Data Sufficiency

Que: If A, B, & C are numbers on the number line, not necessarily in that order, is \(|A−C|\ge10\)?

(1) |A − B| = 60
(2) |B − C| = 50

Solution: To save time and improve accuracy on DS questions in GMAT, learn and apply the Variable Approach.

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.

Visit https://www.mathrevolution.com/gmat/lesson for details.

Now we will solve this DS question using the Variable Approach.

Let’s apply the 3 steps suggested previously.

Follow the first step of the Variable Approach by modifying and rechecking the original condition and the question.

We have to find is |A − C| ≥ 10.

Follow the second and the third step: From the original condition, we have 3 variables (P, Q, and R). To match the number of variables with the number of equations, we need 3 equations. Since conditions (1) and (2) will provide 1 equation each, E would most likely be the answer.

Recall 3- Principles and Choose E as the most likely answer. Let’s look at both conditions together.

Condition (1) tells us that |A − B| = 60 => A – B = ± 60

Condition (2) tells us that |B − C| = 50 => B – C = ± 50

Adding both the equations,

=> A – B + B – C = ± 60 ± 50

=> 60 + 50 = 110 OR 60 – 50 = 10 OR -60 + 50 = -10 OR -60-50 = -110

=> A – C = ± 110 OR ± 10

=> |A − C| = 110 OR 10

=> Is |A − C| ≥ 10 – YES

The answer is unique, YES, and both conditions combined together are sufficient according to Common Mistake Type 1 which states that the answer should be unique Yes or a NO.

Both conditions combined together are sufficient.

Therefore, C is the correct answer.

Answer: C