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What is the maximum number of rectangular cards, each 6 centimeters by

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What is the maximum number of rectangular cards, each 6 centimeters by  [#permalink]

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New post 02 Oct 2017, 01:09
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What is the maximum number of rectangular cards, each 6 centimeters by 16 centimeters that can be made from 10 rectangular pieces of cardboard, each 54 centimeters by 48 centimeters?

(A) 27
(B) 72
(C) 240
(D) 270
(E) 360

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What is the maximum number of rectangular cards, each 6 centimeters by  [#permalink]

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New post 02 Oct 2017, 04:31
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If the rectangular pieces of cardboard are placed next to each other, the total length will be 540 cm.
However the breadth remains the same - 48 cm

Therefore, the maximum number of cards possible are \(\frac{540*48}{16*6} = 90*3 = 270\)(Option D)
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Re: What is the maximum number of rectangular cards, each 6 centimeters by  [#permalink]

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New post 02 Oct 2017, 06:44
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Bunuel wrote:
What is the maximum number of rectangular cards, each 6 centimeters by 16 centimeters that can be made from 10 rectangular pieces of cardboard, each 54 centimeters by 48 centimeters?

(A) 27
(B) 72
(C) 240
(D) 270
(E) 360



First we need to check that if we cut smaller cards from the cardboard, are we able to consume the cardboard in complete, or some portion is left after cutting.

So 48/16 is completely divisible and 54/6 is completely divisible, which means if we cut 16 cm length along 48 cm breadth of the cardboard and 6 cm breadth of card along 54 cm length of cardboard, we will be able to consume the cardboard in totality.

So, From 1 cardboard the no. of cards that can be made = 54*48/(6*16) = 9* 3 = 27
So, from 10 such cardboard, total cards that will be formed = 27*10 = 270..

Note : Which solving question quickly, don't forget there are 10 cardboards, otherwise you will do mistake even after solving the question... it happens with everyone .. silly mistakes.. :)
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Re: What is the maximum number of rectangular cards, each 6 centimeters by  [#permalink]

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New post 02 Oct 2017, 07:56
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here is my thought process on analysis. Please correct me if I am wrong in my approach.

Given card
54 x 48 - This is available area

Required card
6 x 16 - This is area per piece.

If I cut a 6x16 card, I am removing 6x16 area from the original cardboard. Hence (54*48)/(6*16) = 27 pieces
Number of cardboards in hand - 10. Hence 27*10 = 270.

On some thought, I didnt think of remainders while doing this approach but if I did come across remainders I would think that they were scrap that I would throw away if I was physically cutting cardboards with scissors.

If this question were to be rephrased as how many max pieces we can make cutting circles of radius=6? or say max pieces of equilateral triangles of base 6? would my approach be right?
OR
If the question were how many 6x16 cardboards be cut from circular cardboard of radius 54? would my approach be right?
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Re: What is the maximum number of rectangular cards, each 6 centimeters by &nbs [#permalink] 02 Oct 2017, 07:56
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