Grades 3-4 Video Solutions 2012-2012_3-4

Video Transcription

Problem number 19. Gregory forms two numbers with the digits 1, 2, 3, 4, 5, and 6. Both numbers have three digits, and each digit is used only once.  He has these two numbers. What is the greatest sum Gregory can get? These are three digit numbers, and the way we are going to get the biggest number  is by making the 100th digit the biggest, the 10th digit the second biggest, and the 1st digit the lowest.  So for the 100th digits we have 5 and 6, and it does not matter which number gets which numbers. For the 10th digit, we go 4 and 3. It doesn't matter which number these go to.  And then for the 1st digit, we have 2 and 1. Again, these do not matter where they go. Now we are going to add them together. So we have 3, and then 7, and then...  Which means our total is 1,173. Which means our answer is D.

Video Summary

Gregory forms two three-digit numbers using the digits 1, 2, 3, 4, 5, and 6, each used only once. To maximize their sum, he arranges the digits to create the largest possible hundreds, tens, and units places. Using 5 and 6 for the hundreds digit, 4 and 3 for the tens digit, and 2 and 1 for the units digit, he calculates the sum: 654 + 521 = 1,173. Thus, the greatest possible sum Gregory can achieve is 1,173.

Keywords

three-digit numbers

maximize sum

digit arrangement

greatest sum

Gregory