Explanation:

Let’s break it down.

- You’re looking for a pattern connecting these pairs: 396 : 24, ? : 28, and 672 : 30.

- First, look for the relationship between each number in the given pair.

- 396 ÷ 24 = 16.5 — okay, but that’s not an integer. Might be something else.

- Factor sum? Let’s check: The sum of the digits of 396 is 3+9+6=18. Not matching 24. Let’s try prime factors:

- 396 = 2×2×3×3×11.

- Number of factors? Factors of 396 are 12—but this doesn’t fit.

- Maybe 396/24 = 16.5, 672/30 = 22.4. Not matching, let's try subtracting.

- 396-24=372. 672-30=642. Nothing.

- Hang on, let's look for divisor factorization. Let’s check if 396/24 and 672/30 have a simple relationship to 28.

- 672 : 30. 672/30 = 22.4. 672/28 = 24.

- 396/28 = 14.14 (not an integer).

- Maybe try reverse:

- 24×16.5=396, 30×22.4=672.

- What’s missing in the middle? Let's check which option, when divided by 28, yields a simple value:

- 504 ÷ 28 = 18

- 572 ÷ 28 = 20.428...

- 588 ÷ 28 = 21

- 536 ÷ 28 = 19.142...

- Now, compare: See the gap between outputs:

- 24 (first), 28 (middle), 30 (last)

- The “other” number might rise by +4 then +2

- So, look at the ratio.

- For the pairs, the actual pattern is 396/24=16.5, ?/28=?, 672/30=22.4.

- What if we try 588 (from options) for ?

- 588 ÷ 28 = 21, and that fits the pattern: 16.5 > 21 > 22.4

- Look at the increments between the ratios: 16.5 to 21 (+4.5), 21 to 22.4 (+1.4)

- So, the most logical answer is:

Option 3: 588

Quick summary:

- The missing number that fits the pattern is 588.

- It matches the progression in the ratios across the sets.

- 588 divided by 28 gives a whole number (21), aligning perfectly with 396:24 (16.5) and 672:30 (22.4) as a logical sequence.

Your pick (572) doesn’t fit the sequence as smoothly as 588.