ObsessedWithGMAT wrote:
Thanks a lot goutamread! This one is really better. But, I want to know that what made you to split 105 into 100*1.05. This is some thing that is really very important to know because I believe that these are the tactics that one has to think of while attacking a question.
I'm not an expert, rather I'm just another aspirant on the forum. I could try to explain:
See, whenever we deal with a big number/expression, we try to simplify the expression to make it realistic
There could be numerous ways to solve a question, what matters is which one you feel at your ease... now as you mentioned inequality,
assume \(105^{19} > 100^{20}\) lets try to prove whther our assumption is correct or not. If yes, then \(105^{19} > 100^{20}\) and if not then, \(105^{19} < 100^{20}\)
\(105^{19} > 100^{20}\)
Now, don't these expressions scare us. yes they are scary.. so lets try and simplify.
lets divide both side by \(100^{20}\), (as \(100^{20}\) is +ve --> inequality sign wont change)
\(\frac{105^{19}}{100^{20}} > 1\)
\(\frac{105^{19}}{{100^{19}*100}} > 1\)
\((\frac{105}{100})^{19}*\frac{1}{100} > 1\)
\(\frac{(1.05) ^{19}}{100} > 1\) OR \((\frac{26}{25}) ^{19}* \frac{1}{100} > 1\) ==> \(26 ^{19} > 100 * 25^{19}\)
From here its already discussed earlier how to solve the problem. Take away could be : There are various ways to solve a problem, what matters is what suits you, but you should be aware of more than one trick.