M7MBA wrote:If x > y, is x > 6 ?
(1) (x - 7)(y - 7) = 0
(2) x > 18 - 2y
Statement 1: (x - 7)(y - 7) = 0
Case 1: x=7
Here, the answer to the question stem is YES.
Case 2: y=7
Substituting y=7 into x > y, we get:
x > 7.
Thus, the answer to the question stem is YES.
Since the answer is YES in both cases, SUFFICIENT.
Statement 2: x > 18 - 2y
x + 2y > 18
2y > 18 - x
If x=6 in the resulting inequality in blue, then y>6, violating the condition that x>y.
For the value of y to decrease so that x>y, the value of x must INCREASE.
Thus, x>6.
SUFFICIENT.
The correct answer is
D.
An algebraic proof for Statement 2:
Multiplying both sides of x > y by 2, we get:
2x > 2y
Adding together 2x > 2y and x > 18 - 2y, we get:
2x + x > 2y + 18 - 2y
3x > 18
x > 6.
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