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Prat has 128 boxes with him. He has to put atleast 120 [#permalink]

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12 Sep 2003, 23:57

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Prat has 128 boxes with him. He has to put atleast 120 oranges
in one box and 144 at the most. Find the least number of boxes which will
have the same number of oranges.

Hi, I'm new here (notice this is the first post ), but am I missing something here or is this question slightly strange?

Prat has 128 boxes. They're pretty big boxes, seeing as they hold up to 144 oranges each (I assume). He must have a truck or something .

Now he needs to figure out "the least number of boxes which will have the same number of oranges"... The same as what?

each box having the same number of oranges as each other box? in that case I suppose it would be "2", as it seems that we have an "undefined" number of oranges available to place into these boxes... except 2 is not an option.

I go with wonder_gmat's original answer: d.

Am I going nuts or does this question make no sense?

Prat has 128 boxes with him. He has to put atleast 120 oranges in one box and 144 at the most. Find the least number of boxes which will have the same number of oranges.

a) 5 b) 103 c) 6 d) Cannot be determined

let me try this...

The number of boxes containing same number of oranges will be
least when there are maximum boxes containing different number of oranges.

I can have boxes where all of them contain.. say for example...120 oranges and that would be my maximum...right. so 128 boxes is my Maximum.

Now, to have the least number of equal boxes , What do i do...i start filling each box differently...but i got only 25 different possibilities..

In other words, The maximum number of boxes that each contain different number of oranges = 25 (120 thru 144)

So now i can fill the rest of the boxes with say...120 oranges....isnt it..

Therefore the least number of boxes with same number of oranges 128-25 =103

Answer B

Last edited by Praetorian on 14 Sep 2003, 03:38, edited 1 time in total.

thanks praet..
very good question.. but i guess answer would be A) - 5 I feel u were right half way through i.e.
In other words, The maximum number of boxes that each contain different number of oranges = 25 (120 thru 144)

Now if 25 is the number of ways in which first 25 boxes will have different oranges, then i will just reapeat the same arrangement for the remaining boxes. Thus for first 125 boxes i would just repeat the same arrangement of oranges. Thus least boxes with same number of oranges would be 5.
i hope my explanation is clear, concise and idiomatic (as GMAT says... )
- Vicks

thanks praet.. very good question.. but i guess answer would be A) - 5 I feel u were right half way through i.e. In other words, The maximum number of boxes that each contain different number of oranges = 25 (120 thru 144)

Now if 25 is the number of ways in which first 25 boxes will have different oranges, then i will just reapeat the same arrangement for the remaining boxes. Thus for first 125 boxes i would just repeat the same arrangement of oranges. Thus least boxes with same number of oranges would be 5. i hope my explanation is clear, concise and idiomatic (as GMAT says... ) - Vicks

Hey vicky

Well, i did think of it before i got the solution...it appeals to the intuition too..and it may be right too.. And under time pressure, i am sure it will be hard to analyze the problem and come up with 103...

I may be wrong.. but Here is what i think..

if you repeat the arrangement , you wont have all different boxes anymore...remember we are looking for the least number of boxes with the same number of oranges...

Least number of same boxes = Total Boxes - Maximum number of different boxes

praet u wrote:
if you repeat the arrangement , you wont have all different boxes anymore...remember we are looking for the least number of boxes with the same number of oranges...

praet, what do u mean by "all different" boxes...!!
If i repeat the arrangement i land with something like this:
=> 5 boxes with 120 oranges
5 " " 121 org
5 " " 122 org.
.......
5 boxes 144 org and left over 3 boxes with whatever be in them.

With ur answer we land up with something like this:
=> 25 boxes with oranges starting from 120 to 144
& remaining 103 with 120 oranges (as u assumed). and In this case considering ur view point answer should be 104 (why to forget the one box with 120 in the first 25 boxes)

Now considering both scenarios, Question asks: Find the least number of boxes which will have the same number of oranges. still feel answer wud be 5.
I unnderstand the way u are looking at problem but even keeping that in mind answer wud be 104..
wat say.. ?
-Vicks