jamifahad wrote:
Suppose five circles, each 4 inches in diameter, are cut from a rectangular strip of paper 12 inches long. If the least amount of paper is to be wasted, what is the width of the paper strip?
(A) 5
(B) 4+2\(\sqrt{3}\)
(C) 8
(D) 4(1+\(\sqrt{3}\))
(E) 12
First, think what they mean by 'least amount of paper is to be wasted'? Since the dimension of the circles is given, perhaps what they mean is that the width of the paper used must be minimum since the leftover paper will be wasted. So how will you place the 5 circles? The diameter of the circles is 4 each and the length of the paper is 12 so you can place 3 circles neatly across the length. The other two must be placed in a way which reduces width of the paper, which means between two circles rather than edge to edge.
Attachment:
Ques4.jpg [ 23.97 KiB | Viewed 2474 times ]
Once the diagram is ready, the solution is self explanatory. The equilateral triangle in the middle has side 4 because the sides are formed by 2 radii. The width of the paper is the sum of dashed lines, the regular ones are 2 each (radii of circles) and the bold one is the altitude of the equilateral triangle \(= \sqrt{3}*4/2 = 2*\sqrt{3}\).
So width \(= 2 + 2*\sqrt{3} + 2 = 4 + 2*\sqrt{3}\)
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Karishma
Veritas Prep GMAT Instructor
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