If y>=0 , what is the value of x?
1) |x-3|>=y
2) |x-3|<=-y
A) Statement 1) alone is sufficient
B) Statement 2) alone is sufficient
C) Statements 1) and 2) together are sufficient
D) Each statement alone is sufficient
E) Statement 1) and 2) together are not sufficient
the excercise book I'm using gives B) as correct answer, could you explain the reasoning behind it?
thank you
We're given that y is some fixed number >= 0.
The first statement |x-3|>=y tells us that x >= 3 + y or x <= 3 - y. That is, this statement is not sufficient for a unique solution - if you give me any y, I can give you infinitely many x's that satisfy the statement.
The second statement is stronger than this, it forces y = 0, which forces x = 3. That is, it is sufficient to give a unique solution (note, this one of the many possible solutions for the first statement also).
So far then, B) is 'stronger' than A). This then tells us that we can disregard A). Thus, C) gives more information than we need, so while it is sufficient, it contains redundant information.
D) is clearly out, by what we found above.
E) is nonsense, since B) forces a unique solution.
How is that?