Statement 1
if B^A is positive
then
A is even
A can be +ve or -ve
B can be +ve or -ve
B can be even or odd
Hence not sufficient
Statement 2
B is negative
A^B will be positive if B is even or A is positive or both.
Hence Not Sufficient
Combining both the statements
A is even
B is -ve
so A^B can be +ve or -ve
Hence not sufficient.
so the answer is E
A power B
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niketdoshi123
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extending niketdoshi's answer.
Is A^B positive?
If B = 3 and A = -1, B^A = 3^-1 = 1/3 is positive and A^B = -1^3 = -1 and is negative.
We have two different answers to the question Is A^B positive?, So statement I is not sufficient to answer the question.
If B = -1 and A = -3 then A^B = (-3)^(-1) = -1/3 and is negative
IF B = -1 and A = 0 then A^B = 0 and is neither negative nor positive
We have three different answers to the question Is A^B positive?, So statement I is not sufficient to answer the question.
If B = -1 and A = 2 then B^A = 1(Positive) and A^B = (2)^-1 = 1/2 and is positive
We have two different answers to the question Is A^B positive?, So statement I+II combination is not sufficient to answer the question.
Hence E
Is A^B positive?
If B = 2 and A = 3, B^A = 8 is positive and A^B = 3^2 = 9 and is positive.(1) B^A is positive
If B = 3 and A = -1, B^A = 3^-1 = 1/3 is positive and A^B = -1^3 = -1 and is negative.
We have two different answers to the question Is A^B positive?, So statement I is not sufficient to answer the question.
If B = -1 and A = 2 then A^B = (2)^-1 = 1/2 and is positive(2) B is negative
If B = -1 and A = -3 then A^B = (-3)^(-1) = -1/3 and is negative
IF B = -1 and A = 0 then A^B = 0 and is neither negative nor positive
We have three different answers to the question Is A^B positive?, So statement I is not sufficient to answer the question.
IF B = -1 and A = 0 then B^A = 1(Positive) and A^B = 0(neither negative nor positive)From I and II
If B = -1 and A = 2 then B^A = 1(Positive) and A^B = (2)^-1 = 1/2 and is positive
We have two different answers to the question Is A^B positive?, So statement I+II combination is not sufficient to answer the question.
Hence E
Anil Gandham
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