AD

BCE

From the question stem we know that ◻ and △ are single, non-negative integers.

We also see that 864 = (\(3^3\)) * (\(2^5\)), so whatever '3◻' and '2△' are they must have prime factors of only 2 and 3.

1) The sum of ◻ and △ is 10 - our symbols can be pairs of: ( {1, 9}, {2, 8}, {3, 7}, {4, 6}, {5, 5} )

Testing

31 and 29: 31 is prime, this can't be an option

39 and 21: 21 = 3 * 7, thus this can't be an option

32 and 28: 28 = \(2^2\) * 7, thus this can't be an option

38 and 22: 22 = 2 * 11, thus this can't be an option

33 and 27: 33 = 3 * 11, thus this can't be an option

37 and 23: 37 is prime, this can't be an option

34 and 26: 26 = 2 * 13, this can't be an option

36 and 24: both numbers end up with only 2 and 3 as prime factors, option valid

35 and 25: 35 = 5 * 7, this can't be an option

Combining the information from the question stem with the information from Statement 1 leaves us with 1 option - Sufficient

~~BCE~~2) The product of ◻ and △ is 24 - our symbols can be pairs of: ( {3, 8} and {4, 6} )

Testing

33 and 28: 33 = 3 * 11, thus this can't be an option

38 and 23: 23 is prime, this can't be an option

34 and 26: 26 = 2 * 13, thus this can't be an option

36 and 24: both numbers end up with only 2 and 3 as prime factors, option valid

Combining the information from the question stem with the information from Statement 2 leaves us with one option - Sufficient

~~A~~Choice D

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This took me far too long though to answer though.

Is there an easier means of testing our various number combinations like this? In hindsight I likely should've written down the numbers from 20 to 29 and 30 to 39 which prime factors were only 2 and 3, and then compared those options with each statement from there:

{24, 27, 32, 36} vs Statement 1

{24, 27, 32, 36} vs Statement 2