Is PQ 1? (1) P^Q = 1 (2) Q = -1

Question

Is PQ > 1?

(1) P^Q = 1
(2) Q = -1

Vips0000 · Accepted Answer

Statement 1: p^q =1 
=> p could be any number and q=0 
or q could be any number and p=1
or q coule be any even number and p=-1

Clearly not sufficient as PQ could be 0, >1 or <1.

Statement 2: q=-1
Clearly insufficient, no information on p.

Combining statement 1 and 2: if q=-1 and p^q =1 
this gives p = 1, q=-1. Sufficient. (We can answer whether pq>1 or not)

Hence Ans C it is.

duriangris · Answer

look at your possibilities step by step:

1/ p^q=1
means
either q=0 and/or p=1
p=545, q=0 => pq<1 or
p=1, q=8 => pq>1
insufficient

2/ we know nothing about p
example p=100 then pq<1
p=-100 then pq>1
insufficient

1/+2/
if q=-1 then p must be equal to 0 to satisfy the condition of 1/
sufficient

th03 · Answer

Hi,

Consider, 1. p^q=1
If p=10, q=0, then
=> p^q=1 (10^0=1)
=> pq > 1 is false (10*0 = 0 < 1)

If p=-1, q=-2, then
=> p^q=1 (-1^-2=1)
=> p^q > 1 true (-1*-2 = 2 > 1)

We have both true and false considering only first condition. Hence, A and D choices are eliminated.

-------------------

Now, consider 2. q=-1
If p=-2, then p^q>1
If p=2, then p^q<1
So, clearly only 2 is insufficient. Hence, B is eliminated.

-------------------

If p^q=1 and q=-1, then p=1.
Since p and q have definite values, 1. and 2. together are sufficient.

Hence, C is the answer.

nishtil · Answer

1. If P^Q = 1 then P = 1 or Q = 0. consider p = 2 then Q has to be 0. P = 1 then Q can be anything. not suff.
2. Q= -1 then P and can be possibtive and PQ<1 or P can be negative ans PO>1. hence not suff.

combining 1 and 2.

if Q= -1 then P has to be 1 hence PQ <1 suff. answer should be C

Jk8269 · Answer

Ans is C.
when we both consider statetments, we get Q=-1 (given) and P=1 . implies PQ = -1 <1 . So Suffcient to sat that PQ>1 is incorrect always

arvind910619 · Answer

Imo C 
Taking value of P as 1 we will get 1 no matter the value of Q 
If Q=0 then p can take any value 
From statement 2 
P can take any value making it both true and false 
This both are necessary

Sent from my ONE E1003 using  GMAT Club Forum mobile app

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Is PQ > 1? (1) P^Q = 1 (2) Q = -1

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