What should come in place of the question mark (?) in the following number series ?
`"343 , 216, ? , 64 , 27, 8"`

Options

A. 144
B. 100
C. 125
D. 136

Answer

To find the missing number in the series: `343, 216, ?, 64, 27, 8`, we can analyze the pattern of the numbers given.

**Step 1: Identify the numbers in the series.**
The series is:
- 343
- 216
- ?
- 64
- 27
- 8

**Step 2: Recognize the cubes of integers.**
We can express these numbers as cubes of integers:
- \( 343 = 7^3 \)
- \( 216 = 6^3 \)
- \( ? = ? \)
- \( 64 = 4^3 \)
- \( 27 = 3^3 \)
- \( 8 = 2^3 \)

**Step 3: Determine the pattern in the series.**
From the above, we see that the series consists of cubes of integers in descending order:
- \( 7^3, 6^3, ?, 4^3, 3^3, 2^3 \)

**Step 4: Identify the missing integer.**
The integers are decreasing by 1:
- 7, 6, ?, 4, 3, 2

The integer that comes between 6 and 4 is 5.

**Step 5: Calculate the cube of the missing integer.**
Now, we need to find the cube of 5:
- \( 5^3 = 5 \times 5 \times 5 = 125 \)

Thus, the missing number in the series is **125**.

**Final Answer: 125**

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