Determine the value that should replace the question mark in the following number sequence:

12, 48, 24, 96, ?, 192

The correct option is 48.

To find the missing number in the sequence, let us analyze the pattern between consecutive terms:

1. From the 1st term to the 2nd term:

$12\times 2=48$ (Wait, $12\times 4=48$)

Let us look at the operations step-by-step:

• 12 to 48: Multiply by 4 ($12\times 4=48$)

• 48 to 24: Divide by 2 ($48÷2=24$)

• 24 to 96: Multiply by 4 ($24\times 4=96$)

Following this alternating pattern of multiplying by 4 ($\times 4$) and dividing by 2 ($÷2$):

• The next operation after $\times 4$ is to divide by 2 ($÷2$):

$96÷2=48$

• To verify, performing the next operation ($\times 4$) on 48 should give the last term of the sequence:

$48\times 4=192$

This matches the given final number 192 perfectly. Therefore, the value that replaces the question mark is 48.