Inequality from GMAT Prep

[tallynik]

if y>= 0 , what is the value of x?

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

OA c

Please explain how to solve?

[lunarpower]

if y>= 0 , what is the value of x?

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

OA c

Please explain how to solve?

first comment:
it's not that hard to type "<" and ">". just type the normal "<" and ">", but use underline tags.

by the way, that's the wrong OA.

--

statement (1)

we don't know what y is. therefore, we have that |x - 3| is greater than some positive value.
there are all kinds of degrees of freedom here. not only do we not know the value of y, but, even if we did, x - 3 could still be anything whose absolute value equals or exceeds that number.
for instance, if y = 10, then x - 3 could be anything < -10 or > 10. therefore, x could be anything < -7 or > 13.
and that's just for one value of y.
very insufficient.



statement (2)

|x - 3| is an absolute value. the smallest possible value of an absolute-value expression is 0.
since we are given y > 0, it follows that -y is a non-positive expression. therefore, the only way this inequality is possible is if y = 0, because |x - 3| can't be < a negative number.
therefore, |x - 3| < 0
which means |x - 3| = 0 (because negative values are out of the question)
which means x - 3 = 0
which means x = 3
sufficient.

OA should be (b).

[tallynik]

Thanks Ron.

My mistake OA is actually B.

[aj5105]

Ron,

For Statement # 1:

|x-3|> 0 (Considering y=0)

Now, LHS has to be positive.

(x-3)> 0

x> 3

Hence, not sufficient.

Am i right here?

[maihuna]

if y>= 0 , what is the value of x?

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

1. using y>=0 |x-3| >=0
for |x-3| = 0 => x=3
for |x-3| >0 => x-3 >0 or x>3
x-3 <-0 or x<3

2. Mod of a number cannt be negative: |x-3| = 0 or x = 3

Ans is B