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Re: Does z lie between x and y on a number line? [#permalink]
03 Feb 2012, 15:21

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Expert's post

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jj97cornell wrote:

On a 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 a number line?

(1) xyz < 0 (2) xy < 0

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 lies between x and y).

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

(1)+(2) Both case A (answer YES) and case C (answer NO) satisfy the statements. Not sufficient.

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

Re: On the number line, the distance between x and y is greater [#permalink]
03 Feb 2012, 15:36

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1. Statement 1 tells us that xyz<0

Which basically means that either all 3 are negative or one of them is negative. We can draw two scenarios of a number line where z is between x and y and where z is on the right of x and y on the left of x and maintain the condition that all three are negative. Hence Insufficient.

2. Statement 2 tells us that xy<0

Which basically means that either x is negative or y is negative. No statement about z so obviously insufficient.

Now together we know that if either x or y are negative, and one of them is positive, z has to be positive. So again we draw two scenarios on the number line and we find that two cases are possible, one where z is in the middle and one where it is not. Hence both statements combined are insufficient as well.

Answer. E .. I am attaching a diagram to illustrate.

[img]

Attachment:

Number%20Line.jpg

[/img]

Attachments

Number Line.jpg [ 105.17 KiB | Viewed 11946 times ]

_________________

"Nowadays, people know the price of everything, and the value of nothing."Oscar Wilde

Last edited by omerrauf on 03 Feb 2012, 16:04, edited 1 time in total.

Re: On the number line, the distance between x and y is greater [#permalink]
27 Oct 2013, 13:28

omerrauf wrote:

1. Statement 1 tells us that xyz<0

Which basically means that either all 3 are negative or one of them is negative. We can draw two scenarios of a number line where z is between x and y and where z is on the right of x and y on the left of x and maintain the condition that all three are negative. Hence Insufficient.

2. Statement 2 tells us that xy<0

Which basically means that either x is negative or y is negative. No statement about z so obviously insufficient.

Now together we know that if either x or y are negative, and one of them is positive, z has to be positive. So again we draw two scenarios on the number line and we find that two cases are possible, one where z is in the middle and one where it is not. Hence both statements combined are insufficient as well.

Answer. E .. I am attaching a diagram to illustrate.

[img]

Attachment:

Number%20Line.jpg

[/img]

Thanks for the diagram. I selected C mostly because I was unsure how to handle both statements together. I clearly see it now

Re: On the number line, the distance between x and y is greater [#permalink]
30 Oct 2013, 20:41

Bunuel, couldn't it also be possible that the variables are arranged so x is between z and y? For example z->x->y, instead of only x->y->z? It's kind of an incidental point because I got it right, but I want to make sure I am figuring it up the proper way.

Also, when the statements xyz or xy, is that to say how the numbers are located with reference to zero, or is it saying to multiply the numbers?

Re: On the number line, the distance between x and y is greater [#permalink]
31 Oct 2013, 00:40

Expert's post

Stoneface wrote:

Bunuel, couldn't it also be possible that the variables are arranged so x is between z and y? For example z->x->y, instead of only x->y->z? It's kind of an incidental point because I got it right, but I want to make sure I am figuring it up the proper way.

Also, when the statements xyz or xy, is that to say how the numbers are located with reference to zero, or is it saying to multiply the numbers?

We know that the distance between x and y is greater than the distance between x and z. This can happen in 4 ways, shown in my post. You can see there that x CAN be between z and y in cases C and D.