Directions: Determine the number that should replace the question mark (?) in the following number series.

850, 550, 350, ?, 170, 150

The correct option is 230.

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

850 - 550 = 300
550 - 350 = 200
350 - ? = x
? - 170 = y
170 - 150 = 20

Let's examine the pattern in the differences (300, 200, x, y, 20):

300 = 5 × 6 × 10
200 = 4 × 5 × 10
x = 3 × 4 × 10 = 120
y = 2 × 3 × 10 = 60
20 = 1 × 2 × 10

Alternatively, looking at the second differences (the difference between successive differences):

300 - 200 = 100
200 - 120 = 80
120 - 60 = 60
60 - 20 = 40

The second differences decrease consistently by 20 (100, 80, 60, 40).

Applying the difference of 120 to 350 gives:

$350-120=230$

We can check the validity with the next term in the series:

$230-60=170$

This correctly matches the term following the question mark.

Therefore, the number that replaces the question mark (?) is 230.