Tom is going to move, he has three kinds of boxes: large, : DS Archive
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# Tom is going to move, he has three kinds of boxes: large,

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Tom is going to move, he has three kinds of boxes: large, [#permalink]

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11 Sep 2006, 19:23
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Tom is going to move, he has three kinds of boxes: large, medium, and small. Now he has already 11 large boxes, each of which is either empty or filled with 6 medium boxes. Medium boxes are filled in the large boxes and each of them is either empty or filled with 6 small boxes. Small boxes are empty and filled in the medium boxes. How many boxes does Tom have?

1). he has 56 empty boxes

2). he has 42 small boxes

Not sure on OA
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12 Sep 2006, 00:56
rkatl wrote:
Tom is going to move, he has three kinds of boxes: large, medium, and small. Now he has already 11 large boxes, each of which is either empty or filled with 6 medium boxes. Medium boxes are filled in the large boxes and each of them is either empty or filled with 6 small boxes. Small boxes are empty and filled in the medium boxes. How many boxes does Tom have?

1). he has 56 empty boxes

2). he has 42 small boxes

Not sure on OA

Nice question! Suppose x of the 11 large boxes are empty. Then he has 66-6x medium boxes. If y of the medium boxes are empty, he has 396-36x-6y small boxes, all of them empty. The total number of boxes is 473-42x-6y=473-6*(7x+y)

(1) 56 boxes are empty, so x+y+396-36x-6y=396-35x-5y=56

Thus 7x+y=340/5=68 SUFF

(2) He has 42 small boxes => 396-6(6x+y)=42 => 6x+y=59 => y= 59-6x

If x=0, y=59 and we have 473-6*59= 119 boxes
If x=9, y=5, and we have 413-6*68=65 boxes

NOT SUFF

I choose A

Last edited by kevincan on 12 Sep 2006, 01:40, edited 1 time in total.
Re: DS:interesting one...   [#permalink] 12 Sep 2006, 00:56
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# Tom is going to move, he has three kinds of boxes: large,

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