Grades 11-12 Video Solutions 2012-2012_11-12

Video Transcription

Video Summary

Ioana selects two numbers, \(a\) and \(b\), from the set 1 to 26, where their product equals the sum of the remaining 24 numbers. The sum of all numbers from 1 to 26 is 351 after subtracting \(a\) and \(b\), making the equation \(ab + a + b = 351\). Adding 1 to both sides transforms it into \((a+1)(b+1) = 352\). Factoring 352 as \(2^5 \times 11\) and considering constraints, \(a+1 = 16\) and \(b+1 = 22\) (or vice versa), giving \(a\) and \(b\) values of 16 and 22. Their absolute difference is 6.

Keywords

number selection

product and sum

factoring

equation transformation

absolute difference