CAT 2001 | Question: 6

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. $5$
• B. $103$
• C. $6$
• D. Cannot be determined

Answer 1

Each box can have at least 120 and a maximum of 144 oranges.

i.e. totally 25 combinations. i.e. A box can have 120, another box can have 121, next box 122 and so on. Hence there can be 25 boxes with different number of oranges.

There are totally 128 boxes. 

25*5  = 125, hence there will be minimum 5 boxes similar for sure.

128 – 125 = 3, we have 3 more boxes remaining.

These 3 boxes have to be any one of the possible 25 boxes.

Hence,the number of boxes containing the same number of oranges is at least=3!=6

Hence,Option(C)6 is the Answer.

Answer 2

Option 4 cannot be determined

Bcz I guess we need total no. Of oranges in all 128 boxes