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

Author Message
Senior Manager
Joined: 05 Jun 2005
Posts: 424
On the number line, the distance between x and y is greater  [#permalink]

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01 Nov 2006, 22:09
4
19
00:00

Difficulty:

55% (hard)

Question Stats:

67% (01:25) correct 33% (01:35) wrong based on 569 sessions

### HideShow timer Statistics

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
Manager
Joined: 17 Dec 2004
Posts: 71

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01 Nov 2006, 22:25
4
1
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.

VP
Joined: 25 Jun 2006
Posts: 1082

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01 Nov 2006, 22:59
1
yes. it is E.

draw the number line. place the 3 numbers in different relative positions and u'll see the answer.
Manager
Joined: 05 Oct 2008
Posts: 243

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18 Jun 2010, 06:24
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?
Math Expert
Joined: 02 Sep 2009
Posts: 52294

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18 Jun 2010, 06:34
7
4
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

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 52294
Re: On the number line, the distance between x and y is greater  [#permalink]

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10 Jul 2018, 20:13
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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/on-the-numbe ... 27014.html
_________________
Re: On the number line, the distance between x and y is greater &nbs [#permalink] 10 Jul 2018, 20:13
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