93, 309, 434, 498, 521, 533

Options

A. 309
B. 434
C. 498
D. 521

Explanation

To find the wrong number in the series 93, 309, 434, 498, 521, 533, we will follow these steps:

### Step 1: Calculate the Differences
First, we will calculate the differences between consecutive numbers in the series.

- Difference between 309 and 93:
\[ 309 - 93 = 216 \]

- Difference between 434 and 309:
\[ 434 - 309 = 125 \]

- Difference between 498 and 434:
\[ 498 - 434 = 64 \]

- Difference between 521 and 498:
\[ 521 - 498 = 23 \]

- Difference between 533 and 521:
\[ 533 - 521 = 12 \]

### Step 2: List the Differences
Now we have the following differences:
- 216
- 125
- 64
- 23
- 12

### Step 3: Identify the Pattern
Next, we will look for a pattern in these differences.

We notice that:
- \( 216 = 6^3 \)
- \( 125 = 5^3 \)
- \( 64 = 4^3 \)
- \( 23 \) does not fit the pattern of cubes.
- \( 12 \) also does not fit the pattern of cubes.

### Step 4: Determine the Missing Cubes
The expected pattern based on cubes would be:
- The next difference after \( 64 \) should be \( 3^3 = 27 \).
- The difference before \( 64 \) should be \( 2^3 = 8 \).

### Step 5: Find the Correct Number
Since we expect a difference of \( 27 \) after \( 498 \):
\[ 498 + 27 = 525 \]
But we have \( 521 \) in the series, which is incorrect.

### Step 6: Conclusion
Thus, the wrong number in the series is \( 521 \).

### Summary of the Solution
The wrong number in the series 93, 309, 434, 498, 521, 533 is **521**.

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