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 the value of x.
Follow the second and the third step: From the original condition, we have 1 variable (x). To match the number of variables with the number of equations, we need 1 equation. Since conditions (1) and (2) will provide 1 equation each, D would most likely be the answer.
Recall 3- Principles and Choose D as the most likely answer. Let’s look at each condition separately.
Condition (1) tells us that \(3\left(x+y\right)=x+3y\).
=> 3x + 3y = x + 3y
=> 3x - x = 0
=> x = 0
The answer is unique and condition (1) alone is sufficient according to Common Mistake Type 2 which states that the answer should be unique.
Condition (2) tells us that \(x^2+y^2=\left(x+y\right)^2\).
=> \(x^2+y^2=\left(x+y\right)^2\)
=> \(x^2+y^2=x^2+y^2+2xy\)
=> 2xy = 0
=> xy = 0
We don’t have a value of ‘y’ and hence we cannot find the value of ‘x’.
The answer is not unique and condition (2) alone is not sufficient according to Common Mistake Type 2 which states that the answer should be unique.
Condition (1) alone is sufficient.
Therefore, A is the correct answer.
Answer: A
