Of 128 boxes of oranges, each box contains at least 120 and at most 14

Question

Of 128 boxes of oranges, each box contains at least 120 and at most 144 oranges. The number of boxes containing the same number of oranges is at least
A. 97 
B. 103
C. 12
D. 6
E. 17

chetan2u · Answer

Since it is at least, we look at the worst scenario.
 
All have same number of oranges, so 144-120+1 or 25 integer values as number of possible oranges in each box and number of box that will have same number of oranges=128/25 = 5.1 boxes. 
This means at least 6 as 5.1 will go to next integer 6.So even if we distribute oranges event, there will be at least 6 boxes having same number of oranges

D

quantrace · Answer

I don't understand this answer, there are not 128 oranges, there are 128 BOXES of oranges, and each contains 120 to 144 oranges EACH, so I don't think the reasoning of 6 oranges per box is correct.

Here is what I did:

The possible number of oranges per box is between 120 and 144, that is, there are 25 different options for each box (144-120+1). The question asks what is the minimum number of boxes that will all have the same number of oranges per box. Therefore, if we divide 128/25 = 5.1 means that each of the available 25 options can be assigned to 5.1 boxes each, and you round it up to 6 boxes since it must be an integer value. This is the minimum number of boxes that will all have the same number of oranges: 6 boxes will have 120 oranges EACH, 6 boxes will have 121 oranges EACH, 6 boxes will have 122 oranges EACH... etc.

TestPrepUnlimited · Answer

The range of 120 to 144 is  144 - 120 + 1 = 25 .

However, we need to distribute  128  boxes among  25  numbers.

So that means we will have to hit each of the  25  numbers five times at least, since  128/25 = 5  with a remainder of 3. The remaining 3 boxes will hit any 3 numbers for a sixth time, therefore we must see at least six boxes with the same number of oranges.

Ans: D

Feb2024 · Answer

MartyMurray gmatophobia Bunuel KarishmaB @IanStewart

Hello Experts! Can you explain this question in simple terms. The wording of the question is unclear and is inconsistent with the OA.

Thanks in Advance

MartyMurray · Answer

The question is rather unclear. So, you can't expect to make sense of it.

To get some use out of it, you could play around with a few different ideas of what it's meant to ask and figure out how to answer it.

KarishmaB · Answer

There are 128 boxes with oranges in them. 
Each box has at least 120 oranges and at most 144 oranges (so a box can have 120 or 121 or 122 or ... 144 oranges)
So the number of oranges in a box can take 25 different values (from 120 to 144).

Of 128 boxes, say
5 boxes have 120 oranges.
1 box has 121 oranges.
2 boxes have 122 oranges
etc...

Essentially, you have to distrubute these 25 numbers (from 120 to 144) to 128 different boxes. 
Of course multiple boxes will get the same number since there are only 25 distinct numbers.

To  minimize the number of boxes that have the same number of oranges, we should distribute the numbers evenly a smuch as possible. 
So each number should be given to 5 boxes. But we will still have 3 boxes left. Hence 3 numbers should be given to these 3 boxes. 
So at least 6 boxes will have the same number of oranges.

Answer (D)

bumpbot · Answer

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Of 128 boxes of oranges, each box contains at least 120 and at most 14

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Of 128 boxes of oranges, each box contains at least 120 and at most 14

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