Data Sufficiency

153) Distance between x and y is greater than distance between x and z. Does z lie between x and y on the number line?
a. xyz < 0
b. xy < 0


[spoiler]Shudnt the answer be E for above? [/spoiler]

What does xyz< 0 and xy<0 mean here? Are they that angles (doesn't seem to be), distances, or something else?

They are just numbers on the number line...

I still did not get it.

Could you please translate xyz < 0 or xy < 0 by taking an example.

I am not sure if I am missing anything obivious here.

ballubalraj wrote:I still did not get it.

Could you please translate xyz < 0 or xy < 0 by taking an example.

I am not sure if I am missing anything obivious here.

By xyz<0, the original poster must mean x*y*z<0 (ie, thier product is negative)

___________

The correct answer is definitely choice E.

We are told that the distance between x and y is greater than the distance between x and z, or |x-y|>|x-z|

The question is whether z lies between x and y on the number line.

So, set up a number line before going to the statements.

(1) xyz<0


means that their product is negative. So, either all of x, y, and z are negative or else two are positive and one is negative. Certainly not enough to tell whether z lies between x and y. Insufficient.

(2) xy<0

No info about z: insufficient.

(1) + (2):

From (2), we know that x and y have opposite signs. Therefore, in order for the product xyz to be negative, z will have to be positive.

So, we know that z is positive and that one of x or y is positive while the other is negative. Set up a number line:

----y----0---z----x

Here, the distance between x and y is greater than the distance between x and z, and z does lie between x and y.

But here:

---y---------0--x---z

all of the information is also satisfied, and z doesn't lie between x and y.

Choose E.

Testluv wrote:

ballubalraj wrote:I still did not get it.

Could you please translate xyz < 0 or xy < 0 by taking an example.

I am not sure if I am missing anything obivious here.

By xyz<0, the original poster must mean x*y*z<0 (ie, thier product is negative)

___________

The correct answer is definitely choice E.

We are told that the distance between x and y is greater than the distance between x and z, or |x-y|>|x-z|

The question is whether z lies between x and y on the number line.

So, set up a number line before going to the statements.

(1) xyz<0


means that their product is negative. So, either all of x, y, and z are negative or else two are positive and one is negative. Certainly not enough to tell whether z lies between x and y. Insufficient.

(2) xy<0

No info about z: insufficient.

(1) + (2):

From (2), we know that x and y have opposite signs. Therefore, in order for the product xyz to be negative, z will have to be positive.

So, we know that z is positive and that one of x or y is positive while the other is negative. Set up a number line:

----y----0---z----x

Here, the distance between x and y is greater than the distance between x and z, and z does lie between x and y.

But here:

---y---------0--x---z

all of the information is also satisfied, and z doesn't lie between x and y.

Choose E.

Dada,
Great reply!! Just out of curiosity, if at all a question pops up like this, what will it be its range?? I know this is a "very vague question".But,still.....

I'd say about 640-660!

This sounds a time consuming as we need to think through lot of possiblities. Is there any simple approach for the question.

What is the source of the question?

Testluv wrote:

ballubalraj wrote:I still did not get it.

Could you please translate xyz < 0 or xy < 0 by taking an example.

I am not sure if I am missing anything obivious here.

By xyz<0, the original poster must mean x*y*z<0 (ie, thier product is negative)

___________

The correct answer is definitely choice E.

We are told that the distance between x and y is greater than the distance between x and z, or |x-y|>|x-z|

The question is whether z lies between x and y on the number line.

So, set up a number line before going to the statements.

(1) xyz<0


means that their product is negative. So, either all of x, y, and z are negative or else two are positive and one is negative. Certainly not enough to tell whether z lies between x and y. Insufficient.

(2) xy<0

No info about z: insufficient.

(1) + (2):

From (2), we know that x and y have opposite signs. Therefore, in order for the product xyz to be negative, z will have to be positive.

So, we know that z is positive and that one of x or y is positive while the other is negative. Set up a number line:

----y----0---z----x

Here, the distance between x and y is greater than the distance between x and z, and z does lie between x and y.

But here:

---y---------0--x---z

all of the information is also satisfied, and z doesn't lie between x and y.

Choose E.

Thanks Testluv!
Stupid of me..I went with C, since I assumed Y cannot be negative alone.

I thought if its XY...X has to be on the left side of Y always...why the hell did I assume it like this???

BTW I love this questions! Really made me think, calculate and analyse.


P.S. - DS questions I always tend to answer it in YES or NO, instead of finding whether the choices are sufficient or not! BIG Difference!

I love this question. I actually got E first but chose C. cos I did not believe in myself. Thanks for the explanations.

Hi, everyone! This problem took me 4:45 min's. Is it a lot for this problem?

Since the first statement tells nothing besides : 1 or all 3 variables are negative.
The second statement alone lets you know z is positive(+), so x,y are opposite signs.

therefore the order can be:
y,0,z,x
y,0,x,z
x,0,z,y
x,0,y,z
.

