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

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Director
Joined: 03 Sep 2006
Posts: 803
On the number line, the distance between x and y is greater  [#permalink]

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10 May 2010, 09:34
7
00:00

Difficulty:

55% (hard)

Question Stats:

64% (01:06) correct 36% (01:20) wrong based on 278 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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Math Expert
Joined: 02 Sep 2009
Posts: 50044

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10 May 2010, 15:11
4
4
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

_________________
Director
Joined: 03 Sep 2006
Posts: 803

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10 May 2010, 20:56
Thanks and +1. Drawing the number line is faster as it seems from your solution.
Intern
Joined: 18 Jun 2010
Posts: 7

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05 Jul 2010, 18:19
Excellent...

But scared if my mind will work so sharp in this way in that 2 mins provided.

Great explanation
Manager
Joined: 19 Sep 2010
Posts: 141

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16 Oct 2010, 05:47
tough question...
Director
Joined: 09 Jun 2010
Posts: 938
Re: On the number line, the distance between x and y is greater  [#permalink]

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19 May 2015, 05:00
Bunuel 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?

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

amazing explanation. can not say a word. very excellent
Math Expert
Joined: 02 Sep 2009
Posts: 50044
Re: On the number line, the distance between x and y is greater  [#permalink]

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10 Jul 2018, 21:13
LM 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, 21:13
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