Question

If $a, b, c$ are integers, is $(a-b+c)>(a+b-c)$?
I. $b$ is negative.
II. $c$ is positive.

• A. The question cannot be answered even with the help of both the statements taken together.
• B. The question can be answered by any one of the statements
• C. Each statement alone is sufficient to answer the question, but not the other one.
• D. Both statements I and II together are needed to answer the question

Hint:

When comparing two expressions, reduce them to a single term; see what extra data is needed to fix its sign.

Answer 1

The Correct Option is D

We compare: $(a-b+c) - (a+b-c) = -b + c - b + c = -2b + 2c = 2(c-b)$.
I: $b$ is negative $\Rightarrow$ $-b$ positive, but without $c$ we cannot decide sign of $c-b$.
II: $c$ positive, but without $b$ we cannot decide sign of $c-b$.
Together: $c$ positive and $b$ negative $\Rightarrow$ $c-b$ definitely positive $\Rightarrow$ LHS $>$ RHS. %Quick tip