If x/y >2, is 3x+2y<18?
1. x-y is less than 2
2. y-x is less than 2
Since x/y > 2, x and y have the same sign.
If x and y are both negative, then 3x + 2y < 18, and the answer is a definite YES.
Thus, our concern here is what happens to the value of 3x+2y when x and y are both positive.
If x and y are both positive, then x>2y -- information that we can use when we evaluate each statement.
To add inequalities, the <> must face the same direction in each inequality.
Statement 1: x-y<2.
Thus, y+2 > x.
Adding this inequality to x>2y, we get:
(y+2) + x > x + 2y
2 > y.
Since y<2, and x<y+2, x<4.
This means that the upper limit of 3x+2y = 3(4) + 2(2) = 16.
Thus, when x and y are both positive, 3x+2y < 18.
SUFFICIENT.
Statement 2: y-x<2.
Thus, x+2 > y.
Adding this inequality to x>2y, we get:
(x+2) + x > y+ 2y
3y-2x < 2.
If y=2 and x=3, then 3x+2y = 12.
If y=10 and x=15, then 3x+2y = 60.
Since in the first case 3x+2y<18 and in the second case 3x+2y>18, INSUFFICIENT.
The correct answer is
A.
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