Directions: What will come in the place of question mark in following number series?
34,18,?,6,4,3

Options

A. 9
B. 10
C. 12
D. 8

Answer

To solve the number series: 34, 18, ?, 6, 4, 3, we need to identify the pattern in the series.

**Step 1: Identify the differences between consecutive numbers.**
- The difference between 34 and 18 is:
\[ 34 - 18 = 16 \]

**Step 2: Identify the difference between the next numbers.**
- The difference between 18 and the unknown number (let's call it x) is:
\[ 18 - x \]

**Step 3: Identify the difference between the next numbers.**
- The difference between x and 6 is:
\[ x - 6 \]

**Step 4: Identify the difference between the next numbers.**
- The difference between 6 and 4 is:
\[ 6 - 4 = 2 \]

**Step 5: Identify the difference between the next numbers.**
- The difference between 4 and 3 is:
\[ 4 - 3 = 1 \]

**Step 6: Analyze the pattern of differences.**
- We see the differences are:
- 16 (from 34 to 18)
- (18 - x)
- (x - 6)
- 2 (from 6 to 4)
- 1 (from 4 to 3)

**Step 7: Establish a pattern.**
- The differences seem to be decreasing. The difference from 6 to 4 is 2, and from 4 to 3 is 1.
- If we assume that the difference between 18 and x follows the same pattern, we can hypothesize that:
\[ 18 - x = 8 \quad (since 16 is halved to 8) \]

**Step 8: Solve for x.**
- From the equation \( 18 - x = 8 \):
\[ x = 18 - 8 = 10 \]

**Step 9: Verify the pattern.**
- Now, let's check the difference between 10 and 6:
\[ 10 - 6 = 4 \quad (which is half of 8) \]

**Step 10: Conclusion.**
- The number that comes in place of the question mark is 10.

Thus, the answer is:
\[ \text{The number that comes in place of the question mark is } 10. \]