GMAT PREP DS , INEQUALITY

Question

INEQUALITY.JPG

Twoone · Answer

I am getting E.

In both statement, I am getting multiple values of X even after combining both too.
 So both are not sufficient.

scthakur · Answer

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.

bigtreezl · Answer

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

vishalgc · Answer

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

amitdgr · Answer

x cant be zero.
if x is zero then -3 >= 0 which is not possible.

spriya · Answer

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

domleon · Answer

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

amitdgr · Answer

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.

domleon · Answer

thanks amitdgr!!

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

cheers

JohnLewis1980 · Answer

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

yezz · Answer

Text book answer +2 for u :lol:

rampuria · Answer

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.

Why is my answer not correct. Please can someone help me.

madsun · Answer

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.

klb15 · Answer

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.

GMAT PREP DS , INEQUALITY

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