Apex231 wrote:
if y >= 0, What is the value of x?
1) |x-3| >= y
2) |x-3| <= -y
I solved this way -
1) |x-3| >= y
x -3 >=y
x >= y + 3
or
3 - x >=y
x <= 3 - y
so y + 3 <= x <= 3 - y
if y is positive then the above condition is not possible as sum of two positives cant be less than difference of two positives. the other possibility is that y is zero and x = 3. hence sufficient?
2) |x-3| <= -y
x -3 <= -y
x <=3-y
or
3-x <=-y
x>=y+3
so 3-y >= x >= y+3, again since y >=0 , only possibility is that y = 0. hence x = 3. sufficient.
But the OA is different.
If y\geq{0}, what is the value of [b]x?[/b]
(1)
|x - 3|\geq{y}. As given that
y is non negative value then
|x - 3| is more than (or equal to) some non negative value, (we could say the same ourselves as absolute value in our case (
|x - 3|) is never negative). So we can not determine single numerical value of
x. Not sufficient.
Or another way: to check
|x - 3|\geq{y}\geq{0} is sufficient or not just plug numbers:
A.
x=5,
y=1>0, and B.
x=8,
y=2>0: you'll see that both fits in
|x - 3|>=y,
y\geq{0}.
Or another way:|x - 3|\geq{y} means that:
x - 3\geq{y}\geq{0} when
x-3>0 -->
x>3OR (not and)
-x+3\geq{y}\geq{0} when
x-3<0 -->
x<3Generally speaking
|x - 3|\geq{y}\geq{0} means that
|x - 3|, an absolute value, is not negative. So, there's no way you'll get a unique value for
x. INSUFFICIENT.
(2)
|x-3|\leq{-y}. Now, as
|x-3| is never negative (
0\leq{|x-3|}) then
0\leq{-y} -->
y\leq{0} BUT stem says that
y\geq{0} thus
y=0.
|x-3|\leq{0} -->
|x-3|=0=y (as absolute value, in our case |x-3|, can not be less than zero) -->
x-3=0 -->
x=3. SUFFICIENT
In other words:-y is zero or less, and the absolute value (
|x-3|) must be at zero or below this value. But absolute value (in this case
|x-3|) can not be less than zero, so it must be
0.
Answer: B.
There is a following problem with your solution:
If
x<3 -->
-(x-3)\geq{y} -->
3-y\geq{x};
OR:If
x\geq{3} -->
(x-3)\geq{y} -->
x\geq{3+y};
But you can not combine these inequalities and write:
3+y\leq{x}\leq{3-y} as they are OR scenarios not AND scenarios (meaning that depending on the value of x we'll have either the first one or the second one).
Also discussed here:
if-y-geq-0-what-is-the-value-of-x-1-x-3-geq-y-91640.htmlHope it helps..
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40% (01:56) correct
