neeg wrote:What is the smallest integer n for which 25^n > 5^12?

a)6
b)7
c)8
d)9
e)10

First recognize that 5^12 = (5^2)^6 = 25^6
What is the smallest integer n for which 25^n > 25^6?
We need n>6
So, n = 7 is the smallest integer.
Answer = B

Cheers,
Brent

neeg wrote:If I try solving this by rewriting the right side rather than the left side as a common base i.e. 5 ^12 --> 25^ 11 then n would have to be greater than 11 ?

Your mistake is there.
Arithmetic of powers do not work that way.
5^12 = 5*(5^11) NOT 25^11
Or, 5^12 = (5^6)*(5^6) = (5*5)^6 = 25^6

To clear your confusion, let us go back to the very definition of powers,
a^n = a multiplied with it self n times = a*a*a*... (n times)
a^m = a multiplied with it self m times = a*a*a*... (m times)

Now,

• a^(m + n) = (a^m)*(a^n)
  a^(mn) = (a^m)^n = (a^n)^m

Hope that helps.

Hi All,

We’re asked for the SMALLEST possible INTEGER value for N that will make 25^N > 5^12. While the answers to this question are numbers (so we could TEST THE ANSWERS), this prompt is based around some standard Exponent rules, so approaching it with Arithmetic should be fairly quick.

The “base” of an exponent calculation can sometimes be ‘re-written’ (if the base has any factors that are greater than 1, then you can rewrite the calculation while keeping its value the same). Here, 25 can be re-written as 5^2, so the “left side” of the inequality can be re-written as (5^2)^N.

When ‘raising a power to a power’, you multiply the Exponents, meaning that we now have:

5^(2N) > 5^12

Thus, we need 2N > 12…. N > 6. The smallest answer that fits that description is…

Final Answer: B

GMAT Assassins aren’t born, they’re made,
Rich