Data Sufficiency

[Math Revolution GMAT math practice question]

Is a > b - c?

1) |c-b| < a
2) a, b, and c are the lengths of the 3 sides of a triangle.

Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

Is a > b - c?

1) |c-b| < a
2) a, b, and c are the lengths of the 3 sides of a triangle.

$$a\,\,\mathop > \limits^? \,\,b - c$$
$$\left( 1 \right)\,\,\,a\,\, > \,\,\left| {c - b} \right|\,\,\, = \,\,\,\left| {b - c} \right|\,\,\,\, \ge \,\,\,b - c\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,$$
$$\left( 2 \right)\,\, \Rightarrow \,\,\left( 1 \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,$$

The correct answer is therefore (D).


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Condition 1) is sufficient since it yields b - c ≤ | b - c | = | c - b | < a.

Condition 2)
Since the sum of the lengths of two sides of a triangle is greater than the length of the third side, we must have a + c > b. Thus, condition 2) is sufficient.

Therefore, D is the answer.
Answer: D

FYI, Tip 1) of the VA method states that D is most likely to be the answer if conditions 1) and 2) provide the same information.