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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.

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.
_________________

"You have to find it. No one else can find it for you." - Bjorn Borg

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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My experience in my second attempt http://gmatclub.com/forum/p544312#p544312 My experience in my third attempt http://gmatclub.com/forum/630-q-47-v-28-engineer-non-native-speaker-my-experience-78215.html#p588275

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.

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.