neerajkumar1_1 wrote:which of the following describes all the values of y for which y<y^2.
1 < y
-1 < y < 0
y < -1
1/y < 1
0 < y < 1
Approach 1:
y≠0, since 0<0² is not valid.
Thus, y² must be positive, implying that if we divide each side of y < y² by y², the direction of the inequality doesn't change:
y/y² < y²/y²
1/y < 1.
The correct answer is
D.
Approach 2:
Use POE (process of elimination).
Each answer choice represents a RANGE of values.
Plug in values that satisfy y<y².
Look for values that work in some answer choices but not in others.
Let y=2, since 2<2².
Eliminate any answer whose range does not include y=2.
A: 1<y
1<2.
This works. Hold onto A.
B: -1 < y < 0
-1 < 2 < 0.
Doesn't work. Eliminate B.
C: y < -1
2 < -1.
Doesn't work. Eliminate C.
D: 1/y < 1
1/2 < 1.
This works. Hold onto D.
E: 0 < y < 1
0 < 2 < 1.
Doesn't work. Eliminate E.
Let y=-2, since -2<(-2)².
Eliminate any remaining answer whose range does not include y=-2.
A: 1<y
1<-2.
Doesn't work. Eliminate A.
The correct answer is
D.
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