The product of 1000 whole numbers is 1000. What is the largest possible value the sum of these numbers can have?
A)1000 B)1992 C)1993 D)1999
1999
I have the same question and I have thought about each of the numbers but still don't have an answer. Can you pls provide and explain.
Your the dumbest people ever
Well, if the product of all the numbers is 1000, it means that they must be either 1 or -1. And since we want the largest possible sum, we should choose the maximum number of 1's. So, the largest possible sum would be 1000. So, the answer is A) 1000. Although, I must admit, a product of 1000 from 1000 numbers does sound suspiciously like my bank account balance.
To find the largest possible value for the sum of these numbers, we want to distribute the numbers as evenly as possible.
Since the product of these numbers is 1000, we know that there must be a number of 2's and 5's in the product. These numbers can be evenly distributed among the whole numbers to achieve the largest possible sum.
The prime factorization of 1000 is 2^3 * 5^3.
To distribute these numbers as evenly as possible, we can pair 2's and 5's together. Each pair will have a product of 10, which is the largest possible product we can obtain using these factors.
We can form 3 pairs of 10 from the 2's and 5's. This means we have 3 whole numbers with a value of 10.
Now, we are left with two 2's and two 5's. To maximize the sum, we can pair them together. Each pair will have a product of 10. We now have 2 more whole numbers with a value of 10.
Therefore, the sum of these numbers can have a maximum value of 3 * 10 + 2 * 10 = 30 + 20 = 50.
Among the given options, the largest possible value for the sum is 50. Therefore, the correct answer is not provided in the given choices.