Once you attempt the question then PrepInsta explanation will be displayed.

##### Evaluate Statement (1) ALONE: (y - 3)(x - 4) = 0

If product of the two terms (y - 3) and (x - 4) is 0, then at least one of the two terms equals 0.

(y - 3) = 0 or (x - 4) = 0 or both (y - 3) and (x - 4) equal 0.

i.e., either y = 3 or x = 4 or that both y = 3 and x = 4.

If x = 4, y could take any value. The value of 'y' could be 3 or it could be some other value and the product will still be a 0.

Example: x = 4 and y = 5. The equation holds good. y ≠ 3.

Counter example: x = 4 and y = 3. The equation holds good. y = 3

We CANNOT determine whether 'y' is 3 from this statement.

**Statement 1 ALONE is NOT sufficient.**
Eliminate choices A and D. Choices narrow down to B, C or E.

##### Step 3 of solving this GMAT algebra DS question:

Evaluate Statement (2) ALONE: (x - 4) = 0

The statement provides no information about y.

**Statement 2 ALONE is NOT sufficient.**
Eliminate choice B. Choices narrow down to C or E.

##### Step 4 of solving this GMAT DS question:

Evaluate Statements (1) & (2) Together: (y - 3)(x - 4) = 0 & (x - 4) = 0

When x = 4, (y - 3)(x - 4) will be 0 irrespective of the value that y takes.

Can 'y' be 3? Yes 'y' can be 3.

Is y = 3?** Not necessary**.It can take values other than 3 and the data in the two statements will still hold good.

Eliminate choice C.

##### Statements TOGETHER are NOT sufficient. Choice D is the answer.