Diagnostic - AMC8

What is the value of the following expression? $1+2-3+4+5-6+7+8-9+10+11-12$

Casey went on a road trip that covered $100$ miles, stopping only for a lunch break along the way. The trip took $3$ hours in total and her average speed while driving was $40$ miles per hour. In minutes, how long was the lunch break?

A poll asked a number of people if they liked solving mathematics problems. Exactly $74\%$ answered "yes." What is the fewest possible number of people who could have been asked the question?

Five runners completed the grueling Xmarathon: Luke, Melina, Nico, Olympia, and Pedro. Nico finished $11$ minutes behind Pedro. Olympia finished $2$ minutes ahead of Melina, but $3$ minutes behind Pedro. Olympia finished $6$ minutes ahead of Luke. Which runner finished fourth?

In the figure below, each circle will be filled with a digit from 1 to 6. Each digit must appear exactly once. The sum of the digits in neighboring circles is shown in the box between them. What digit must be placed in the top circle?

Elijah has a large collection of identical wooden cubes which are white on 4 faces and gray on 2 faces that share an edge. He glues some cubes together face-to-face. The figure below shows 2 cubes being glued together, leaving 3 gray faces visible. What is the fewest number of cubes that he could glue together to ensure that no gray faces are visible, no matter how he rotates the figure?

Consider all positive four-digit integers consisting of only even digits. What fraction of these integers are divisible by $4$?

Miguel is walking with his dog, Luna. When they reach the entrance to a park, Miguel throws a ball straight ahead and continues to walk at a steady pace. Luna sprints toward the ball, which stops by a tree. As soon as the dog reaches the ball, she brings it back to Miguel. Luna runs 5 times faster than Miguel walks. What fraction of the distance between the entrance and the tree does Miguel cover by the time Luna brings him the ball?

Charlotte the spider is walking along a web shaped like a $5$-pointed star, shown in the figure below. The web has $5$ outer points and $5$ inner points. Each time Charlotte reaches a point, she randomly chooses a neighboring point and moves to that point. Charlotte starts at one of the outer points and makes $3$ moves (re-visiting points is allowed). What is the probability she is now at one of the outer points of the star?

The integers from 1 through 25 are arbitrarily separated into five groups of 5 numbers each. The median of each group is identified. Let $M$ equal the median of the five medians. What is the least possible value of $M$?