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

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

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10 May 2010, 08:34
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Difficulty:

55% (hard)

Question Stats:

62% (01:07) correct 38% (01:19) wrong based on 268 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
[Reveal] Spoiler: OA

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Kudos [?]: 1128 [0], given: 33

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10 May 2010, 14:11
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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?

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

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Director
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10 May 2010, 19:56
Thanks and +1. Drawing the number line is faster as it seems from your solution.

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05 Jul 2010, 17:19
Excellent...

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

Great explanation

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Manager
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16 Oct 2010, 04:47
tough question...

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

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25 Oct 2014, 08:30
Hello from the GMAT Club BumpBot!

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

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19 May 2015, 04:00
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
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Re: On the number line, the distance between x and y is greater [#permalink]

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07 Aug 2016, 09:11
Hello from the GMAT Club BumpBot!

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

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15 Nov 2017, 00:04
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: On the number line, the distance between x and y is greater   [#permalink] 15 Nov 2017, 00:04
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