Explanation:

Alright, let’s take a smart, direct look at this.

First, the given set: (9, 21, 124)

- Let’s try to connect the numbers. Notice:

9 × 21 + (9 + 21) = 189 + 30 = 219 (not matching)

Try: 9² + 21² = 81 + 441 = 522 (nope)

Maybe: 9 × 21 - 9 = 189 - 9 = 180 (not it)

How about: (9 + 21) × 4 = 120 (close to 124)

Let’s check another: 9 × 21 + 9 + 21 + [some operation], still no.

- Another option: 9 × (21 - 9) = 9 × 12 = 108 (no)

- One more: 9 × 21 + 1 × 4 = 189 + 4 = 193 (no)

Let’s look for a pattern in options:

Option 1: (5, 16, 220)

- 5 × 16 + (5 + 16) = 80 + 21 = 101

- 5² + 16² = 25 + 256 = 281

- (5 + 16) × 4 = 21 × 4 = 84

Option 2: (14, 58, 112)

- 14 × 58 + (14 + 58) = 812 + 72 = 884

- (14 + 58) × 4 = 72 × 4 = 288

Option 3: (11, 64, 131)

- 11 × 64 + (11 + 64) = 704 + 75 = 779

- (11 + 64) × 4 = 75 × 4 = 300

Option 4: (17, 37, 220)

- 17 × 37 + (17 + 37) = 629 + 54 = 683

- (17 + 37) × 4 = 54 × 4 = 216 (getting closer—very close to 220)

But hang on. None are quite 124 with those methods.

Now, let's shift gears—maybe something factorial or exponential.

Check the given pair: (9, 21, 124)

- 9³ - 21 = 729 - 21 = 708 (no)

- 9 × 21 + (9 × 2) = 189 + 18 = 207 (no)

- How about: (9 + 21)4? That’s 304, which is way too big.

Let’s try adding squares and subtracting one:

- (9 × 21) + (9²) = 189 + 81 = 270

Let’s check if the pattern could be: Third number = First number × Second number + First number

For the given set:

9 × 21 = 189; 189 + 9 = 198 (not matching)

Different approach: Third number = first × second - first

9 × 21 = 189; 189 - 9 = 180

This isn’t working.

Let’s look at the difference between the first and second numbers:

21 - 9 = 12

Check if 124 divided by 12 is close to 10: 124 / 12 = 10.33 (nope)

Let’s try:

Third number = first × (second + third number) / something

Out of curiosity, what about option 1—(5, 16, 220):

5, 16 — difference is 11, 220/11 = 20

But, let's try cubes:

- 9³ + 21 = 729 + 21 = 750

- 9³ - 21 = 729 - 21 = 708

Try cubes for others:

- 5³ + 16 = 125 + 16 = 141

- 17³ + 37 = 4913 + 37 = 4950

Try sum of cubes:

- 9³ + 21³ = 729 + 9261 = 9990

Hmm. What about something like first × second + first × second = 2 × 189 = 378

Alright, let's look for a pattern in the third number across options.

Option 1: 5, 16, 220

- 5 × 16 = 80

- 80 × 2 = 160 (no)

- 16 × 5 = 80, add 16 + 5 = 101, still not 220

Option 2: 14, 58, 112

- 14 × 58 = 812, way more than 112

Option 3: 11, 64, 131

- 11 × 64 = 704, again, way more than 131

Option 4: 17 × 37 = 629

Wait, but 124... if I check:

Is 21 × 6 = 126; 124 is 2 less, not fitting

Let’s try this:

Is 124 = (9 + 21) × 4 = 30 × 4 = 120 (very close, just off by 4—maybe it’s (sum × 4) + 4:

(9 + 21) × 4 + 4 = 120 + 4 = 124

Let’s try that with the options:

Option 1: (5 + 16) × 4 + 4 = 21 × 4 + 4 = 84 + 4 = 88

Option 2: (14 + 58) × 4 + 4 = 72 × 4 + 4 = 288 + 4 = 292

Option 3: (11 + 64) × 4 + 4 = 75 × 4 + 4 = 300 + 4 = 304

Option 4: (17 + 37) × 4 + 4 = 54 × 4 + 4 = 216 + 4 = 220

Here’s the thing—the only option matching the pattern is Option 4.

- Direct calculation:

- Sum the first two numbers, multiply by 4, then add 4.

- (A + B) × 4 + 4 = C

Let’s recap:

- Option 4: (17 + 37) × 4 + 4 = 220

- All other options, the math doesn’t fit

So, to sum up:

- Only option 4 follows the same logic as the original set.

- Option 4: (17, 37, 220) is correct.

Option 4 is the answer.