Forget the conventional way to solve DS questions.
We will solve this DS question using the variable approach.DS question with 3 variables and 1 Equation: Let the original condition in a DS question contain 3 variables and 1 Equation. Now, we know that each condition (1) and (2) would usually give us an equation each and we need 2 equations to match the numbers of variables and equations in the original condition, therefore the most likely answer is C.
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Let’s apply the 3 steps suggested previously. [Watch lessons on our website to master these 3 steps]
Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question.We have to find value of 'z' .=> \(x^2z - 4xy + y = 0\)
Second and the third step of Variable Approach: From the original condition, we have 3 variables (x, y, and z) + 1 equation (x^2z - 4xy + y = 0) .To match the number of variables with the number of equations, we need 2 equations. Since conditions (1) and (2) will provide 1 equation each, C would most likely be the answer.Let's take both conditions together.From condition(1), z = 32x and from the condition(2) z = 4y
=> z = 32x = 4y
=> 4y = 32x or y = 8x
=> \(x^2 * 32x - 4x(8x) + (8x) = 0\)
=> \(32x^3 - 32x^2 + 8x = 0 \)
=> \(8x (4x^2 - 4x + 1) = 0\)
=> \(8x (2x - 1)^2 = 0\)
=> 'x' is not equal to zero and hence, \((2x - 1)^2 = 0\)
=> \((2x - 1)^2 = 0\) or x = \(\frac{1}{2}\).
Therefore, z = 32x = 32 * \(\frac{1}{2}\) = 16
Since the answer is unique, both conditions together are sufficient by CMT 2.So, C is the correct answer.Answer: C _________________