jrk23 wrote:
can any expert plz reply on this. so many variance in answer. Range concept is also correct as per me. so plz explain.
Hi
jrk23,
I'm no expert, but taking the liberty to explain.
S1: max power of 4 in n! is 7.
\(4=2^2\). The maximum power of 4 in n! will be given by [(max power of 2 in n!)/2]. The [ ] indicate the highest integer value less than or equal to (max power of 2 in n!)/2.
This implies the numerator can be 14 or 15. In either case, the value will be 7. Next, we need to find the values of n for which maximum power of 2 is 14 or 15.
For,
n=15, the maximum power of 2 will be 11
n=16, max power of 2 is 15
As you can see, the power of 14 doesn't occur. So, power of 2 in n! will be 15. Sufficient.
S2: The max power of 6 in n! will be equal to the max power of 3 in n!. So, max power of 3 in n! equals to 6.
For,
n=14, max power of 3 is 5.
n=15, max power of 3 is 6, max power of 2 is 11.
n=16, max power of 3 is 6, max power of 2 is 15. (we can stop checking here as we obtained a different value for max power of 2)
n=17, max power of 3 is 6, max power of 2 is 15.
Thus, we can't determine if the max power of 2 in n! is 11 or 15. Not sufficient.
Hope it helps!
Thanks
Lipun