**Que:**If P, Q, & R are numbers on the number line, not necessarily in that order, is |P − R| \(\ge\) 18?

(1) |P − Q| = 80.

(2) |Q − R| = 90.

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00:00

**A**

**B**

**C**

**D**

**E**

(1) |P − Q| = 80.

(2) |Q − R| = 90.

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- [email protected] Revolution
- Elite Legendary Member
**Posts:**3991**Joined:**24 Jul 2015**Location:**Las Vegas, USA**Thanked**: 19 times**Followed by:**36 members

00:00

**A**

**B**

**C**

**D**

**E**

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 |P − R| ≥ 18.

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 (2) tells us that |Q − R| = 90 => Q – R = ± 90

Adding both the equations,

=> P – Q + Q – R = ± 80 ± 90

=> 80 + 90 = 170 OR 80 – 90 = -10 OR -80 + 90 = 10 OR -80-90 = -170

=> P – R = ± 170 OR ± 10

=> |P − R| = 170 OR 10

=> If |P − R| = 170 ≥ 13 – YES

If |P − R| = 10 ≥ 13 – NO

The answer is not a unique YES or a NO; both conditions combined are not sufficient according to Common Mistake Type 1 which states that the answer should be a unique YES or a NO.

Therefore, E is the correct answer.

Answer: E

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