In the following number series only one number is wrong. Find out the wrong number.
`18" "119" "708" "3534" "14136" "42405`

Options

A. 708
B. 3534
C. 14136
D. 42405

Answer

To find the wrong number in the series `18, 119, 708, 3534, 14136, 42405`, we will analyze the pattern step by step.

### Step 1: Identify the Pattern
We need to find a consistent pattern between the numbers in the series. Let's denote the numbers as follows:
- \( a_1 = 18 \)
- \( a_2 = 119 \)
- \( a_3 = 708 \)
- \( a_4 = 3534 \)
- \( a_5 = 14136 \)
- \( a_6 = 42405 \)

### Step 2: Calculate the Relationship Between Consecutive Terms
1. From \( a_1 \) to \( a_2 \):
- We can try multiplying \( a_1 \) by a certain number and then subtracting a value.
- \( 18 \times 7 = 126 \)
- \( 126 - 7 = 119 \)

2. From \( a_2 \) to \( a_3 \):
- \( 119 \times 6 = 714 \)
- \( 714 - 6 = 708 \)

3. From \( a_3 \) to \( a_4 \):
- \( 708 \times 5 = 3540 \)
- \( 3540 - 6 = 3534 \) (This seems incorrect; let's check the next step)

4. From \( a_4 \) to \( a_5 \):
- \( 3534 \times 4 = 14136 \)
- \( 14136 - 4 = 14136 \) (This is correct)

5. From \( a_5 \) to \( a_6 \):
- \( 14136 \times 3 = 42408 \)
- \( 42408 - 3 = 42405 \) (This is also correct)

### Step 3: Identify the Incorrect Number
Now, let's summarize the calculations:
- \( a_1 \) to \( a_2 \): \( 18 \times 7 - 7 = 119 \) (Correct)
- \( a_2 \) to \( a_3 \): \( 119 \times 6 - 6 = 708 \) (Correct)
- \( a_3 \) to \( a_4 \): \( 708 \times 5 - 6 = 3534 \) (This should be \( 3540 - 6 = 3534 \), but we need to check if \( 3540 \) is correct)
- \( a_4 \) to \( a_5 \): \( 3534 \times 4 = 14136 \) (Correct)
- \( a_5 \) to \( a_6 \): \( 14136 \times 3 - 3 = 42405 \) (Correct)

### Conclusion
The term \( 3534 \) is incorrect. It should have been \( 3540 \) instead.

Thus, the wrong number in the series is **3534**.

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