Is y = 7?
(1) (x - 4) = 0
(2) (x - 3)(y - 7) = 0
The OA is the option C.
Why is C? Just with the statement (2) is not sufficient? Experts, may yo clarify this for me? Thanks.<i class="em em-disappointed"></i>
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Is y = 7?
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ErikaPrepScholar
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Statement 1
This tells us nothing about y, so it's clearly insufficient on its own. It *does* tell us that x =4, which will be useful information later.
Statement 2
For (x-3)(y-7) to equal zero, either x-3 or y-7 must equal zero. So this statement can be true if x =3 (no matter what y equals) or if y=7 (no matter what x equals). So if x=3, y may equal 7, but it doesn't have to. Insufficient.
Both
Statement 1 tells us that x=4, which means that x-3 equals 1, not zero. This means that y must equal 7 to make (x-3)(y-7) equal zero. Sufficient.
This tells us nothing about y, so it's clearly insufficient on its own. It *does* tell us that x =4, which will be useful information later.
Statement 2
For (x-3)(y-7) to equal zero, either x-3 or y-7 must equal zero. So this statement can be true if x =3 (no matter what y equals) or if y=7 (no matter what x equals). So if x=3, y may equal 7, but it doesn't have to. Insufficient.
Both
Statement 1 tells us that x=4, which means that x-3 equals 1, not zero. This means that y must equal 7 to make (x-3)(y-7) equal zero. Sufficient.
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