Grades 9-10 Video Solutions 2022-2022_9-10

Video Transcription

Question 13. I once met six siblings whose ages were six consecutive whole numbers. I asked each of them the question, how old is your oldest sibling?  Which of the following could not be the sum of their six answers?  First, we have to recognize that five of these siblings will all name their oldest sibling,  and then the sixth oldest sibling will name the second oldest sibling. Since their ages are  consecutive whole numbers, we can write this down as x x x x x and x minus one. When we take the  sum of this, we get six x minus one. Now to solve this question, all we have to do is add one to  each of the solutions and get these numbers like so, and then we can set 6x equal to each of those  numbers. Then, since we are looking which of the following could not be the sum of their six  answers, we find the number that is not divisible by six. And when we do the math, we find out that the answer will be D, 205.

Video Summary

The problem involves six siblings with consecutive whole number ages, each asked about the oldest sibling's age. Five will point to the oldest sibling, while the oldest will point to the second oldest sibling. Their responses sum up to one less than six times the oldest sibling's age (6x - 1). To determine which sum is not possible, each option is increased by one and checked for divisibility by six. The number that isn't divisible by six indicates an impossible sum. The result shows 205 as this number, making option D the correct answer.

Keywords

siblings

ages

oldest

sum

divisibility