer a quicker way to do this?
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Re: DS-Number line [#permalink]

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New post 18 Jun 2010, 07:34
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study wrote:
Bunuel, the expert, is there a better way to solve this problem. I just took the Prep test and took me a long time to test each number. Is theer a quicker way to do this?


This is a hard problem. Below is another way of solving it:

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?

The distance between x and y is greater than the distance between x and z, means that we can have one of the following four scenarios:
A. y--------z--x (YES case)
B. x--z--------y (YES case)
C. y--------x--z (NO case)
D. z--x--------y (NO case)

The question asks whether we have scenarios A or B (z lie between x and y ).

(1) xyz <0 --> either all three are negative or any two are positive and the third one is negative. We can place zero between y and z in case A (making y negative and x, z positive), then the answer would be YES or we can place zero between y and x in case C, then the answer would be NO. Not sufficient.

(2) xy<0 --> x and y have opposite signs. The same here: We can place zero between y and x in case A, then the answer would be YES or we can place zero between y and x in case C, then the answer would be NO. Not sufficient.

(1)+(2) Cases A (answer YES) and case C (answer NO) both work even if we take both statement together, so insufficient.

A. y----0----z--x (YES case) --> xyz<0 and xy<0;
C. y----0----x--z (NO case) --> xyz<0 and xy<0

Answer: E.
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Re: On the number line, the distance between x and y is greater [#permalink]

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Best technique is to draw and visualize their positions in the numberline...

1. xyz < 0
Try x and y and z as all negative...
<---(z)---x--(z)---y-----0------------>

Just this scenario is already giving us two possibilities...
INSUFFICIENT

2. xy < 0
This means x and y has opposite signs...

<----(z)---x--(z)--0-------y------>

Just this scenario is already giving us two possibilities...
INSUFFICIENT

Now, let us combine...
If x and y has opposite signs then for xyz to be negative z must be positive...

scenario 1: <---------x-----0-(z)-------y--------------> YES z is in between
scenario 2: <---------y-----0-----(z)-------x------(z)-------> NO z is not in between

STILL INSUFFICIENT

Answer: E
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Re: On the number line, the distance between x and y is greater [#permalink]

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New post 08 Dec 2017, 11:45
uvs_mba 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


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
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Re: On the number line, the distance between x and y is greater [#permalink]

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New post 19 Feb 2018, 13:07
Hi All,

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. 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:

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:

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Re: On the number line, the distance between x and y is greater   [#permalink] 19 Feb 2018, 13:07
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