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

Video Transcription

My age is a two-digit integer, which is a power of five,  and my cousin's age is a two-digit integer, which is a power of two. The sum of the digits of our ages is an odd number. What is the product of the digits of our ages?  So the only two-digit power of five is 25. So that means we know that my age is 25.  Now, the other two-digit integers, which are powers of two, are 16, 32, and 64. So now we just need to use this last condition right here,  that the sum of the digits of our ages is an odd number.  So the sum of these two is seven, which is odd.  The sum of the everything in total has to be odd. That means the sum of the digits of this power of two has to be even.  Well, this one is odd. This one is odd. This one is even. That means my cousin's age is 64.  And so the product of the digits of this thing is 2 times 5 times 6 times 4, which is 240.

Video Summary

The problem involves determining two ages based on specific conditions. One age, a two-digit power of five, is 25. The cousin's age must be a two-digit power of two: 16, 32, or 64. The sum of the digits of both ages must be odd. Thus, the age with an even sum of digits is selected, which is 64. Calculating the product of the digits of these ages (2, 5, 6, and 4) results in 240.