A certain number of desks and bookshelves, at least one each, are to

Since a desk occupies 2m and a bookshelf occupies 1.5m, we should try to maximise the amount of bookshelves (to maximise the overall number). But there should be at least 1 desk also. So lets first place one desk, it will occupy 2m space.

In the remaining space, we should now try to place all bookshelves. Remaining space is 16-2 = 14m.
Number of bookshelves possible in 14m = 14/1.5.. This gives a quotient of 9 and a remainder of 0.5

So 9 bookshelves can be arranged in 14m space. The leftover space will thus be 0.5m. Hence A answer

since the question is giving us a condition that the number of desks and bookshelves should be maximum, we need to keep the maximum number of bookshelves and a minimum number of desks . so we can place maximum 9 bookshelves and 1 desk and after this, we are left with only 0.5 m.

so answer is 16 -9*1.5 -2 = .5m.

answer is A

In the replies so far, we have:

4 desks and 5 bookshelves = 15.5 pushpitkc

7 desks and 1 bookshelf = 15.5 (from me)

9 bookshelves and 1 desk = 15.5 (from me) and amanvermagmat and brs1cob

The first has nothing to do with maximizing either piece of furniture, which makes sense upon reflection because the question doesn't exactly ask for maximum number of pieces of furniture - it asks for maximum length that can be created with those pieces of furniture.

If number of pieces of furniture were the key, we should not have total 9, 8, and 10, respectively, that all yield the correct answer.

I've thought about remainders, divisibility, ratio of desk length to bookshelf length ...

I can't see the pattern.

Hi Bunuel, VeritasKarishma, I think there are two possible answers to this, one which is in the options and one which isn't:

To maximize the number of bookshelves and tables ensuring 1 of each, let us consider 1 of the longer one (i.e., the table) and maximize the shorter one (i.e., the bookshelf).

Thus, 2(1) + (1.5)(8) = 2 + 12 = 14m

That leaves 2m yet to be filled.

This 2m can either be filled by 1.5m length bookshelf or a 2m length table, both ways the maximum number of bookshelves and tables would be 10.

If a table is used, then space remaining = 0m (i.e., 8 bookshelves + 2 tables)
If a bookshelf is used, then space remaining = 0.5m (i.e., 9 bookshelves + 1 table)

Thus, I think two answers are possible. This might make a good data sufficiency question.

Let me know what you think or if there's something wrong in my approach.

Yes, you're right - we can certainly maximize the number of pieces of furniture while leaving no unused space at all. There isn't a unique answer to the question, and there needs to be to any PS question unless one answer choice says "cannot be determined", or unless the question asks "how much space could be left over?".