31. 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-
31. 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-
The correct option is C c) 5
Ans:31) (c) This is a typical Pigeon-hole principle problem. We have 128 boxes that can have 120, 121..... 144 oranges.If we start filling the boxes with 120, 121, 122..... 144 oranges, we will be able to fill 25 boxes with distinct number of oranges.
The remaining boxes will have a non-distinct number of oranges. Hence, we can fill 25 × 5 = 125 boxes with the number of oranges from 120 to 144 (both inclusive), i.e. 5 boxes having the same number of oranges. There are however 3 more boxes. If we start from 120 oranges again, we will have 6 boxes containing 120, 121 and 122 oranges each.
∴ the minimum number of boxes is 6.
Hence c, the third digit has to be 5
c) 5
Ans:31) (c) This is a typical Pigeon-hole principle problem. We have 128 boxes that can have 120, 121..... 144 oranges.If we start filling the boxes with 120, 121, 122..... 144 oranges, we will be able to fill 25 boxes with distinct number of oranges.
The remaining boxes will have a non-distinct number of oranges. Hence, we can fill 25 × 5 = 125 boxes with the number of oranges from 120 to 144 (both inclusive), i.e. 5 boxes having the same number of oranges. There are however 3 more boxes. If we start from 120 oranges again, we will have 6 boxes containing 120, 121 and 122 oranges each.
∴ the minimum number of boxes is 6.
Hence c, the third digit has to be 5
