Which of the following numbers will replace the question mark (?) in the given series?
80, 101, 120, ?, 168

The correct answer is 145.

Let us analyze the pattern of the given series:
80, 101, 120, ?, 168

Let's find the differences between consecutive terms of the series:

First term = 80

Second term = 101
Difference = 101 - 80 = 21

Third term = 120
Difference = 120 - 101 = 19

We notice that the differences are decreasing consecutive odd numbers: 21, 19, ...
If this pattern continues, the next differences should be 17 and then 15.

Let's calculate the missing number using the next expected difference (17):
Missing number = Third term + 17
Missing number = 120 + 17 = 137

However, let's check if 137 works for the next term:
137 + 15 = 152, which is not 168.

Since the simple descending odd differences pattern (21, 19, 17, 15) does not lead to 168 (it would give 152), let's look for alternative mathematical patterns for each term.

Let's observe the relation of each number to perfect squares:
80 can be written as $9^2-1$ (since $81-1=80$)
101 can be written as ${10}^2+1$ (since $100+1=101$)
120 can be written as ${11}^2-1$ (since $121-1=120$)

Following this alternating square pattern ($n^2\pm 1$):
For the 4th term (with n = 12), the expression should be:
${12}^2+1$
Calculating this value:
$144+1=145$

Let's verify this pattern for the 5th term (with n = 13):
The expression should be:
${13}^2-1$
Calculating this value:
$169-1=168$

This matches the last term in the series (168) perfectly. Therefore, the missing number is indeed 145.