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This problem trains for: SAT-I, AMC-8, GMAT.

Let a, b, c be real numbers such that:

equation

and

equation

Which of the following statements cannot be true?

a is positive, c is negative. Therefore, the sum of these numbers can be anything: positive, negative or zero. I can be true.

Same with II, the sum of a and c can be in any relation to b.

However, the difference a-c is strictly positive and cannot be smaller than or equal to b, even if b=0.

b+c is strictly negative and cannot be equal to a, which is positive.