If p and q are integers, is p^q 1 ? (1) pq

Question

If p and q are integers, is p^q >1

(1) pq < 0

(2) q^p < 1

chetan2u · Answer

If p and q are integers, is p^q >1?

When will this happen :- when p>1 and q>0 or even when q is even >0 and p^2>1

i)pq<0
p and q are of OPPOSITE signs..
p is 3 and q<0...ans will be NO as 3^(-1)=1/3<1
If p -2 and q is 2... Ans will be yes
Insufficient

ii)q^p<1
Same example as in statement I
Insuff

Combined
Same examples remain
Insufficient

E

akurathi12 · Answer

If p and q are integers, is p^q > 1?

(1) pq < 0

(2) q^p < 1

DavidTutorexamPAL · Answer

The answer is E.

1) This could be true in two tays:
- p>0 and q<0, in which case 0<p^q<1 (ex: 3^(-1) = 1/3) - answer is yes!
- p<0 and q>0, in which case p^q can be greater than 1 (ex = -2^2=4), or smaller than it (ex: -2^-1=-1/2) - inconclusive!
insufficient.

2) This could be true in the exact same two ways as in (1). This means this as well is inconclusive.

Bunuel · Answer

______________
Merging topics.

Wgs · Answer

p^q > 1 at three different conditions:-
1. p>1 & q>0
2. p lies between 0&1 and q<0
3. p<0 & q!=0 & q is even

!= means not equal to

pq<0 implies p&q have opposite signs and p!=0 and q!=0
This is not sufficient bcoz not satisfying any of the above mentioned conditions.

q^p < 1 implies:-
1. q>1 and p<0
2. q lies between 0&1 and p>0
3. q<-1 and p<0 or odd
4. q lies between -1&0 and p>0 or odd
This is also insufficient.

Taking both one and two together also don’t give definite yes or no.
So the right answer is option E.

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If p and q are integers, is p^q >1 ? (1) pq < 0 (2) q^p < 1

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