Is 3 to the power of P > 2 to the power of q ?

(1) q = 2p

(2) q > 0


Can anyone explain this.

From my understanding the answer to this question is E.

But the explainantion says the correct ans is C.

There is an explanation for this problem or simply an answer?

Experts will explain but here is what I would have done.

Is 3^P > 2^Q

I would start with statement 2. We know Q is positive but this tells us nothing about P. Perhaps P is positive but maybe not. You can easily pick some numbers here to prove this statement is insufficient.

If Q were 1 and P were 2, the question would be true. But if Q were 2 and P was 1 the question would be false. INSUFFICIENT


Statement 1 tells us that Q = 2P

Pick some smart numbers to prove insufficiency

Q = 2P

1 = 2(1/2) --> Our question above would be FALSE
-2 = 2(-1) --> Our question above would be TRUE

INSUFFICIENT



Combining the statements we know Q is positive (which also implies that P is positive) AND Q = 2P

Q = 2P

1 = 2(1/2)
2 = 2(1)
3 = 2(3/2)
4 = 2(2)
6 = 2(3)


Testing each number in to our question up top yields a definitive "NO". Thus, both statements together are sufficient.

hi,
from now on, you should actually say what "your understanding of the problem" is; it's hard to respond to your post if we have to mind-read.

kyle's approach (testing cases) works.

if you have statement 2, you can also substitute q = 2p into the question:
Is 3^p > 2^q ?
Is 3^p > 2^(2p) ?
which is the same as...
Is 3^p > (2^2)^p ?
Is 3^p > 4^p ?

The answer to this question is No if p is non-negative and Yes if p is negative. therefore, if you have the two statements together, it's a definite No.

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