Johny and Jerry each picked independently a number, not necessarily an integer.
Later they rounded them up to the closest integers.
The product of the new numbers was 100.
It is obvious that you cannot guess the original numbers, but surely you can find out what could be the maximal product if the rounding was down to the nearest integer.
Please do.
Call the numbers A and B. Wlog A<B.
And we are given Ceil(A)*Ceil(B) = 100
For any non-integer x, Floor(x)=Ceil(x)-1
so lets list all possible values of Ceil(A), Ceil(B), new product.
1,100,0
2,50,49
4,25,72
5,20,76
10,10,81
-1,-100,202 <-- Maximum
-2,-50,153
-4,-25,130
-5,-20,126
-10,-10,121
The highest product comes from both numbers being negative and their floors even smaller. Therefore having A or B integers will not increase this result.
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Posted by Jer
on 2021-06-15 08:01:18 |
Solution
