Grades 11-12 Video Solutions 2022-2022_11-12

Video Transcription

How many positive three-digit integers are divisible by 13?  So first, we know that 13 times 7 is 91 and that 13 times 8 is 104. So that means we have to start at 13 times 8. Multiplying this guy by 10, we have that 13 times 70 is 910.  And adding 13 times 7 on both sides, we have that 13 times 77 is 1001.  That means we have to go from 13 times 8 all the way up to 13 times 76,  which is the last three-digit number we're considering. For a total of 76 minus 8 plus 1 is 69 numbers.  That means our answer is B.

Video Summary

The problem is to find how many three-digit integers are divisible by 13. The first three-digit integer divisible by 13 is 104 (13 times 8), and the last is 988 (13 times 76). Therefore, the range of these integers is from 104 to 988. Calculating the number of these integers, we have 76 − 8 + 1, which equals 69. Thus, there are 69 positive three-digit integers divisible by 13.