word bank - eq, ineq & vics #19

Question #19:
Is 3^p > 2^q ?

(1) q = 2p

(2) q > 0

Answer is C (Data Sufficiency).

I thought it was E because what if p is a fraction? If raised to a fraction, isn't the value smaller?

Many thanks!

Is 3^p > 2^q ?

(1) q = 2p

(2) q > 0

Answer is C (Data Sufficiency).

I thought it was E because what if p is a fraction? If raised to a fraction, isn't the value smaller?

with 1, we get: is 3^P > 2 ^[2p] => is 3^p> 4^p [u see this right?]. Now, p could be +ve or -ve; so we don't know.

taking 2 together with 1, we know that P>0, so we know that 3 [raised to something positve] will always be smaller than 4 [raised to the same positive number]. Even if that positive is a fraction, it doesn't mater. take 3^1/2 [square root of 3]- what is it? it is a number that has to multiplied twice [since the fraction is 1/2] to get 3. similary, 3^1/3 will be a number that needs to be multiplied by itself 3 times to get 3 and so on. So, comparing 3^[some positive fraction] with 4 ^[same positive fraction], we know that what we will get for the the former will be smaller than what get for the latter as the number that has to be multipled by itself "wahtever" times would need to be bigger to get 4 as the end result.

hope this helps....

thx

thanks so much. appreciate it!

A little tip: don't post things in the general math and verbal folders if they qualify to go in one of the more specific folders. Questions in those other folders usually get answered faster. :)

Is 3^p > 2^q ?

(1) q = 2p

(2) q > 0

Solution:

(1) q = 2p
With this statement, we can simplify the question: 2^q = 2^2p = 4^p ... so the question is asking ... is "3^p > 4^p" ?

Consider the positive scenario: let p = 2. So 3^2 = 9 and 4^2 = 16. We can see 9 < 16. So this provides the "no" answer to the question "is 3^p > 4^p ?"
Consider the negative scenario: let p=-2. So 3^-2 = 1/3^2 = 1/9. And 4^-2 = 1/4^2 = 1/16. We can see that 1/9 > 1/16. So this provides the "yes" answer to the question "is 3^p > 4^p?".
In order for (1) to be sufficient, it needs to provide a "yes" or "no" answer to all scenarios. So it is INSUFF in this case. Now lets look at (2)

(2) q > 0
This tells us that q is positive. But it provides no information on p. So we have no way of determining if 3^p > 2^2q.

With both statements (1) and (2) ...
based on our working for (1), we found that in a positive scenario will be able to answer the question with "no", and with a negative scenario, the answer to the question will be "yes".
No we now that q must be positive ... this means that the answer to the question will always be "no", using the information from (1) and (2). Hence the answer to the overall question is (C).

Any comments on my "way of working" / logic for solving this question are appreciated.

Stacy,
Is there anyway of simplifying the question: "Is 3^p > 2^q" ? I was only able to simplify it for statement (1) ... to Is 3^p > 4^p.

Thanks

yes, your logic is good. And, no, there isn't a great, simple way to rephrase that question - the rephrasing here comes with the statements rather than the question stem.