Solution: To save time and improve accuracy on DS question 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.
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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 x divisible by 10’ when \(x^2+y^2\) + 2xy = 16.
Follow the second and the third step: From the original condition, we have 2 variables (x and y) and 1 equation (\(x^2+y^2\) + 2xy = 16). To match the number of variables with the number of equations, we need 1 more equation. Since conditions (1) and (2) will provide 2 equations, 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 \(x^2+y^2\) = 8, if we substitute this equation into \(x^2+y^2\) + 2xy = 16, then we get 8 + 2xy = 16 => 2xy = 8, or xy = 4.
Also, from \(\left(x\ +\ y\right)^2\) = \(x^2+y^2\) + 2xy = 8 + 8 = 16, we get x + y = ±4, and since xy = 4, we get x=y=2 or x = y = -2. In both cases, x = 2 or -2 which are not divisible by 10, we get no as an answer.
The answer is unique, no, the condition is sufficient according to Common Mistake Type 1 which states that the answer should be unique Yes or a NO.
Condition (2) tells us that y = 2, from which we get \(x^2+y^2\) + 2xy = 16 => \(x^2 + 2^2\)+ 2x(2)=16 => \(x^2\) + 4 + 4x =16 => \(x^2\) + 4x - 12 = 0.
If we factorize that equation we get (x+6)(x-2)=0, or x=-6 or 2. In both cases, x=-6 or 2 which are not divisible by 10, we get no as an answer.
The answer is unique, no, the condition is sufficient according to Common Mistake Type 1 which states that the answer should be unique Yes or a NO.
According to Tip 1, if the value of the condition (1) is equal to the value of condition (2), we get D as an answer.
Each condition alone is sufficient
D is the correct answer.
Answer: D
