Grades 9-10 Video Solutions 2014-Grades 9-10 Video Solutions 2014 problem5

Video Transcription

Question number 5. In the number 2014, the last digit is bigger than the sum of the other three digits. How many years ago did this last occur? We see that the answers here are  pretty small, so we can just count backwards in time and check which year and how many years ago that was satisfies our property. So one year ago we had 2013 and here the sum  of the first three digits gives us 3 and that is equal to 3, so this is not what we want. We go to 2012 and here we have again 3 is bigger than 2, so that's not what we want.  2011, we have 3 is bigger than 1, that's not what we want. 2010, 3 is bigger than 0, that's  not what we want. And so in 2009 we finally see that 2 plus 0 plus 0 is 2 and that is  less than the last digit 9, so that is exactly what we want since we have 2014 now. The last  time the third digit in the year was bigger than the sum of the other three was in 2009, which is 5 years ago, so the answer here is C, 5.

Video Summary

In the video, the problem involves determining when the last digit of a year was greater than the sum of the other three digits. Starting from 2014, the speaker checks years in reverse. In 2009, the digits 2, 0, and 0 sum to 2, which is less than the last digit, 9. This satisfies the condition, indicating that 2009 is the last year this occurred. Since 2014 minus 2009 equals 5, the answer is that it happened 5 years ago. Thus, the solution is 5 years, or option C.

Keywords

year digits

sum comparison

2009

reverse check

mathematical problem