Does x = 3?
(1) (x−3)(y−1)=0
(2) (x−3)^2+(y−1)^2=0
The OA is the option B.
I do not understand why the first statement is not sufficient and the second is. Can someone clarify this for me? Please. <i class="em em-confused"></i>
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Does x = 3?
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GMATGuruNY
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Statement 1: (x−3)(y−1) = 0M7MBA wrote:Does x = 3?
(1) (x−3)(y−1)=0
(2) (x−3)^2+(y−1)^2=0
If y-1=0 -- implying that y=1 -- then x-3 can be equal to ANY VALUE.
For example:
x=3 and y=1, with the result that (x-3)(y-1) = (3-3)(1-0) = 0*0 = 0.
x=4 and y=1, with the result that (x-3)(y-1) = (4-1)(1-0) = 3*0 = 0.
Since the answer to the question stem is YES in first case but NO in the second case, INSUFFICIENT.
Statement 2: (x−3)² + (y−1)² = 0
Since the square of a value must be NONNEGATIVE, the equation above implies the following:
NONNEGATIVE + NONNEGATIVE = 0.
Since neither term can be negative, the equation in blue requires that both terms be equal to 0.
Thus:
(x-3)² = 0 and (y-1)² = 0, with the result that (x−3)² + (y−1)² = 0 + 0 = 0.
Since (x-3)² = 0, x=3.
Thus, the answer to the question stem is YES.
SUFFICIENT.
The correct answer is B.
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Hello M7MBA.
The reason is the following:
(1) (x-3)(y-1)=0
This statement implies that x=3 OR y=1.
Only one condition is needed to get (x-3)(y-1)=0. Then, we cannot be sure if x=3 or not. Hence, this statement is NOT SUFFICIENT.
(2) (x-3)^2+(y-1)^2=0
This statement implies that x=3 AND y=1. Hence, we are sure that x=3. Therefore, this statement is SUFFICIENT.
Hence, the answer is the option C.
The reason is the following:
(1) (x-3)(y-1)=0
This statement implies that x=3 OR y=1.
Only one condition is needed to get (x-3)(y-1)=0. Then, we cannot be sure if x=3 or not. Hence, this statement is NOT SUFFICIENT.
(2) (x-3)^2+(y-1)^2=0
This statement implies that x=3 AND y=1. Hence, we are sure that x=3. Therefore, this statement is SUFFICIENT.
Hence, the answer is the option C.
