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# GMAT PREP DS , INEQUALITY

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Senior Manager
Joined: 02 Dec 2007
Posts: 433
GMAT PREP DS , INEQUALITY [#permalink]

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26 Sep 2008, 06:05
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Intern
Joined: 02 Sep 2008
Posts: 45
Re: GMAT PREP DS , INEQUALITY [#permalink]

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26 Sep 2008, 06:47
I am getting E.

In both statement, I am getting multiple values of X even after combining both too.
So both are not sufficient.
SVP
Joined: 17 Jun 2008
Posts: 1507
Re: GMAT PREP DS , INEQUALITY [#permalink]

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28 Sep 2008, 05:18
C for me (took a while to figure out the problem...more than 5 mins).

since |x-3| is greater than or equal to y and also less than and equal to -y and since y is greater than or equal to 0, only y = 0 will satisfy both the statements. Now, if y = 0 then only x = 3 will satisfy both the statements.
Director
Joined: 23 May 2008
Posts: 762
Re: GMAT PREP DS , INEQUALITY [#permalink]

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28 Sep 2008, 13:12
y>= 0

1) l x-3 l >= y
x-3 is equal or greater than 0, x could be anything from 3 up
insuff

2) l x-3 l <= -y
so - l x-3 l >= y

x has to be 0 since y>=0
suff

i go with B
Manager
Joined: 09 Oct 2008
Posts: 93
Re: GMAT PREP DS , INEQUALITY [#permalink]

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18 Oct 2008, 23:46
IMO B:

2) l x-3 l <= -y
so - l x-3 l >= y => -ve >= +ve ..this is possible only when y = 0 so |x-3| =0 and x =3..

What is OA...its good one
VP
Joined: 30 Jun 2008
Posts: 1022
Re: GMAT PREP DS , INEQUALITY [#permalink]

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19 Oct 2008, 00:13
bigtreezl wrote:
y>= 0

1) l x-3 l >= y
x-3 is equal or greater than 0, x could be anything from 3 up
insuff

2) l x-3 l <= -y
so - l x-3 l >= y

x has to be 0 since y>=0
suff

i go with B

x cant be zero.
if x is zero then -3 >= 0 which is not possible.
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VP
Joined: 17 Jun 2008
Posts: 1329
Re: GMAT PREP DS , INEQUALITY [#permalink]

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19 Oct 2008, 00:14
IMO B
given : y>=0
Question x=?

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

considr 1) when y>=0 |x-3| is always +ve hence >=y

for all x ,hence INSUFFI

2) |x-3|is postive hence <=-y is only vali for y=0

hence x-3=0 or -x+3=0 =>x=3 only unique soln of x => SUFFi

IMO B
Good question
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cheers
Its Now Or Never

Manager
Joined: 14 Jun 2007
Posts: 158
Location: Vienna, Austria
Re: GMAT PREP DS , INEQUALITY [#permalink]

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19 Oct 2008, 00:52
guys,

can someone tell me why 2) |x-3|is postive hence <=-y is only vali for y=0 ??

what´s the reason for Y being 0??

thanks
VP
Joined: 30 Jun 2008
Posts: 1022
Re: GMAT PREP DS , INEQUALITY [#permalink]

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19 Oct 2008, 01:13
domleon wrote:
guys,

can someone tell me why 2) |x-3|is postive hence <=-y is only vali for y=0 ??

what´s the reason for Y being 0??

thanks

mod of |any variable| is always positive.

Now if given |x-3| <= -(y) ---- where y is always 0 or positive

method 1 )

we know |x-3| cant be negative. and we know y cant be negative either to make -(y) positive.

The only possibility the above equation will hold true is y=0.

method 2)

we know |anything| is always >=0.

what if -(y) is negative ---- The equation does not hold good .. a positive (|x-3|) cannot be less than negative
what if -(y) is positive ----- This cant be true, for -(y) to be positive y has to be negative, but we have been given y>=0
what if -(y) is zero ---- Yes !! This is possible. |something| can be zero.
_________________

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Manager
Joined: 14 Jun 2007
Posts: 158
Location: Vienna, Austria
Re: GMAT PREP DS , INEQUALITY [#permalink]

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19 Oct 2008, 02:03
thanks amitdgr!!

i really aprpeciate the that you´ve take you the time to type the comprehensive explaintion into the forum!

cheers
Senior Manager
Joined: 21 Apr 2008
Posts: 479
Schools: Kellogg, MIT, Michigan, Berkeley, Marshall, Mellon
Re: GMAT PREP DS , INEQUALITY [#permalink]

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19 Oct 2008, 12:00
Hi guys,

IMO: B

1 |x-3|>=3 for me, this statement does not help to limit the range of x (the absolute value function is always >=0, like y). Therefore, becasue we don't know y, x can be any integer. Not suff.

2 for me it's easier to rewrite the eq as -|x-3|>=y. Because it's given that y>=0, the only possible value for x that satisfies the eq is x=3

OA?

Cheers
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Retired Moderator
Joined: 05 Jul 2006
Posts: 1741
Re: GMAT PREP DS , INEQUALITY [#permalink]

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19 Oct 2008, 13:34
amitdgr wrote:
domleon wrote:
guys,

can someone tell me why 2) |x-3|is postive hence <=-y is only vali for y=0 ??

what´s the reason for Y being 0??

thanks

mod of |any variable| is always positive.

Now if given |x-3| <= -(y) ---- where y is always 0 or positive

method 1 )

we know |x-3| cant be negative. and we know y cant be negative either to make -(y) positive.

The only possibility the above equation will hold true is y=0.

method 2)

we know |anything| is always >=0.

what if -(y) is negative ---- The equation does not hold good .. a positive (|x-3|) cannot be less than negative
what if -(y) is positive ----- This cant be true, for -(y) to be positive y has to be negative, but we have been given y>=0
what if -(y) is zero ---- Yes !! This is possible. |something| can be zero.

Text book answer +2 for u
Manager
Joined: 04 Sep 2008
Posts: 239
Location: Kolkata
Schools: La Martiniere for Boys
Re: GMAT PREP DS , INEQUALITY [#permalink]

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19 Oct 2008, 23:44
Please consider my approach below. Where have i gone wrong?

y =< -|x-3|

since 0 =< y, 0 must also be =< -|x-3|

i.e. |x-3| =< 0

which gives us the solution x>= 3 and x =< 3

Hence not solvable.

_________________

Thanks
rampuria

Intern
Joined: 15 Apr 2008
Posts: 38
Re: GMAT PREP DS , INEQUALITY [#permalink]

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20 Oct 2008, 23:06
IMO B.

From (1) -> x-3<= -y or x-3>=y not suf.

From (2) -> y<= x-3<=-y
But y>=0 so y must be 0 -> x-3=0 -> x=3 suf.

B it is.
Manager
Joined: 21 May 2008
Posts: 83
Re: GMAT PREP DS , INEQUALITY [#permalink]

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21 Oct 2008, 01:58
Since y >= 0,
(1) Many values of X possible for equation to hold => Insuff
(2) Since |x-3| >= 0, for equation to hold, y must be 0. Hence unique value for X => Suff.

Ans is B.
Re: GMAT PREP DS , INEQUALITY   [#permalink] 21 Oct 2008, 01:58
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