pappueshwar wrote:IS t^2 > t/3?
1) t>0
2) |t|>1/3
OA IS B. heavily confused
t² > t/3
3t² > t
3t²-t > 0
t(3t-1) > 0.
The lefthand side is equal to 0 if t=1 or t=1/3.
These are the CRITICAL POINTS: the values where t²=t/3.
When t is ANY OTHER VALUE, t²>t/3 or t²<t/3.
To determine the range where t²>t/3, test one value to the left and right of each critical point.
t<0:
Let t=-1.
(-1)² > 1/3.
1 > 1/3.
This works.
Thu, t<0 is part of the range where t² > t/3.
0<t<1/3:
Let t=1/4.
(1/4)² > (1/4)/3.
1/16 > 1/12.
Doesn't work.
Thus, 0<t<1/3 is not part of the range where t² > t/3.
t>1/3:
Let t=1.
(1)² > 1/3.
1 > 1/3.
This works.
Thus, t>1/3 is part of the range where t² > t/3.
Thus, the only range where it is NOT true that t² > t/3 is 0≤t≤1/3.
Question rephrased: Is 0≤t≤1/3?
Statement 1: t>0
No way to determine whether 0≤t≤1/3.
INSUFFICIENT.
Statement 2: |t|>1/3
Thus, it is not possible that 0≤t≤1/3.
SUFFICIENT.
The correct answer is
B.
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