Grades 9-10 Video Solutions 2025-2025_9-10

Video Transcription

Problem 8. The 4-digit number 8, 0, blank, blank is missing its last 2 digits. This number is divisible by 8 and 9. What is the product of the 2 missing digits? So we know that the  number is divisible by 9, and this means that its sum, the sum of its digits, is divisible by 9. So because 8 plus 0 is 8 mod 9, then the sum of the 2 missing digits needs to be  1 mod 9, so that the sum of all the digits is 0 mod 9. We also know that because the number is divisible by 8, the last 3 digits have to be divisible by 8. But since the first  of the last 3 digits is a 0, this means that just the missing 2 digits needs to be divisible by 8. Now, we can go through all the multiples of 8 that are 2 digits and see which one  of them is 1 mod 9, and the only answer that we find is 64. So the product of 6 times 4 is 24, and our answer is D.

Video Summary

Problem 8. The 4-digit number 8, 0, blank, blank is missing its last 2 digits. This number is divisible by 8 and 9. What is the product of the 2 missing digits? So we know that the number is divisible by 9, and this means that its sum, the sum of its digits, is divisible by 9. So because 8 plus 0 is 8 mod 9, then the sum of the 2 missing digits needs to be 1 mod 9, so that the sum of all the digits is 0 mod 9. We also know that because the number is divisible by 8, the last 3 digits have to be divisible by 8. But since the first of the last 3 digits is a 0, this means that just the missing 2 digits needs to be divisible by 8. Now, we can go through all the multiples of 8 that are 2 digits and see which one of them is 1 mod 9, and the only answer that we find is 64. So the product of 6 times 4 is 24, and our answer is D.

Keywords

divisibility

4-digit number

missing digits

product

multiples of 8