Bunuel wrote:

If xy = z, what is the value of y ?

(1) x = 3z

(2) x > 1

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

There are 3 variable and 1 equation. Thus C could be the answer most likely.

Condition 1)

Since \(x = 3z\) and \(xy = z\), we have \(3zy = z\) or \(z(3y-1) = 0\).

Then \(z = 0\) or \(y = 1/3\)

Thus we have solutions \(y = 1\), \(z = 1\) and \(y = 1/3\), \(z = 1\)

The answers are not unique. This condition alone is not sufficient.

Condition 2)

Since \(x > 1\) and \(y = z/x\), we can't identify the value of \(y\).

This condifition alone is not sufficient, either.

Condition 1) & 2)

Since \(x = 3z\) and \(xy = z\), we have \(3zy = z\) or \(z(3y-1) = 0\).

\(z = 0\) or \(y = 1/3\)

However, \(z\) cannot be zero since \(x = 3z\) and \(x > 1\).

Thus \(y = 1/3\).

Both conditions together are sufficient.

Therefore, C is the answer as expected.

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