OG 13 DS #169

[Mk.d]

[deleted by Stacey; please see below]

I don't have any issue solving this question, however, I noticed that depending on how you manipulate the question stem, you can get different results. For example:

Result #1 - (1/10)^n < (1/10)^2 --> is n < 2?

Result #2 - (1/10)^n < (1/10)^2 --> 10^(-n) < 10^(-2), this becomes -n < -2 or n > 2.

So effectively, I could have rephrased the question into "is n < 2 or n > 2". While this does not impact solving a Y/N type DS question, which one is technically more correct?

I understand that the reason I have two solutions is because I changed the base and I had to flip the sign (when in the base of 10). I am just not sure whether this could come up in a different way in which case only one of them is the correct rephrase.

[StaceyKoprince]

Please read (and follow!) the forum guidelines before posting.

OG is a banned source; it is against copyright law to post OG questions anywhere on the web (even though people do).

I'm still going to answer your question though because it's really a theory question. :)

When dealing with exponential inequalities, there are some weird rules for dropping the bases and setting the exponents equal. If the two bases are greater than 1 (as in your second example), then you can do exactly what you did. If the two bases are between 0 and 1, then you have to reverse the inequality sign. Don't use this "drop the bases" method at all when the bases are 1 (as you did in your first example).

So your second rephrase (n > 2) was the one to use. In your first rephrase, the base was between 0 and 1, so the symbol should have been reversed and you should also have ended up with n > 2. :)