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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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20 Sep 2008, 11:52
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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

I have got the answer but is there any short cut to do these kind of questions???
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20 Sep 2008, 23:49
vivektripathi 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

I have got the answer but is there any short cut to do these kind of questions???

(2)clearly answers since if count of small boxes is known we can get the rest
1)this needs to be worked ,
we want total numbr of medium boxes > tital number of empty medium boxes
Total medium=TM
say empty medium = EM
empty large=EL
now (11-EL )*6 = TM >EM
EM+EL=56 =>(11-EL)*6>=56-EL => EL<2 => EL=2 or 1 hence again two boxes => hence both the cases count of total number of boxs varies !!!
IMO B
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21 Sep 2008, 07:35
IMO C, using stmt 2 you can only find out that number medium boxes filled is 7. It does not tell you how many large boxes are filled.

The solution goes like this:
stmt 1 says 56 empty boxes, which can be written as

11-FL + 6FL-FM + 6FM = 56

where FL = filled large and FM = filled medium

FL + FM = 9

from stmt 2 we get that FM = 7, hence FL = 2

What is the OA?
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21 Sep 2008, 08:51
C

Without statement 1 the Number of medium filled/not filled can vary, leading to a differenet number of boxes.

With 1 and 2 I found boxes = 65
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25 Sep 2008, 07:39
I am getting D.

Both statements are sufficients.

The statements are very tricky. So, please correct me if I am wrong.

Large Box and Midum Box are either empty or filled with 6 boxes medium and small respectively.

Small boxes can not be empty.

So, from st1: 56 boxes are empty.

Let's start with Large box. We have total 11 boxes. So we can fill 66 medium boxes.

If only one Large box filled then 10 Large box is empty. so there has to be 60 medium boxes empty. So, 10 + 60 = 70 not equal to 56.

So if two large box filled then , 9 large and 54 medium boxes are empty. Total 63 which is not equal to 56.

Now if 3 large box filled then 8 large box and 46 medium boxes are empty. Total 56 boxes are empty so we can count total boxes.

As each medium box has another 6 small boxes.

Same with St2: 42 boxes are small box. So we can figureout medium boxes and same with Large boxes.

So I believe both statements are sufficients.

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25 Sep 2008, 08:38
Twoone wrote:
I am getting D.

Both statements are sufficients.

The statements are very tricky. So, please correct me if I am wrong.

Large Box and Midum Box are either empty or filled with 6 boxes medium and small respectively.

Small boxes can not be empty.

So, from st1: 56 boxes are empty.

Let's start with Large box. We have total 11 boxes. So we can fill 66 medium boxes.

If only one Large box filled then 10 Large box is empty. so there has to be 60 medium boxes empty. So, 10 + 60 = 70 not equal to 56.

So if two large box filled then , 9 large and 54 medium boxes are empty. Total 63 which is not equal to 56.

Now if 3 large box filled then 8 large box and 46 medium boxes are empty. Total 56 boxes are empty so we can count total boxes.

As each medium box has another 6 small boxes.

Same with St2: 42 boxes are small box. So we can figureout medium boxes and same with Large boxes.

So I believe both statements are sufficients.

Question says "small boxes are empty"
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25 Sep 2008, 09:20
Thanks Suresh.

I agree with you..
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27 Sep 2008, 01:20
i get c.

the thing is that small boxes must be empty- so the equation is

(11-x/6) + (x-7) + 42 = 56
large&empty medium&empty small&empty total empty

where x is the number of medium boxes.

=> x=12

=> total boxs = 65

thus- the right answer is C
Re: DS - Tricky   [#permalink] 27 Sep 2008, 01:20
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