Find the wrong number in the following number series:
250 260 291 314 340 370 405

Options

A. 370
B. 314
C. 260
D. 405

Answer

To find the wrong number in the given series: 250, 260, 291, 314, 340, 370, 405, we will analyze the differences between consecutive numbers.

**Step 1: Write down the series.**
- The series is: 250, 260, 291, 314, 340, 370, 405.

**Step 2: Calculate the differences between consecutive numbers.**
- 260 - 250 = 10
- 291 - 260 = 31
- 314 - 291 = 23
- 340 - 314 = 26
- 370 - 340 = 30
- 405 - 370 = 35

So, the differences are: 10, 31, 23, 26, 30, 35.

**Step 3: Analyze the differences.**
- The differences do not follow a clear pattern initially. Let's examine them more closely.
- The differences seem to be increasing but not in a consistent manner.

**Step 4: Look for a pattern in the differences.**
- If we look at the differences more closely:
- The first difference is 10.
- The second difference is 31.
- The third difference is 23.
- The fourth difference is 26.
- The fifth difference is 30.
- The sixth difference is 35.

**Step 5: Identify the inconsistency.**
- If we assume the differences should increase by a certain amount, we can see:
- From 10 to 31, there is an increase of 21.
- From 31 to 23, there is a decrease of 8 (which is inconsistent).
- From 23 to 26, there is an increase of 3.
- From 26 to 30, there is an increase of 4.
- From 30 to 35, there is an increase of 5.

**Step 6: Check the expected pattern of differences.**
- If we were to follow a consistent pattern, we might expect the differences to increase by a consistent amount.
- For example, if we had started with 250 and added 20, we would expect the next number to be 270 (not 260).

**Step 7: Conclusion.**
- Given that the second number should have been 270 instead of 260 to maintain a consistent pattern, we conclude that 260 is the wrong number in the series.

**Final Answer:**
- The wrong number in the series is **260**.

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