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.
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