prashantjanghel
Kinshook
Asked: What is the value of \(\frac{(n+13)!+(n+14)!}{(n+11)!+(n+12)!}\) ?
\(\frac{(n+13)!+(n+14)!}{(n+11)!+(n+12)!} = \frac{(n+13)! (1+ n+14)}{(n+11)!(1 + n+12)} = \frac{(n+13)(n+12)(n+15)}{(n+13)} = (n+12)(n+15)\)
IMO A
Can anyone explain this?
prashantjanghel if you find it a little confusing might I suggest a slightly different approach. We know that \(n\) is a constant, and we have not been given any limitations on \(n\). In this case we can assign any value to \(n\). The easiest would be to let \(n = 0\). Plugging that in gives us:
\(\frac{(0+13)!+(0+14)!}{(0+11)!+(n+12)!}\)
\(\frac{13!+14!}{11!+12!}\)
\(\frac{13!(1+14)}{11!(1+12)}\)
\(\frac{13!(15)}{11!(13)}\) which can be rewriten as \(\frac{11!*12*13(15)}{11!(13)}\)
\(12(15)\)
As we made \(n=0\) there is no need to do any calculations with the answer choices, answer choice A is identical to the answer. Therefore, the answer is A.