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
(1) 5 (2) 103 (3) 6 (4) Cannot be determined

Answer 1

Answer:

It is given that the number of orange boxes is 128.

However, it is not given that these 128 boxes contain how many oranges, that is , the total number of oranges are not given.

Only a range is given, that is 120-144 oranges are present in each box.

So, let first box contain 120 oranges. Since, we are asked for least boxes, that is, minimum boxes must contain same number of oranges.

So, let each box contain difference number of oranges. Box 1 contains 120 oranges, box 2 contain 121 oranges and 25th box contains 144 oranges.

So, now 25th box will have any number of oranges between 120 and 144 and this.

Now , in a total of 50 boxes, 2 boxes have same number of oranges.

Further, 25 boxes will be covered and then 3 boxes will have same number of oranges.

In another 25 boxes, that is a total of 100 boxes, 4 boxes will have same number of oranges.

In 125 boxes, 5 boxes will have same number of oranges.

Now , 126th, 127th and 128th boxes will again repeat any number of oranges.

Hence, a total of 6 boxes will have same number of oranges.

so, the answer is 6.

Answer 2

Answer:

6

Step-by-step explanation:

Here we are asked for ATLEAST , so we need to evaluate for possible scenario where there is least duplication in number of oranges in the box.

So we consider the distribution equi- probable starting from Box 1 and assigning 120 to 144 and then again starting from 120.

Consider boxes and below & number of oranges in it:-

Box 1 -> 120

Box 2 -> 121

Box 3 -> 122

So on..

Box 24 -> 143

Box 25 -> 144

Box 26 - > 120 -- We start again from 120 oranges

Box 27 -> 121

So on..

Box 50 -> 144

Box 51 -> 120

And So On...

Box 76 -> 120

Box 101 -> 120

Box 126 -> 120

So total 6 boxes.