AJWILL wrote:is x/3+3/x>2?
1)x<3
2)x>1
If x<0, then x/3 + 3/x = negative + negative = negative.
Thus, x must be positive.
To determine the positive values of x that satisfy x/3 + 3/x, identify the CRITICAL POINTS.
The critical points are the values of x where the lefthand side is EQUAL to the righthand side or is UNDEFINED.
x/3 + 3/x = 2 when x=3.
x/3 + 3/x is undefined when x=0.
Thus, the critical points are 0 and 3.
Test one value value to the left and right of each critical point.
0<x<3:
If x=1, then x/3 + 3/x = 1/3 + 3/1 = 10/3, which is greater than 2.
Thus, 0<x<3 is a valid range.
x>3:
If x=6, then x/3 + 3/x = 6/3 + 3/6 = 2.5, which is greater than 2.
Thus, x>3 is a valid range.
Since 0<x<3 and x>3 are both valid ranges, only one positive value is not valid: x=3.
Question rephrased: Is x a positive number not equal to 3?
Statement 1: x<3.
Since x could be positive, negative, or equal to 0, INSUFFICIENT.
Statement 2: x>1.
Since x could be equal to 3 or not equal to 3, INSUFFICIENT.
Statements 1 and 2 combined:
Since 1<x<3, x must be a positive number not equal to 3.
SUFFICIENT.
The correct answer is
C.
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