Question

Find the wrong number in the series. 3, 31, 131, 351, 739, 1343, 2211, 3291, 4931

• A. 1343
• B. 2211
• C. 3291
• D. 4931

Hint:

For number series that don't follow simple arithmetic or geometric patterns, the method of differences is very powerful. Keep finding the differences between terms (first, second, third, etc.) until you find a constant value or a simple, recognizable pattern.

Answer 1

The Correct Option is C

Step 1: Understanding the Problem
We need to identify the number in the given series that does not follow the underlying pattern.

Step 2: Analyzing the Pattern
A common method for complex series is to check the differences between consecutive terms (first differences), and if that doesn't reveal a pattern, check the differences of the differences (second differences).
1. Calculate First Differences:

\(31 - 3 = 28\)
\(131 - 31 = 100\)
\(351 - 131 = 220\)
\(739 - 351 = 388\)
\(1343 - 739 = 604\)
\(2211 - 1343 = 868\)
\(3291 - 2211 = 1080\)
\(4931 - 3291 = 1640\)
The first differences are: 28, 100, 220, 388, 604, 868, 1080, 1640. No obvious pattern here.
2. Calculate Second Differences:

\(100 - 28 = 72\)
\(220 - 100 = 120\)
\(388 - 220 = 168\)
\(604 - 388 = 216\)
\(868 - 604 = 264\)
\(1080 - 868 = 212\) \(\leftarrow\) The pattern seems to break here.
\(1640 - 1080 = 560\)
Let's examine the second differences before the break: 72, 120, 168, 216, 264.
3. Calculate Third Differences (or check the pattern in second differences):

\(120 - 72 = 48\)
\(168 - 120 = 48\)
\(216 - 168 = 48\)
\(264 - 216 = 48\)
The pattern is clear: the third difference is a constant 48. The second differences form an arithmetic progression.
4. Find the point of error:
The second difference after 264 should be \(264 + 48 = 312\). The series has 212. This means the first difference that was used to calculate it (1080) is incorrect. The first difference `3291 - 2211 = 1080` is where the error originates. This implies the term 3291 is wrong.
5. Verify by correcting the series:

The correct second difference should be 312.
The correct first difference should be \(868 + 312 = 1180\).
The correct term after 2211 should be \(2211 + 1180 = 3391\). The series has 3291.
Let's check the next term. The next second difference should be \(312 + 48 = 360\).
The next first difference should be \(1180 + 360 = 1540\).
The next term in the series should be \(3391 + 1540 = 4931\). This matches the last term in the given series.
This confirms that 3291 is the wrong number.

Step 4: Final Answer
The wrong number in the series is 3291. Therefore, option (C) is the correct answer.