Discussion Forum

AMC 8 Mock 1 Questions

Picture of Hanming Li
AMC 8 Mock 1 Questions
by Hanming Li - Monday, November 20, 2023, 6:12 PM


I did an AMC 8 Mock test a few days ago and got these 2 wrong. How do I solve these efficiently?

Picture of John Lensmire
Re: AMC 8 Mock 1 Questions
by John Lensmire - Tuesday, November 21, 2023, 9:51 AM


For the first one (the grid), you want to find the lower right-hand square, so try to focus on the right column first. For example, what about the upper-right hand (top right) square? What numbers is it already in a row with? What number is already in it's column? There is actually only one number left for it to be!

The other word problem is a little tricky. Suppose there are $N$ students. Consider what each arrangement of the students tells us about $N$.

  1. If the students are standing in rows of $15$, we definitely know that $15$ is a factor of $N$.
  2. One long row doesn't tell us much, but we can think of as $N$ is a factor of $N$.
  3. Rows of one student each can be thought of as saying $1$ is a factor of $N$.
  4. Rows of $6$ students in each row says $6$ is a factor of $N$.

So far, we know that $6$ and $15$ are factors of $N$, so $N$ is divisible by $2$, $3$, and $5$. The actual key piece of information is that after June 12th there are NO new ways the students can stand in a row. How many factors does $N$ need to have?

Hope this helps!