Is a^n b^n? (1) a b (2) ab

Question

Is  a^n > b^n ?

(1)  a > b 
(2)  ab < 0

chetan2u · Answer

Is  a^n > b^n ?

(1)  a > b 
Will also depend on the value of n and range of a and b. 
In very simple terms 
If n=0, answer is no. 
If n=1, answer is yes.

(2)  ab < 0 
We just know a and b are of opposite sign.

Combined 
Following still stands 
If n=0, answer is no. 
If n=1, answer is yes. 
Insufficient

E

Crytiocanalyst · Answer

(1)  a > b 
a=2 , b=-10 yes for n=3 
and no for n=2 
Clearly insufficient

(2)  ab < 0 
same arguemnt as 1 can be carried out

Even when 1 and 2 is combined we can argue on a similar line of reasoning

Therefore IMO E

Crytiocanalyst · Answer

I guess there is a small typo error in the end

JerryAtDreamScore · Answer

Rephrase the question:   
> We would really want to know something about n before simplifying the question. Is n positive? Is it negative? Is it 0? We always have to consider the case of n = 0 which would give us  a^n = b^n = 1  regardless of the value of  a  and  b .

Statement 1 Alone:   
> If n > 0, and  a > b > 0 , then we answer YES.
> If n = 0 , we will always answer NO. Then this statement is insufficient.

Statement 2 Alone:   
> We may reapply the logic in statement 1 to say this statement is insufficient.

Both Statements Combined:   
> Statement 1 and 2 used the same examples, so even when we combine statements we may still recycle the two examples. Thus combined it is still insufficient.

Answer: E

Is a^n > b^n? (1) a > b (2) ab < 0

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