Select the number from among the given options that can replace the question mark (?) in the following series.
13, 20, 33, 52, ?, 118, 161
Looking at the difference between the give numbers, we see that
20-13 = 7
33-20 = 13
52-33 = 19
and towards the end,
161-118 = 43
One noticeable thing is that all of these are prime numbers.
Writing down the prime number,
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and so on.
We see that the prime numbers in the difference are prime numbers in an alternating sequence, leaving one prime number in between
The two numbers which should be included in this sequence are:
7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43
29 and 37
Adding 29 to 52, we get 81.
Adding 37 to 81, we get 118.
This fits prefectly into our series, therfore the missing number is 81.