Explanation:

Let’s break it down.

First, look at the original sets:

(8, 388, 18)

(11, 137, 4)

We're told not to break the numbers apart, so think: what operation links the first and third numbers to make the second? Try plugging things in:

- 8 × 18 = 144 (not 388)

- 8 + 18 = 26

- 8 × something (but not 18) = 388

- 8 × 18 + something? Let's check: 8 × 18 = 144. 388 – 144 = 244. Not a direct relation.

Reverse:

- 388 ÷ 8 = 48.5

- 388 ÷ 18 = 21.555

- 388 – 8 = 380

- 388 – 18 = 370

Maybe try:

Is 388 divisible by 8 or 18? No.

Try squaring or similar:

- 8² = 64

- 18² = 324

Then, 8² + 18² = 64 + 324 = 388

—this fits!

Now, (11, 137, 4)

11² = 121, 4² = 16. 121 + 16 = 137

—Bingo, same relationship.

They’re using: (a, b, c) ? a² + c² = b

Now, check your options:

Option 1: (15, 230, 2)

15² = 225, 2² = 4, 225 + 4 = 229 Not 230.

Option 2: (3, 51, 7)

3² = 9, 7² = 49, 9 + 49 = 58 Not 51.

Option 3: (10, 118, 9)

10² = 100, 9² = 81, 100 + 81 = 181 Not 118.

Option 4: (14, 221, 5)

14² = 196, 5² = 25, 196 + 25 = 221

This follows the same pattern.

So, your logic is straight on point here.

Correct Answer:

Option 4 (14, 221, 5)

- The rule: a² + c² = b, do not split numbers into digits.

- Only option 4 fits.

- The question is all about recognizing the sum of perfect squares.

Simple as that.