Data Sufficiency

Que: If ‘P, Q, and R’ are points on the number line, what is the distance between Q and R?

(1) The points P and Q are 20 units apart.
(2) The points P and R’ are 25 units apart.

Solution: To save time and improve accuracy on DS questions in GMAT, learn, and apply 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 ‘distance between Q and R’ when ‘P, Q and R’ are on a number line’.

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 combined together.

Condition (1) tells us that the points P and Q are 20 units apart.

Condition (2) tells us that the points P and R are 25 units apart.

=> If the points are as: P_____Q____R, then the distance between Q and R is 25 – 20 = 5
=> But if the points are as: Q_____P____R, then the distance between Q and R is 25 + 20 = 45

The answer is not unique and both conditions combined together are not sufficient according to Common Mistake Type 2 which states that the answer should be a unique value.

Both conditions combined together are not sufficient

E is the correct answer.

Answer: E