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# If y is greater than or equal to 0, what is the value of x?

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Manager
Joined: 07 Sep 2007
Posts: 80
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If y is greater than or equal to 0, what is the value of x? [#permalink]  08 Sep 2007, 11:58
If y is greater than or equal to 0, what is the value of x?

(1) |x-3| >= y
(2) |x-3| <= -y
VP
Joined: 10 Jun 2007
Posts: 1463
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Kudos [?]: 143 [0], given: 0

Re: absolute value [#permalink]  08 Sep 2007, 13:16
A.Haung wrote:
If y is greater than or equal to 0, what is the value of x?

(1) |x-3| >= y
(2) |x-3| <= -y

I get B

Given: y>=0

(1) |x-3| >= y
Use the given: 0 >= -y
|x-3| >= 0
This means that x can be pretty much anything.
INSUFFICIENT

(2) |x-3| <= -y
Use the given: 0 <= y
Do the same thing...get
|x-3| <= 0
Since |x-3| is always positive, the only possible solution for this is:
|x-3| = 0
x=3
SUFFICIENT
Director
Joined: 03 May 2007
Posts: 888
Schools: University of Chicago, Wharton School
Followers: 6

Kudos [?]: 75 [0], given: 7

Re: absolute value [#permalink]  27 Sep 2007, 21:26
A.Haung wrote:
If y is greater than or equal to 0, what is the value of x?

(1) |x-3| >= y
(2) |x-3| <= -y

B. since Y cannot be -ve, so lx-3l must be 0.
CEO
Joined: 29 Mar 2007
Posts: 2585
Followers: 17

Kudos [?]: 244 [0], given: 0

Re: absolute value [#permalink]  27 Sep 2007, 22:19
[quote="A.Haung"]If y is greater than or equal to 0, what is the value of x?

(1) |x-3| >= y
(2) |x-3| <y>=0 or -x+3>=0

What am I missing I get D???

S1:

x-3>=0 or -x+3>=0

x>=3 3>=x So 3=<x<=3

S2:

x-3<=0 or -x+3<=0

x<=3 or 3<=x 3<=x<=3
Current Student
Joined: 28 Dec 2004
Posts: 3387
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 14

Kudos [?]: 186 [0], given: 2

I get E cause we dont know the exact value of y...

suppose if Y=1 ?

(1) |x-3| >= y
(2) |x-3| <= -y

(1)
if x>3

x-3 >0; x>3 but x could be 4 if y=1..x could be 5 if y=2

if x<3

-(x-3) >0
-x+3>0 -x>-3 which means x<3 if y=0 x<3 if y=1 x<2 if y=2 x<1

(2)
x>3
x-3 <-0 x< 3 if y=0, x<2 if y=1 x<1

if x<3
-(x-3) <-0
-x+3 <-0
-x<-3 x>3 if y=0 if y=1 x>4 if y=2 x>5

Insuff..

I get E ..what am i doing wrong?
Manager
Joined: 18 Apr 2007
Posts: 121
Followers: 1

Kudos [?]: 5 [0], given: 0

I get D

[1] |x-3| >= y --> from this we can deivse two equations and can solve each for x:
1) x-3 >= y --> x >= y+3
2) 3-x >= y --> -x >= y-3 --> x <= 3-y

Putting both together we get: y+3 <= x <3>= 0 we can start plugging in numbers.
For y=0 we get 3<=x<=3 and therefore x = 3
For y=1 we get 4<=x<=2 and obviously this cannot work
Therefore, the only way the above inequality works is if y=0 and x=3
SUFFICIENT

[2] |x-3|<y> we can solve this the same way as [1] and get the same inequality: y+3 <= x <= 3-y
Therefore, SUFFICIENT
Intern
Joined: 28 Nov 2005
Posts: 33
Followers: 0

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

I get D.

1)
X>=Y+3
X<=-Y+3
Y>=0
=> Only one solution : (X;Y) = (3;0)
=> SUFF

2)
X<=-Y+3
X>=Y+3
Y>=0
=> Only one solution : (X;Y) = (3;0)
=> SUFF

Therefore ans D !
What's the OA ?
Director
Joined: 17 Sep 2005
Posts: 927
Followers: 3

Kudos [?]: 41 [0], given: 0

Re: absolute value [#permalink]  28 Sep 2007, 13:38
A.Haung wrote:
If y is greater than or equal to 0, what is the value of x?

(1) |x-3| >= y
(2) |x-3| <= -y

ST1:

|x-3| >= y

Given that , y>=0

=> |x-3| >= y >= 0
=> |x-3| >=0

So x can have many values hene NOT SUFF.

ST2:

|x-3| <= -y

Given that y>=0
Multiple both sides by (-1), we get,

-y<=0

Not put the above value in ST2, we get,

|x-3| <= -y <=0

=> |x-3| <=0
Absolute value can not be -ve so x has to 3 to make '|x-3|' zero.

Hence B is SUFF.

- Brajesh
Re: absolute value   [#permalink] 28 Sep 2007, 13:38
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