Explanation:

Let’s break it down, starting with your original set: (16, 12, 32).

- Look for a pattern. 16 – 12 = 4, and 16 + 12 = 28, but 32 doesn’t fit cleanly there. Try this: 16 * 2 = 32, and 12 is 16 - 4. Still, not a direct match. But if you see: First number is multiplied by 2 = third number (16 * 2 = 32), the middle number? It’s irrelevant to the operation from first to third.

- So the real pattern is: Third number = First number × 2

Now, let’s test the options:

- Option 1: (20, 15, 42) ? 20 * 2 = 40 (not 42)

- Option 2: (76, 57, 176) ? 76 * 2 = 152 (not 176)

- Option 3: (36, 27, 77) ? 36 * 2 = 72 (not 77)

- Option 4: (56, 24, 68) ? 56 * 2 = 112 (not 68)

None fit the exact “first×2 = third” pattern. But wait—let’s check if any match another operation. Take the differences:

- Option 1: 20 + 22 = 42

- Option 2: 76 + 100 = 176 (odd jump)

- Option 3: 36 + 41 = 77

- Option 4: 56 + 12 = 68

But all of these are inconsistent with the original set.

So, what’s really happening in (16, 12, 32)? Check if it’s first + second = third. 16 + 12 = 28 (not 32). Or maybe first, second, first×2? That would fit.

So, in all options, see who follows the idea of third being double the first:

- None fit.

- But if the expected answer is Option 3, let's see: (36, 27, 77). 36 × 2 = 72, but third is 77, so it doesn’t work.

The logic seems off for all choices, but based on the most direct pattern of “third = first×2,” none are a perfect fit. If you have to pick closest, none directly match. If there's a different pattern you see, let me know. But with the info given, the answer isn’t Option 3.