All of them are possible so hence, E

I have a question on this.
Though I was able to identify that Z doesn't lie between x and y but can not understand why should the answer be E.
We are able to arrive at the a conclusion based on statement 1 and 2, so should'nt it be C. We ultimately are able to find the answer.
I agree answer is "Z doesn't lie between x and y" but we certainly reached to this answer. I always get confused in this case when we reach to conclusion but the answer to question asked is "NO".
Does this mean unless we dont arrive at "Yes", question is not answered. My understanding is whether you can reply the question or not (Yes or No whatever) based on the information given.

Testluv wrote:

ballubalraj wrote:I still did not get it.

Could you please translate xyz < 0 or xy < 0 by taking an example.

I am not sure if I am missing anything obivious here.

By xyz<0, the original poster must mean x*y*z<0 (ie, thier product is negative)

___________

The correct answer is definitely choice E.

We are told that the distance between x and y is greater than the distance between x and z, or |x-y|>|x-z|

The question is whether z lies between x and y on the number line.

So, set up a number line before going to the statements.

(1) xyz<0


means that their product is negative. So, either all of x, y, and z are negative or else two are positive and one is negative. Certainly not enough to tell whether z lies between x and y. Insufficient.

(2) xy<0

No info about z: insufficient.

(1) + (2):

From (2), we know that x and y have opposite signs. Therefore, in order for the product xyz to be negative, z will have to be positive.

So, we know that z is positive and that one of x or y is positive while the other is negative. Set up a number line:

----y----0---z----x

Here, the distance between x and y is greater than the distance between x and z, and z does lie between x and y.

But here:

---y---------0--x---z

all of the information is also satisfied, and z doesn't lie between x and y.

Choose E.

Hi

We are not able to arrive at a conclusion based on statement 1 and 2 Because z can both lie between or not lie between x & y.So we cant say anything with surety or arrive at a definite answer. So cant be C.

Hope that helps.

shivaniKaushal wrote:I have a question on this.
Though I was able to identify that Z doesn't lie between x and y but can not understand why should the answer be E.
We are able to arrive at the a conclusion based on statement 1 and 2, so should'nt it be C. We ultimately are able to find the answer.
I agree answer is "Z doesn't lie between x and y" but we certainly reached to this answer. I always get confused in this case when we reach to conclusion but the answer to question asked is "NO".
Does this mean unless we dont arrive at "Yes", question is not answered. My understanding is whether you can reply the question or not (Yes or No whatever) based on the information given.

Testluv wrote:

ballubalraj wrote:I still did not get it.

Could you please translate xyz < 0 or xy < 0 by taking an example.

I am not sure if I am missing anything obivious here.

By xyz<0, the original poster must mean x*y*z<0 (ie, thier product is negative)

___________

The correct answer is definitely choice E.

We are told that the distance between x and y is greater than the distance between x and z, or |x-y|>|x-z|

The question is whether z lies between x and y on the number line.

So, set up a number line before going to the statements.

(1) xyz<0


means that their product is negative. So, either all of x, y, and z are negative or else two are positive and one is negative. Certainly not enough to tell whether z lies between x and y. Insufficient.

(2) xy<0

No info about z: insufficient.

(1) + (2):

From (2), we know that x and y have opposite signs. Therefore, in order for the product xyz to be negative, z will have to be positive.

So, we know that z is positive and that one of x or y is positive while the other is negative. Set up a number line:

----y----0---z----x

Here, the distance between x and y is greater than the distance between x and z, and z does lie between x and y.

But here:

---y---------0--x---z

all of the information is also satisfied, and z doesn't lie between x and y.

Choose E.

For those who have trouble solving this mentally,

Option 1 i.e., for x*y*z<0, consider the following possibilities and the values for x,y and z are simply assumptions
a) for x*y*z<0, either of x,y,z has to be -ve
1) x -ve, y +ve, z +ve , [x,y,z] = [-1,4,3] (z lies b/w x and y)
2) x +ve, y -ve, z +ve , [x,y,z] = [1,-4,3] (z does not lie b/w x and y)
3) x +ve, y +ve, z -ve , [x,y,z] = [1,4,-3] (z does not lie b/w x and y)
OR
b)
4) all three are -ve i.e,. x,y,z<0 , [x,y,z] = [-1,-4,-3] (z lies b/w x and y)

Since the answer oscillates between yes and no (lies and does not lie), this option is not sufficient

Option 2 i.e., for xy<0, consider the following possibilities
c) for x*y<0, either of x,y has to be -ve

i) if x<0,
5) if z>0, [x,y,z] = [-1,4,3] (z lies b/w x and y)
6) if z<0, [x,y,z] = [-1,4,-3] (z does not lie b/w x and y)
ii) if y<0,
7) if z>0, [x,y,z] = [1,-4,3] (z does not lie b/w x and y)
8) if z<0, [x,y,z] = [1,-4,-3] (z lies b/w x and y)

Again here the answer oscillates between yes and no (lies and does not lie), this option is also not sufficient

Considering both would be the subset of previous option again
if x*y<0 and x*y*z<0, z will be always >0
i) either x<0 is same as 5 above which says (z lies b/w x and y)
ii) either y<0 is same as 7 above which says (z does not lie b/w x and y)

Yes and No again. Hence E.

This looks lengthy and complex on the first time, but if you start working it out with pen and paper (or mentally), this should get solved in less than a minute.



Thanks
Krishna.