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

Question

A certain number of desks and bookshelves, at least one each, are to be placed along a library wall that is 16 meters long. Each desk is 2 meters long, and each bookshelf is 1.5 meters long. If the maximum possible number of desks and bookshelves are to be placed along the wall, then the space along the wall that is left over will be how many meters long?

(A) 0.5
(B) 1.0
(C) 1.5
(D) 2.0
(E) 3.0

(A) 0.5
(B) 1.0
(C) 1.5
(D) 2.0
(E) 3.0

pushpitkc · Answer

Let the number of desks of x and the number of book shelves be y.
From the data in the question, the desk is 2 meters long and the book shelf is 1.5 meters long.

Also, the total length of the library wall is 16 meters.

So, the equation that will be formed is 2x + 1.5y should be as close to 16.
If x=4,y=5, 2x + 1.5y = 15.5(which is 0.5 less) (Option A)

generis · Answer

We have 16 meters of space that we want to fill as fully as possible ("maximum number" of desks and bookshelves).

I started with the equation 2D + 1.5B = 16 ... But that didn't look promising.

So I worked from the answer choices, trying to get 0.5.

Maximize one kind of furniture and minimize the other.

You can have 7 desks and 1 bookshelf:
 
(7 * 2) + (1 * 1.5) = 15.5, leaving 0.5 meters.

Or you can have 9 bookshelves and 1 desk:

(9 * 1.5) + (1 * 2) = 15.5, leaving 0.5 meters.
 
Answer A

pushpitkc  got yet another combination that has nothing to do with maximum and minimum. I don't know what to think about this problem!

amanvermagmat · Answer

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

brs1cob · 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

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

answer is A

generis · Answer

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. :-(

Awa327 · Answer

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.

IanStewart · Answer

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?".

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards