Data Sufficiency

[GMAT math practice question]

$$If\ x\ne2y,\ then\ \sqrt{\frac{x-3y}{x-2y}}=?$$

$$\left(1\right)\ \frac{y}{x}=\frac{y}{1}$$
$$\left(2\right)\ \frac{y}{x}=\frac{2}{1}$$

=>
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.

When a question asks for a ratio, if one condition includes a ratio and the other condition just gives a number, the condition including the ratio is most likely to be sufficient. Since √x-3y/√x-2y = 1-3(yx)1-2(yx) , knowing the value y/x, allows us to determine the value of √x-3y/√x-2y. This tells us that B is most likely to be the answer to this question.

Condition 1)
y/x= y/1 is equivalent to y = xy, that is, y(x-1) = 0.
So, y = 0 or x = 1.
If y = 0 and x = 2, then √x-3y/√x-2y =1.
If x = 1 and y = 1/3, then √x-3y/√x-2y =0.
Since we don't have a unique solution, condition 1) is not sufficient.

Condition 2)
y/x= 2/1 is equivalent to y = 2x.
√x-3y/√x-2y = √x-6x/√x-4x = √-5x/√-3x=√5/√3
Since we have a unique solution, condition 2) is sufficient.

Therefore, B is the answer

Answer: B,