If it is possible to form a number with the second, the fifth and the eighth digits of the number 3 1 5 4 9 7 8 6, which is the perfect square of a two-digit even number, which one of the following will be the second digit of that even number?

Options

A. 1
B. 4
C. 6
D. No such number can be formed

Explanation

To solve the problem, we need to follow these steps:

### Step 1: Identify the relevant digits
We are given the number 31549786. We need to identify the 2nd, 5th, and 8th digits of this number.
- 2nd digit: 1
- 5th digit: 9
- 8th digit: 6

### Step 2: Form all possible combinations of the digits
Using the digits 1, 9, and 6, we can form the following three-digit numbers:
- 196
- 169
- 916
- 961
- 619
- 691

### Step 3: Identify two-digit even perfect squares
Next, we need to check which of these combinations are perfect squares of two-digit even numbers. The two-digit even numbers are 10, 12, 14, 16, 18, etc. Their squares are:
- 10² = 100 (not two-digit)
- 12² = 144 (not two-digit)
- 14² = 196 (valid)
- 16² = 256 (not two-digit)
- 18² = 324 (not two-digit)

From our combinations, we find that 196 is the only valid perfect square of a two-digit even number (14).

### Step 4: Identify the second digit of the even number
The two-digit even number we found is 14. The second digit of 14 is 4.

### Conclusion
Thus, the second digit of the two-digit even number is **4**.

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