Directions: Identify the number that should replace the question mark (?) to complete the given series.

150, ?, 186, 209, 238, 269

The correct option is 167.

To find the missing number in the given series, let's analyze the differences between consecutive known terms:

$269-238=31$

$238-209=29$

$209-186=23$

The differences between consecutive terms (23, 29, 31) are consecutive prime numbers in increasing order.

Following this pattern backward, the prime numbers preceding 23 are 19 and 17.

Therefore, the difference between 186 and the missing number (?) must be 19:

$186-19=167$

We can verify this by checking the difference between 167 and the first term (150):

$167-150=17$

Since 17 is the prime number preceding 19, the pattern is fully consistent throughout the series:

150 + 17 = 167
167 + 19 = 186
186 + 23 = 209
209 + 29 = 238
238 + 31 = 269

Thus, the number that should replace the question mark (?) is 167.