In this question a number series is given. Only one number is wrong which doesn’t fit in the series. Find out the wrong number: 12, 13, 30, 117, 734, 6745.

Steps to Solve

1. Identify the Pattern in the Series

Look at the given numbers: 12, 13, 30, 117, 734, 6745. We need to find a consistent pattern.

2. Examine Basic Operations Between Consecutive Numbers

Start checking if there’s a relationship between consecutive numbers:

• From 12 to 13: Increase by 1
• From 13 to 30: Increase by 17
• From 30 to 117: Increase by 87
• From 117 to 734: Increase by 617
• From 734 to 6745: Increase by 6011

3. Find the Ratio of Consecutive Numbers

Next, check the ratios of each number to the previous:

• $\frac{13}{12} \approx 1.0833$
• $\frac{30}{13} \approx 2.3077$
• $\frac{117}{30} \approx 3.9$
• $\frac{734}{117} \approx 6.2821$
• $\frac{6745}{734} \approx 9.1775$

The ratios show a pattern of increasing, but they don't follow a specific formula.

4. Re-evaluate Based on Exponential Growth

Notice that as the numbers increase, the differences between them grow larger. This suggests a potential exponential or polynomial pattern. After careful inspection, identify that every number in the sequence, after the first few, appears to grow significantly.

5. Identify the Outlier

After checking the pattern and growth rates, you’ll find:

• The jump from 30 to 117 is too large based on the previous growth pattern (12, 13, 30).
• Hence, 30 may not fit the growing pattern, indicating that it is likely the wrong number.