Essentially, we only care about the ratio of desks to tables from the Madison warehouse. The ratio of the chairs to the tables or the desks is irrelevant.

Therefore, the ratio we want to look at is Desks:Tables = 5:9.

So, at the Madison wearhouse, we can have:
5 desks and 9 tables
10 desks and 18 tables
15 desks and 27 tables
and so on.

Notice the total number of furniture are multiples of 14:
5 desks and 9 tables = 14 total
10 desks and 18 tables = 28 total
15 desks and 27 tables = 42 total
and so on.

So if we send any multiple of 14 total pieces of furniture to the York Warehouse, this should increase their inventory by 20%.

This can be written as:
[Inventory Before Transfer](1.2) = [Inventory After Transfer]

Example:
10(1.2) = 12 (20% increase from 10 to 12)
100(1.2) = 120 (20% increase from 100 to 120)
*note we are not using the multiple of 14 restriction here*

And it'll be helpful to have this equation, just to conceptually understand what's going on:
[Inventory After Transfer] - [Inventory Before Transfer] = [Some multiple of 14 (pieces of furniture sent from Madison Warehouse)]

Example:
14 - 0 = 14 (14 is a multiple of 14)
140 - 14 = 126 (126 is a multiple of 14)
*note we are not using the restriction of 20% increase here*



I used backsolving and both equations above to get the answers:
(I'll denote [Inventory Before Transfer] as I_B, and plug in the answer choices to [Inventory After transfer])


A. 168 ...->... (I_B)(1.2) = 168 ...->... I_B = 140 ...->... 168 - 140 = 28 ...->... 28 is a multiple of 14, so A works (10 desks and 18 tables)

B. 280 ...->... (I_B)(1.2) = 280 ...->... I_B = 233.3333 ...->... The Inventory from before cannot be a decimal, so B does not work.

C. 290 ...->... (I_B)(1.2) = 290 ...->... I_B = 241.6667 ...->... The Inventory from before cannot be a decimal, so C does not work.

D. 336 ...->... (I_B)(1.2) = 336 ...->... I_B = 280 ...->... 336 - 280 = 56 ...->... 56 is a multiple of 14, so D works (20 desks and 36 tables)

E. 504 ...->... (I_B)(1.2) = 504 ...->... I_B = 420 ...->... 504 - 420 = 84 ...->... 84 is a multiple of 14, so E works (30 desks and 54 tables)

F. 600 ...->... (I_B)(1.2) = 600 ...->... I_B = 500 ...->... 600 - 500 = 100 ...->... 100 is not a multiple of 14, so F does not work

So the answers are A,D, and E