Find the wrong number in the following number series.
124,140,108,156,92,172,78

Options

A. 108
B. 124
C. 78
D. 92

Answer

To find the wrong number in the series 124, 140, 108, 156, 92, 172, 78, we will analyze the pattern of the series step by step.

### Step 1: Identify the pattern
First, observe the series:
- 124, 140, 108, 156, 92, 172, 78

We can see that the series alternates between increasing and decreasing numbers.

### Step 2: Separate the increasing and decreasing sequences
- **Increasing sequence**: 124 to 140, then 108 to 156, and finally 92 to 172.
- **Decreasing sequence**: 140 to 108, then 156 to 92, and finally 172 to 78.

### Step 3: Find the differences
Now, let’s calculate the differences between the numbers in the increasing and decreasing sequences.

**Increasing sequence:**
1. From 124 to 140:
- 140 - 124 = 16
2. From 108 to 156:
- 156 - 108 = 48
3. From 92 to 172:
- 172 - 92 = 80

**Decreasing sequence:**
1. From 140 to 108:
- 140 - 108 = 32
2. From 156 to 92:
- 156 - 92 = 64
3. From 172 to 78:
- 172 - 78 = 94

### Step 4: Analyze the differences
We can see that the increasing sequence has a consistent pattern of adding 16, but the decreasing sequence does not follow a consistent pattern.

### Step 5: Check the expected values
If we follow the pattern:
- After 124 (increase by 16) → 140
- After 140 (decrease by 32) → 108
- After 108 (increase by 48) → 156
- After 156 (decrease by 64) → 92
- After 92 (increase by 80) → 172
- After 172 (decrease by 94) → should be 78

### Step 6: Identify the wrong number
Now, we can see that if we decrease 172 by 94, we should get:
- 172 - 94 = 78 (which is correct)

However, if we check the decrease from 156 to 92:
- 156 - 64 = 92 (which is correct)

But if we check the expected decrease from 108:
- 108 - 16 = 92 (which is not correct)

Thus, the number 78 seems to be incorrect in the series.

### Conclusion
The wrong number in the series is **78**.

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