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

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A certain number of desks and bookshelves, at least one each, are to  [#permalink]

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New post 07 Jul 2017, 00:39
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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

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Re: A certain number of desks and bookshelves, at least one each, are to  [#permalink]

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New post 07 Jul 2017, 01:26
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)
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A certain number of desks and bookshelves, at least one each, are to  [#permalink]

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New post 07 Jul 2017, 20:16
Bunuel wrote:
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

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!
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Re: A certain number of desks and bookshelves, at least one each, are to  [#permalink]

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New post 07 Jul 2017, 21:55
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
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Re: A certain number of desks and bookshelves, at least one each, are to  [#permalink]

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New post 08 Jul 2017, 06:08
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
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A certain number of desks and bookshelves, at least one each, are to  [#permalink]

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New post 08 Jul 2017, 07:04
Bunuel wrote:
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

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. :-(
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A certain number of desks and bookshelves, at least one each, are to   [#permalink] 08 Jul 2017, 07:04
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