The average of 38,84,63,45,32 and n lies between 50 and 60.If n is an integer greater than the average of the above numbers, then n lies between?

Question

The options are

1. 53 < n <97
2. 50 < n < 100
3. 52 < n < 98

I added the values along with n to get 43.66 + n/6.I then tried plugging in values from the options and tried arriving at the answer by means of elimination but that didn't work.

Answer 1

What we know about $n$ is $50<n<60$ and $n>\dfrac{262+n}{6}$. This second inequality implies that $n>52.8$. Thus $52.8<n<60$. So this leaves no correct choice. $(1)$ would have been correct had it been stated as $53\le n<97$ instead of $53<n<97$. Was that a typo in the question?