tallynik wrote: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.
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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).
Ron has been teaching various standardized tests for 20 years.
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