Just a caveat - you need to be careful here. You aren't using all of the information in the question: we know the distance between x and y is greater than the distance between x and z. So several of the cases you've considered are actually not applicable. Fortunately here it doesn't affect the answer, but in general, in DS, if you are not using all of your information, you'll very often think a Statement is insufficient when it actually is sufficient. So if you are going to pick numbers in DS, do always confirm that you've accounted for all of the information given.krishnakumar.ks wrote: 3) x +ve, y +ve, z -ve , [x,y,z] = [1,4,-3] (z does not lie b/w x and y)
points on a number line.
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1. xyz < 0 means odd number of digits are negative in this case 1 or 3. No real information and hence not sufficient.
2. xy<0 means x and y are on opposite side of the number line . Hence x<0 & y> 0 or x>0 and y<0. This information is also not sufficient.
With 1 & 2 we have z > 0 as out of x and y only 1 is negative.
But we still don't know out of x,y which one is negative. So lets check both the options.
let x > 0 & y < 0 . In this case as z could be on either side of x and would still satisfy the condition that |x-z| < |x-y|. As this option itself yields 2 solution there is no need to check for other condition answer should be E.
2. xy<0 means x and y are on opposite side of the number line . Hence x<0 & y> 0 or x>0 and y<0. This information is also not sufficient.
With 1 & 2 we have z > 0 as out of x and y only 1 is negative.
But we still don't know out of x,y which one is negative. So lets check both the options.
let x > 0 & y < 0 . In this case as z could be on either side of x and would still satisfy the condition that |x-z| < |x-y|. As this option itself yields 2 solution there is no need to check for other condition answer should be E.
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we can rephrase the question stem that x,y,and z must be positive or 2 of them must be negativeashforgmat wrote: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]
in statement o1, 1 or 3 variables could be negative so insufficient
in statement 02, here 1 variable must be negative, so insufficient
combined 1 or 3 variables could be negative so insufficient
correct me if my reasoning is wrong
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Hey I arrived to (E). Just wanted to post the way I solved it.
|x - y| > |x - z|; Is x < z < y ? OR y < z < x ?
Find the positive ABS:
x - y > x - z
-y > -z
y < z
STMT 1: Insufficient
x y z < 0
+ + - < 0
+ - + < 0
- + + < 0
STMT 2: Insufficient
x y < 0
+ - < 0
- + < 0
Combined 1 & 2, only these two scenerios are posible:
x y z < 0
+ - + < 0
- + + < 0
But from the positive ABS we know that y < z, so y must be negative and z positive so the only possible sceneario is:
x y z < 0
+ - + < 0
So it turns out that y < z ? x. If we look at |x - y| > |x - z| the value of x could equal z, but there's no way to confirm that.
So picked (E)!!!
|x - y| > |x - z|; Is x < z < y ? OR y < z < x ?
Find the positive ABS:
x - y > x - z
-y > -z
y < z
STMT 1: Insufficient
x y z < 0
+ + - < 0
+ - + < 0
- + + < 0
STMT 2: Insufficient
x y < 0
+ - < 0
- + < 0
Combined 1 & 2, only these two scenerios are posible:
x y z < 0
+ - + < 0
- + + < 0
But from the positive ABS we know that y < z, so y must be negative and z positive so the only possible sceneario is:
x y z < 0
+ - + < 0
So it turns out that y < z ? x. If we look at |x - y| > |x - z| the value of x could equal z, but there's no way to confirm that.
So picked (E)!!!
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Just saw so many lengthy replies on the previous page.
We should simply take few values and solve this question
It can be done in 1:30 mins approx
From statement 1 we know that either one out of x,y,or z is negative or all three are negative
Hence we cannot find out the answer
From second statement we cannot find put any information about z
Hence, insufficient
Even after using both the statements together we cannot find the answer
Hence, E
We should simply take few values and solve this question
It can be done in 1:30 mins approx
From statement 1 we know that either one out of x,y,or z is negative or all three are negative
Hence we cannot find out the answer
From second statement we cannot find put any information about z
Hence, insufficient
Even after using both the statements together we cannot find the answer
Hence, E
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E:
(1) either all three should be negative or one of them:
x=-2
y=-4
z=-3 or -1 => Insuficient
(2) either x or y should be negative. z can be before and after x
(1+2)
tells that z is positive but no restrictions for z to be on the line between x and y
(1) either all three should be negative or one of them:
x=-2
y=-4
z=-3 or -1 => Insuficient
(2) either x or y should be negative. z can be before and after x
(1+2)
tells that z is positive but no restrictions for z to be on the line between x and y
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I don't know, I think it's about as hard as absolute value and inequalities can get, IMO. 700+. Seriously, most people it would take 5 minutes to figure out, or most would guess.Testluv wrote:I'd say about 640-660!
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Pasting the question again --prashant misra wrote:i am still not able o get this question how the answer choice E is correct
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
SOLUTION: --
statement 1--
product of xyz is less than zero
this implies either 1 of them or all of them are negative
Suppose only 1 of them is negative (say z)
let's choose values -- Z= -1
X= 0
Y = 5
this fulfills the condition ..
Distance between XY (5) is greater than distance between XZ (1)
Here Z is not present between X and Y.
Now suppose all of them are negative
X= -1
Y = -5
z= -2
In this case as well the condition given in the question is fulfilled.
But, here Z lies betwen X and Y.
Hence Statement 1 is INSUFFICIENT
Statement 2 --
Product of XY is less than zero
nothing is given about Z .. So Z can be anything (NEGATIVE or POSITIVE) -- Hence, we cannot conclude anything about Z's position.
Hence Statement 2 is INSUFFICIENT
Now let's combine the 2 conditions..
we have XY <0 [mean either X or Y is NEGATIVE) and xyz < 0 [ Since we know that either X or Y is negative and the whole product is also negative , Z is POSITIVE)
(I hope this point is clear to you)
let's assign some values
X = -1
Y = 4
Z = 2
This satisfies the condition [ distance between XY (5) is greater than distance between XZ (3)] -- here Z is between X and Y
now say Z is negative
X = 1
Y = 10
Z = -2
This also Satisfies the condition [ distance between XY (9) is greater than distance between XZ (3)] -- Here Z is NOT between X and Y
Therefore, even the two statments combined cannot give us any unique answer.
CORRECT ANSWER = E
Here is another solution:saketk wrote:Pasting the question again --prashant misra wrote:i am still not able o get this question how the answer choice E is correct
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
Plug in numbers:
a. xyz<0
x=-1, y=0, z=1 - False
x=1, y=0, z=-1 - False
x=1, y=-1, z=0 - True
Not sufficient - No A&D
b.xy<0
No info on Z, so we cannot conclude since the sign of z (+ or -) can decide the result.- No B
Now, C or E?
C? - Together xyz<0 and xy<0, now we know Z is positive and greater than zero
Again plugin the first set with positive z value alone
x=-1, y=0, z=1 - False
x=2, y=0, z=1 - True
Still both results are possible, so insufficient.
So choose E. Hope it helps. It's about two minutes to plugin and find out.