Find the wrong number in following number series.
`2," "6," "12," "48," "240," "1440," "10080`

Options

A. 12
B. 6
C. 2
D. 48

Answer

To find the wrong number in the series `2, 6, 12, 48, 240, 1440, 10080`, we will analyze the pattern in the series step by step.

### Step 1: Identify the Pattern
Let's look at the series closely:
- The first number is **2**.
- The second number is **6**.
- The third number is **12**.
- The fourth number is **48**.
- The fifth number is **240**.
- The sixth number is **1440**.
- The seventh number is **10080**.

### Step 2: Check Multiplication Factors
Now, let's check how each number relates to the previous number:
- From **2 to 6**: \(2 \times 3 = 6\)
- From **6 to 12**: \(6 \times 2 = 12\)
- From **12 to 48**: \(12 \times 4 = 48\)
- From **48 to 240**: \(48 \times 5 = 240\)
- From **240 to 1440**: \(240 \times 6 = 1440\)
- From **1440 to 10080**: \(1440 \times 7 = 10080\)

### Step 3: Analyze the Multiplication Pattern
Now, let's summarize the multiplication factors:
- \(2 \times 3 = 6\) (factor is 3)
- \(6 \times 2 = 12\) (factor is 2)
- \(12 \times 4 = 48\) (factor is 4)
- \(48 \times 5 = 240\) (factor is 5)
- \(240 \times 6 = 1440\) (factor is 6)
- \(1440 \times 7 = 10080\) (factor is 7)

### Step 4: Identify the Anomaly
Looking at the factors, we notice:
- The factors should ideally follow a sequence: \(3, 2, 4, 5, 6, 7\).
- However, the second factor is **2**, which disrupts the expected pattern.

### Step 5: Correct the Series
To maintain a consistent pattern, the second number should be:
- After multiplying **2** by **2**, the next number should be **4** (not **6**).
- If we replace **6** with **4**, the sequence would be:
- \(2 \times 2 = 4\)
- \(4 \times 3 = 12\)
- \(12 \times 4 = 48\)
- \(48 \times 5 = 240\)
- \(240 \times 6 = 1440\)
- \(1440 \times 7 = 10080\)

### Conclusion
Thus, the wrong number in the series is **6**.